BULLETIN 447JUE17 JUNE 1973 REILATIONSH IP BE~f\EEF IIN [N I)ENSITY i\EASLJRLI\INTS AND) SUBSEQUENT GRO\\ T111 OF R IC U LTU RA L EX S O PER T IM EN ENAG T STA TIO N A U BU RN R. Dennis Rouse, Director U NI V ERS IT Y Auburn, Alabama CONTENTS Page INTRODU CTIO N --------------------------- --- 3 METHODS OF EXPRESSING POINT DENSITY-4 Competing Basal Area Per Unit Ground Area-4 Growing Space (Area) Available to Tree Competitive Influence Zone Overlap-11 --Miscellaneous Methods -- -------- 10 -24 -26 -29 SOURCE OF DATA -- -- -- -- -- -- -- -- -- -- -- -STATISTICAL DESIGN--------------------- POINT DENSITY EXPRESSIONS TESTED-31 RESULTS AND DISCUSSION ----------C row n Classes -------------------------------------Method of Expressing Growth ---- D ata se ts - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -34 35 36 37 ------------------------ Point-Density Expressions ---------------------------Shape of Relationship ------------------------------- 39 42 C ON CLU SIO NS-- - - - - - --- -- --- - --- - - -- - - - - -- - - - - - -- - -- - - - -42 LITERATURE A P PEN DIX CITED ----------------------------------- 44 A -- - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - -45 A PPEN DIX B -- - -- - - -- - - - - - - - - - - - - -- - - - - - - - - -- - - - - --- 51 F ig ures - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5 1 A P PEN DIX B -- - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - 85 Tab les - - - - - - - - - - - - -- - --- - -- - - - -85 FIRST PRINTING 3M, JUNE 1978 Relationship Between Point Density Measurements and Subsequent Growth of Southern Pines E. W. JOHNSON 1 INTRODUCTION growing in forest stands necessarily compete with one another for sunlight, air, water, and soil nutrients. The degree of competition varies from tree to tree and is dependent on a host of interacting variables. No practical way has been found to assess all these factors to arrive at a measure of the competitive pressure exerted against an individual tree. However, attempts have been made to approach this problem indirectly through the use of a number of different concepts or ideas. These procedures yield measures of what has been named "point density." 2 This bulletin describes some of these procedures and the result of tests in which the procedure results were correlated with subsequent periodic annual increment in diameter breast high (d.b.h.) and basal area for loblolly (Pinus taeda, L.), longleaf (P. palustris, Mill.), and slash (P. elliotti, Engelm.) pines grown in plantations in eastcentral Alabama. Professor, Department of Forestry. Spurr (1962) defined point density as "the stand basal area as measured at a given point within the stand rather than over a given area." This definition is somewhat limited since the term appears to be quite suitable for a number of methods, not involving basal area, that can be used to estimate the competitive pressure against individual trees. Consequently, in this paper the term "point density" will be used for all the measures considered. TREES 4 ALABAMA AGRICULTURAL EXPERIMENT STATION METHODS OF EXPRESSING POINT DENSITY Competing Basal Area Per Unit Ground Area This is the most commonly used measure of stand density. It is determined by summing the basal areas of the trees growing on a plot of land of a given size. Usually it is expressed in square feet of basal area per acre, or square meters per hectare. Conventionally, basal area per unit ground area is obtained from a relatively large plot (0.2 to 0.25 acre) and is not a good measure of point density or competitive pressure on any particular tree in the plot because the procedure merely averages conditions over the entire plot. Since few stands are uniformly stocked, the pressure of competition will differ from tree to tree within the plot, depending on the degree of clumping of the trees and the position of the sample tree with respect to nearby trees. A procedure that would tend to overcome this averaging problem is to use a small, fixed-radius plot centered on the sample tree. Figure 1 and Appendix A.1. show how such a fixed-radius plot might be used. Steneker and Jarvis (28) employed this procedure to provide them with one of the several competition indices they used while studying the effect of competitive pressure on individual white spruces (Picea glauca ( Moench.) Voss). Plots with radii of 25 feet were used in their study. The optimum plot size would necessarily depend on a number of variables and probably could be determined only through empirical means. However, it seems logical to assume that the trees growing closest to the sample tree would exert the greatest competitive pressure. Consequently, the plot size should be large enough to include as many as possible of these but not so large as to include many trees of negligible influence. Thus, in dense stands of small trees, the plots probably should be kept small while in more open stands, or in stands made up of larger trees, the plots probably should be relatively large. In a situation such as this it is possible to compute the basal area per unit land area in either one or two ways. One can either include or exclude the basal area of a sample tree. It would appear logical to exclude the sample tree, since one is interested in the pressure against that tree and not in the total basal area on the plot. The idea of varying plot size in proportion to tree size leads directly to the "angle-count" method of estimating basal area per GROWTH OF SOUTHERN PINES 5 O 8.0", 28' 6.0",36' 0 8.0", 19'0 o 5.0",24' Scale of diameters twice that of location. Plot radius Basal area/acre, excluding sample tree = , including sample tree = Steneker-Jarvis competition indices: - 15.0 feet 75.2 sq. ft. 91.7 sq. ft. Isi = ISJ2 = 0.017 0.369 2.586 ISJ3 -21.122 IsJ4 = FIG. 1. Example of the use of fixed radius plots, centered on the sample tree, to obtain basal area per acre and the Steneker-Jarvis competition indices IsJ1, IsJ2, ISJ 3, and IsJ4. Computations shown in Appendices A. 1, and A. 2. unit of land area, originated by Bitterlich (3) and further developed by Grosenbaugh (8,9). In this approach to point density measurement, the sample tree may be considered to be at the center of an infinite number of concentric circular plots. Each competing tree is associated with one of these plots through the relationship: BAF 2 Cr2 R (1) the number of square where BAF ="Basal area factor"units of basal area (square feet, square meters, etc.) per unit of land area (acre, hectare, etc.) represented by one tree; 6 ALABAMA AGRICULTURAL EXPERIMENT STATION C - 43,560 when stand density is in terms of square feet of basal area per acre. It is 10,000 when stand density is expressed in terms of square meters of basal area per hectare; r = d.b.h. 2 2 =radius of competing tree, in the same units as R; R - radius of plot associated with the competing tree. The basal area factor (BAF) is arbitrarily chosen (e.g., 10 square feet of basal area per acre). Any tree whose distance (R) from the center of the sample tree is less than: R=l C r2 BAF (2) is assumed to be competing with the sample tree and the measure of its competition is equal to the BAF. Consequently, the sum of these BAF values for the competing trees is a measure of the competitive pressure against the sample trees expressed in basal area per unit of land area. Figure 2 shows the angle-count method being used with the same sample tree and surrounding stand depicted in Figure 1. As with the fixed-radius plots, it is possible to estimate the basal area per unit land area including or excluding the sample tree and again it would appear logical to exclude the sample tree. A variety of basal area factors can be used in measurements of this type. However, one would expect that the smaller the BAF the more the measure of point density would represent average stand conditions rather than the conditions immediately adjacent to the sample tree. Conversely, the larger the BAF, the more specific would be the measure of point density. This reasoning, however, is not supported by the results of a study carried out by Lemmon and Schumacher (17,18) in ponderosa pine (Pinus ponderosa Laws). They used four different basal area factors (10, 20, 30, and 40 square feet per acre), and the response variable was periodic annual volume increment in cubic feet. The 10 square feet per acre BAF yielded the highest correlation between point density and increment. The reasons for this divergence from theoretical results are not known. GROWTH OF SOUTHERN PINES 7 Out Borderline I0.0" 13.75 '6. Out .0 15' t' ut --.. 8.0", 28' 7.0 Out 8.0",19' , Out 5.0", 8' 49. / " 6' Out /5.0") 24' Out Scale of diameters twice that of location. Basal area factor = 40 sq. ft. basal area/acre/tree Sweeping angle = 3 28' (Angle shown is to above scales and thus is 6' 56'). Count of "in" trees = 11/2, excluding sample tree = 21/2, including sample tree Basal area/acre = 60 sq. ft., excluding sample tree 100 sq. ft., including sample tree FIG. 2. Example of the use of Bitterlich's angle-count method of obtaining basal area per acre centered on the sample tree. Spurr (26) originated a variant of the angle-count method, which he called the "angle-summation" method. In this procedure (see Figure 3 and Appendix A.3.) the angles subtended by the trees surounding the sample tree are measured or computed, then ranked in magnitude. An arbitrarily chosen number of the highest ranked trees is used in the subsequent computations (e.g., if four trees are to be used the four trees subtending the largest angles are used). An estimate of basal area per unit of land area is made, first assuming that the tree subtending the largest angle is an exact borderline tree with only half of its basal area within the plot. The basal area per unit of land area is computed by using a modification of the basic formula used in the Bitterlich method: BB 0.5 C r21 R21 (3) where: B1 = estimate of basal area per unit of land area 8 ALABAMA AGRICULTURAL EXPERIMENT STATION A46.0", 15' B D 8.0", 28' Angle rank 7 Angle rank = 6 10.0", 13.75' XAngle rank= 2 E 7.0" 8.0",19' F : Angle rank= 5 9.0", 6' 1 5.0", 8' Angle rank = 3 C 6.0", 36' Ange rank=9 SAngle rank = I H 9.0", 20' 9, Angle I 5.0", 24' rank = 4 Angle rank= 8 Scale of diameters twice that of location Using four trees 68.12 sq. ft., excluding sample tree Basal area/acre = = 131.87 sq. ft., including sample tree FIG. 3. Example of the use of Spurr's angle-summation method of obtaining basal area per acre centered on the sample tree. (Computations shown in Appendix A. 3.) based on the tree subtending the largest angle; 0.5 = expansion factor (Since only half the tree is inside the plot, only half its basal area contributes to the basal area per unit of land area.); ri = radius of highest competing tree; R1 = distance between sample tree and highest ranked competitor. Then a second estimate of the basal area per unit of land area is made assuming that the tree subtending the second largest angle is an exact borderline tree. The basal area per unit of land area is computed as follows: 2 B - 1.5 Cr 2 1(4) R22 where: B2 =estimate of basal area per unit of land area 2 based on the two trees subtending the largest angles; 1.5 = expansion factor (All of the first tree and half GROWTH OF SOUTHERN PINES 9 of the second tree are contributing to the basal area per unit of land area.); r2 radius of second highest ranked competitor; R 2 = distance between sample tree and second highest ranked competitor. This procedure is repeated with succeeding trees until the desired number is reached. All of these estimates are then averaged, yielding the point density value in terms of basal area per unit of land area. As in the case of the preceding methods, the sample tree may be excluded or included and probably should be excluded. Figure 4 shows the pattern of change in the magnitude of the estimates of basal area per unit of land area, for the same stand shown in Figure 3, with different numbers of competing trees involved and the sample tree excluded. This pattern of change is associated with situations where the differences between the values of r 2/R 2 for successively ranked trees are relatively large. This occurs in nonuniform stands with wide ranges in stem diameters and highly variable distances between trees, as is the case in the stand being used as an example. In more uniform stands the pattern of change is reversed so that the estimate of basal area per unit of land area increases as the number of competing trees included in the computations increases. Spurr tested the angle-summation procedure using data from a Douglas fir (Pseudotsuga menziesii (Mirb. Franco)) plantation in New Zealand and found the rising pattern. He attributed the rise to the exclusion of the sample tree from the estimates. This exclusion would make the estimates of basal area per unit of land area too small. When only one competitor is used, this negative bias will be relatively large. As the number of competitors used in the computations increases, the effect of the exclusion of the sample tree becomes less and less and the estimates become larger and larger. This is sound reasoning and the phenomenon undoubtedly occurs in all cases where the sample tree is excluded. However, if the stem diameter and tree spacing are sufficiently irregular, the typical rising of the basal area estimates may be overridden to produce a downward trend. The pattern of rising or falling of the basal area estimates is of importance to the angle-summation method only in that it provides a basis for choosing the number of competitors which 10 ALABAMA AGRICULTURAL EXPERIMENT STATION __1___1 Bosal area per ocre (sq. ft.) 90 85 80 75 70 65 60 55 I 2 3 4 5 6 7 Number of trees in sample 8 9 FIG. 4. Relationship between the estimate of the basal area per acre and the number of trees used in Spurr's angle-summation method. should be used in the estimate. Theoretically, the basal area estimate should stabilize at or near the size sample that yields the actual basal area per unit of land area of the entire stand. This point of stabilization can be used as a guide to the number of trees needed for an estimate. If one desires to measure point rather than stand density he should use a sample size that is smaller than that at which stabilization occurs. Spurr, using data from the Douglas fir plantation in New Zealand, found that stabilization began to occur when approximately 9 trees were used. Growing Space (Area) Available to Tree Brown (4) has devised a method of expressing point density in terms of the ground area that could be assigned to the sample GROWTH OF SOUTHERN PINES 11 GROWTH OF SOUTHERN PINES 1'I )6.0" 9.0" Scale of diameters twice that of location The solid line shows area defined by Brown's Method. The dashed line shows area defined by the modification. Area potentially available to sample tree: 105.75 = 105.75 sq. ft. Brown's method Modification of Brown's method = 96.01 sq. ft. to sample tree using FIG. 5. Growing space or "area potentially available" Brown's method and a modification of his method. tree. This is done by first connecting the sample tree to all the surrounding trees with line segments, Figure 5. The smallest closed figure, or polygon, formed by the perpendicular bisectors of these line segments encloses the ground area that is assigned to the sample tree. Area of the polygon is an inverse measure of competitive pressure. Competitive Influence Zone Overlap The space that a tree occupies is three-dimensional. This space may be thought of as an irregularly shaped "solid" that extends vertically from the deepest root to the tip of the bole and horizontally, aboveground, to the tips of the branches and, underground, to the tips of the widest spread roots. Only in the case of isolated, free-growing trees does this space reach its maximum potential size. This is termed maximum potential growing space (M.P.G.S.), whose magnitude is directly proportional to size of the tree. Furthermore, evidence indicates that the horizontal extent of the M.P.G.S. probably is greater underground than it is above ground (10,11,21,23,25). 12 ALABAMA AGRICULTURAL EXPERIMENT STATION If the M.P.G.S. of any other plant (tree or otherwise) encroaches on that of a given tree, competition for the overlapping space probably occurs. Several methods of expressing point density that are based on the idea of measuring the amount of overlap of these growing spaces have been devised. A direct evaluation of the volume of overlap between M.P.G. spaces is not possible because there is no way of knowing what the bounds of the spaces would have been if no competition existed. The best that can be done is to use a mathematical model that approximates the actual situation. One such model can be developed by assuming that the M.P.G.S. is a right circular cylinder, centered on the tree, with an end area equal to the horizontal cross-sectional area of the actual M.P.G.S. and that the cylinder has a total altitude equal to the total vertical length of the actual M.P.G.S. Any overlap or interpenetration constitutes an estimate of that competition. The vertical dimension of the interpenetration in a model of this type is of little significance since a right cylinder is a poor approximation of the actual vertical configuration of the M.P.G.S. Consequently, with this model, it is logical to ignore the vertical dimension and to use the magnitude of the overlap between horizontal cross-sections of the right circular cylinders as a measure of competitive pressure. These horizontal cross-sections were named "competition circles" by Staebler (27), "zones of influence" by Opie (22), and "competitive influence zones" by Bella (1,2). Bella's term will be used in this report. Before overlaps of competitive influence zones (C.I.Z.'s) can be measured, it is necessary to define the sizes of the circles. Their areas should be equal to the areas of the maximum horizontal cross-sections of the M.P.G. spaces, which probably would involve root extent rather than crown spread. Since root extent cannot be determined in a non-destructive manner, studies involving the evaluation of tree growth following point density assessment must be based on the use of approximations rather than actual C.I.Z. areas. In the absence of firm information about root extent, the best indicator of the size of the C.I.Z. is crown spread. However, crown spread itself is strongly influenced by competition, which means that its correlation with actual C.I.Z. may be quite poor. Workers in the field of point density evaluation have approached the problem of C.I.Z. extent in several ways. These will be mentioned as each worker's procedures are described. Staebler (27), working with Douglas fir, apparently was the first GROWTH OF SOUTHERN PINES 13 to use the concept of overlapping C.I. Zones to evaluate competitive pressure against individual trees. To express zone size, he related zone diameter to tree diameter through the simple linear function: (5 ) ............. ......... A = a (D ) + k ............. where: A = diameter of C.I. Zone, in feet; D = d.b.h.o.b. of tree, in inches; a = arbitrarily chosen multiplying coefficient (values used were 0.8, 1.2, and 1.9); k = arbitrarily chosen y intercept (values used were 3, 5, and 7). Staebler's basis for this model was the "D times" and "D plus" relationships sometimes used in thinning. Staebler considered the area of overlap of C.I.Z. circles to be the most desirable measure of competition. However, his opinion was that the mathematical expression required to compute this area was too complicated (he did this work prior to the widespread availability of electronic computers). Consequently, he discarded the idea of area overlap and, instead, used the length of the portion of the line connecting the centers of the two, circles and lying within both circles, Figure 6 and Appendix A.4. If more than one competitor was involved, the sum of the lengths would be the measure of competition or point density. Staebler referred to this sum as an "index of competition." Its formula is: n (6) di i=1 where: Isi =index of competition; di =length of line segment within the circles of the sample tree and the ith competitor; n -- number of competing trees. Staebler recognized further than a single large overlap would indicate a greater degree of competition than would an equal sum of several short overlaps. To compensate for this difference in competition he developed a second index of competition (IS2), the sum of the squared overlaps: n Isi= IS2 = d2 i (7) i=1 14 ALABAMA AGRICULTURAL EXPERIMENT STATION Scale of diameters twice that of locations and C.I. Zones. Radius of C.I.Z. in feet = d.b.h. of tree in inches +1. 23.2 feet = IIs Is,/F = 0.86 Is2/F = 7.67 Is 3 /F Is4/F = = 7.04 65.05 Is5 = 145.% FIG. 6. Competitive influence zone overlap using Staebler's competition indices Is, Is/F, IS2 /F, Is3/F, Is 4 /F, and Is5. (Is5 is explained in the section "Point Density Expressions Tested." See Appendix A. 4. for computations.) To compensate for tree size differentials he developed a third index (Is3) which was the sum of the products of the overlaps and the d.b.h.'s of the competing trees: n Is3 = (di Di) (8) i=l where: D i = d.b.h. of the ith competing tree. In good measure, he also developed the index (Is4): n IS4 = (d 2 i Di) - (9) i-=1 Staebler further recognized that a large sample tree in a given situation usually would have a larger index of competition than would a small sample tree. However, in the case of the larger GROWTH OF SOUTHERN PINES 15 tree, the competition would be less severe because the tree had a higher degree of dominance over its neighbors. In any investigation relating growth to competitive pressure, this fact would have to be recognized. Staebler solved this problem by dividing each of his indices by an area proportional factor which he labelled «F." F = [ a(DS 2 = + Da) + k]2,/10 (10) arbitrarily chosen multiplying coefficient (values used were 0.8, 1.2, and 1.9); DS = d.b.h.o.b. of sample tree; D, = d.b.h.o.b. of average tree in stand; k = arbitrarily chosen y-intercept (values used were 3, 5, and 7). He rounded F to the nearest digit. Staebler tested his procedure by means of multiple linear regression. The dependent variable was the residual from the curve of d.b.h. growth over d.b.h. This dependent variable was chosen because it helped to compensate for the fact that large trees grow faster than small trees. The regression model he tested was: y = a +bl(Isx/F) + b 2 (IS2/F) +b 3 ( 3 /F) + b 4 (Is 4/F) where: a (11) In spite of the foregoing elaborate and well-reasoned procedures, designed to compensate for dominance and competition differences, the best multiple correlation coefficient that Staebler obtained was only 0.575. Newnham (20), in the course of developing a stand growth model for Douglas fir, devised a competition index that makes use of overlapping C.I. Zones. However, instead of using either the length of linear overlap or the area of overlap, he determined the proportion of the total circumference of the C.I.Z. of the sample tree that was occupied or overlapped by the C.I. Zones of the competing trees, Figure 7 and Appendix A.5.: IN IN = 2 ri= 1 [ai (A/As)] (12) index of competition; ai = the angle, measured at the center of the C.I.Z. of the 16 ALABAMA AGRICULTURAL EXPERIMENT STATION Scale of diameters twice that of locations and C.I. Zones Radius of C.I.Z., in feet = d.b.h., in inches, +1 IN = 120% 103% IN2 = FIG. 7. Competitive influence-zone overlap using Newnham's competition indices IN and IN2* (IN2 is explained in the Section "Point Density Expressions Tested." See Appendix A. 5. for computations.) sample tree, subtended by the portion of the circumference overlapped by the ith competitor, in radians. If ai is expressed in degrees, 360 should be sustituted for the 2r term; Ai = diameter of the C.I.Z. of the ith competitor; AS = diameter of the C.I.Z. of the sample tree. The (Ai/AS) term is a weighting factor used to take into account the relative sizes of the trees. A tree with a crown larger than another tree usually is also taller and has an additional competitive advantage. Since it is possible for many C.I. Zones to overlap that of the sample tree it is possible for IN to exceed 1.00, or 100 per cent. Krajicek et al (13,14), in their development of the crown competition factor, made use of an idea, apparently first suggested by Lane-Poole (15), that the C.I.Z. is closely approximated by the crown-spread of open-grown trees and that this crown-spread is GROWTH OF SOUTHERN PINES 17 closely related to d.b.h. This relationship can be established by using regression, e.g.: A = a + b D, or some higher polynomial (13) where: A = diameter of crown (i.e., C.I.Z.), in feet; D = d.b.h.o.b., in inches; a and b = regression coefficients. By this procedure, the C.I.Z. for any tree can be approximated, regardless of competition, provided its d.b.h. is known. Newnham (20) used this approach, with modification, to define C.I. Zones. He recognized that the actual C.I.Z. of a tree in a closed stand probably did not coincide with the crown spread of an open-grown tree of the same d.b.h. Furthermore, the lack of coincidence probably was a function of stand age and initial spacing. To overcome this problem he included the correction factor (K) in Equation 14: = bDK (14) A a+ Using empirical methods not clearly delineated, he developed a series of curves showing the value of K for different combinations of stand age and initial spacing. These values ranged from 0.6 to about 1.0, increasing with age and initial spacing. Within the context of his stand model, Newnham used this correction factor to compensate for changes in competitive pressure brought by mortality among the competitors. Newnham's procedure can lead to some anomalies unless the investigator is careful to evaluate exactly what has occurred in each case. For example, Figure 8 shows a series of situations where a tree competes with a larger sample tree. Assume that this competing tree can be moved toward or away from the sample tree. When the two trees are separated so that their C.I.Z. circles are tangent (situation A) the angle a is equal to zero and it would be assumed that no competition exists. If the competing tree is moved toward the sample tree (situations B and C) the angle a increases in magnitude, correctly indicating increasing competitive pressure, and reaching a maximum when the overlap is as in situation D. However, if the convergence is continued, a will begin to decrease (situation E). If continued still further, the C.I.Z. of the competitor will be brought entirely inside that of the sample tree (situation F). Since a is intended to be a measure of competitive pressure, the pressure in situations E and 18 -I ALABAMA AGRICULTURAL EXPERIMENT STATION Sample , Comp. Sample A B Om0 O 0 Sample Comp. Sample Co p. C No 0 D ex sts Sample E Comp. E 0 0 Sample Comp. F FIG. 8. Effect of size of competitive influence-zone and distance between competing trees on Newnham's competition indices when the competitor is smaller than the sample tree. F could be mistakenly interpreted to be less than that at D. Newnham did not acknowledge this problem but apparently accepted the value of a as computed, regardless of the situation. When situation F occurred, he assigned a value of zero to a. Although Newnham's treatment of situations like E and F appears illogical, the effects on the end results probably were minimal. Any competitor small enough to occur under these situations probably exerts too little pressure to be of consequence. When the sample tree is smaller than the competitor, the situa- GROWTH OF SOUTHERN PINES 19 tions shown in Figure 9 may occur. Situations A, B, and C are similar to those already encountered. In situation D, a reaches 180 ° , or ?r radians. As the distance between the competitors continues to decrease, a increases to a maximum of 360 °, or 2r radians, then vanishes. Newnham accepted a as shown except in the case of situation F, where he arbitrarily assigned a value of 860 ° , or 2r radians. Except for the arbitrary assignment of a value in F, these actions are consistent with the theory. In the case of situation F, some recognition should be made of differences in separation distances between competitors. However, this could O o Comp. Comp. 0 o Comp. Comp. C 0 Comp. E FIG. 9. Effect of size of competitive influence-zone and distance between competing trees on Newnham's competition index when the sample tree is smaller than the competitor. 20 ALABAMA AGRICULTURAL EXPERIMENT STATION not be accomplished within the framework of Newnham's procedure. Consequently, his decision probably is as practical a solution to the problem as could be devised. While working on an individual tree growth study of beech (Fagus grandifolia Ehrh.) in Ohio, Fritts (5) developed a measure of point density that involved the overlapping of C.I. Zones. This apparently was done completely independently of Staebler's work. In Fritt's procedure, the C.I.Z. size was governed by the following relationship: A= 2 D D _______-(15) d.b.h.o.b. of tree, in inches. where: A = diameter of C.I.Z. circle, in feet; = The source of this relationship was not stated. Fritts cites Rogers (23), who stated that the roots of apple trees growing on sand in Kent, England, spread 2 to 3 times as far as do the branches, while in loam and clay the root spread was about 1.6 times as great as the branch spread. The tie between this and Fritts' relationship is tenuous at best. To arrive at his competition index, Fritts mapped the sample tree and its competitors, drew in the C.I. Zones on the map, and measured the overlap areas within the C.I.Z. of the sample tree with a planimeter, Figure 10 and Appendix A.6. The sum of these overlap areas was divided by the area of the sample tree C.I.Z. to obtain the proportion under competition, then multiplied by 100 to convert to percentage: IFG -= 10 S ( i=1 Oi )-(16) where: IFG = competition index in per cent of sample tree C.I.Z.; S = area of the C.I.Z. of the sample tree; of = overlap area of the C.I.Z. of the ith competition. Gerrard (6,7) independently derived essentially the same competition index as the one used by Fritts (Equation 16). However, Gerrard based the size of the C.I.Z. circles on an empirically obtained value for the coefficient b in the equation: (17) -R = b D- GROWTH OF SOUTHERN PINES GROWTH OF SOUTHERN PINES 21 21 06.0' 09.0" Scale of diameters twice that of locations and C.I. Zones Radius of C.I.Z., in feet = d.b.h. of tree, in inches, +1 IFG = IB = 124.52% 188% Io = 86.79 sq. ft./acre of basal area FIG. 10. Competitive influence-zone overlap using the Fritts-Gerrard, (IFG), the Bella (IB), and the Opie (Io), competition indices. (See Appendices A. 6, A. 7., and A. 8. for computations.) where: R = radius of C.I.Z., in feet; b D = = radius factor; d.b.h.o.b., in inches. Gerrard chose an arbitrary sequence of values for b, then tested the resulting indices for predicting basal area increment. He used the value for b that resulted in highest correlation between his index and basal area increment. Using data from an area in southern Michigan, he found that the values for b yielding the best correlations were about 2.25 for red oak (Quercus borealis Michx.), 1.75 for black oak (Q. velutina Lan.), and 1.25 for hickories (Carya spp.) and maples (Acer spp.). In the course of his study, Gerrard compared his competition index with several other indices or methods of expressing point density: Spurr's, a modification of Spurr's, and Newnham's. He found his index to be consistently the most effective for predicting future basal area growth. 22 ALABAMA AGRICULTURAL EXPERIMENT STATION Keister (12) accepted the Fritts-Gerrard index in a study he made of point density in plantations of slash and loblolly pine in Louisiana. However, he defined the C.I.Z. in different terms: R - hl(18) hl m where: R = radius of C.I.Z.; h = total height of tree; m = height to base of live crown; 1 = radius of crown at base of live crown, with all in the same units. His rationale for using this procedure was that the magnitude of the C.I.Z. is not a function of d.b.h. alone but is also influenced by both tree height and length of live crown. If two trees have the same d.b.h., the one that is taller and/or has a deeper live crown should have a competitive advantage over the other. This argument appears sound. Keister, recognizing the difficulty of evaluating the variables in his equation, substituted estimated values for h and 1 which had been derived from equations with d.b.h. as the independent variable. Therefore, h and 1 became synthetic variables whose magnitude depended entirely upon d.b.h. and, per se, furnished no information. Like most workers in the field, Keister related his point density index to growth using regression analysis and evaluated the results using correlation coefficients. The equation used in these tests was: y = a + bIK + bn + bln(IK /n)---------3 where: y = (19) d.b.h. growth over growth period; IK = index of competition; n = number of trees whose C.I. Zones overlapped that, of sample tree. In(IK/n) = natural logarithm of IK/n The IK/n term was included to account for the fact that any given degree of overlap with several competitors has less impact on the growth of a sample tree than the same amount of overlap coming from a single competitor. In most cases, this second index GROWTH OF SOUTHERN PINES 23 proved to be more effective than the first in reducing the residual sum of squares. Bella .(1,2) also developed a competition index based on the ratio of the sum of the overlap areas of the C.I. Zones to the area of the C.I.Z. of the sample tree, Figure 10 and Appendix A.7. However, he apparently borrowed a couple of ideas from Newnham (20) and used them while developing a modification of the Fritts-Gerrard procedure. The magnitudes of the C.I. Zones in the Bella method are based on the relationship between the crown diameters of open-grown trees and their d.b.h.o.b.'s which must be established empirically for each species considered. Bella, like Newnham, recognizing that the C.I.Z. is not necessarily coincident with the extent of open-grown trees of a given d.b.h., applied a correction factor (K) to the predicted crown diameters: A = P K ........ ....... ....... ........ ....... (2 ) 0 where: A = diameter of C.I.Z.; P = predicted crown diameter; K - correction factor. Bella believed that the magnitude of K would be dependent on species and, probably, age and site as well. Using empirical methods, he found that a K of approximately 3.00 worked well with aspen (Populus spp.), while a value between 2.7 and 3.2 seemed appropriate for jack pine (Pinus banksiana Lamb.) and Douglas fir, and 1.5 for red pine (Pinus resinosa Ait.). Bella, again like Newnham, recognized that a given per cent overlap of C.I. Zones is not a fully satisfactory measure of intertree competition since it does not take into account the relative sizes of the trees. To overcome this deficiency, Bella used essentially the same method used by Newnham. He multiplied the per cent overlap for each competitor by the ratio of the d.b.h.o.b. of the competitor to the d.b.h.o.b. of the sample tree. This weights the per cent overlap according to the size of the competitor. Bella, however, did not stop here. He reasoned that the tree size effect would differ by species and, perhaps, for other reasons. Consequently, he raised the ratio of diameters to a variable power (x), which he evolved empirically. He estimated the value of x to be approximately 2.0 for aspen, jack pine, and red pine, while for Douglas fir it should be about 1.2. 24 ALABAMA AGRICULTURAL EXPERIMENT STATION Expressed mathematically, Bella's competition index takes the form: Sn IB[(Oi) S i=1 (Di/Ds)x] (21) where: IB = index of competition; S - area of C.I.Z. of sample tree; Oi = overlap area of the C.I.Z. of the ith competitor; Di = d.b.h.o.b. of ith competitor; Ds = d.b.h.o.b. of sample tree; X = variable power. Bella compared the results obtained from his index with those from both the Fritts-Gerrard and the Opie (22) indices. He found that his procedure yielded a significantly better estimate of growth than either of the others. Miscellaneous Methods Steneker and Jarvis (28), when studying the effect of competitive pressure on individual white spruce trees, used a series of competition indices that involved the trees on a small plot of a fixed radius (25 feet), centered on the sample tree. One of these, the sum of the basal areas of the competing trees, has already been mentioned. The remaining indices were: IsiISJ2 , ISJ3Is4 = n (Ds/CGi) i-=1 n (22) (23) (24) (D/G 2 i-=1 n 1) ~ (D2 s/Gi) i-=1 = 2 (D2s/G i=1 n 2i)------ __ (25) ____ indices of competition; where: ISJ1 through SJ4 = n = number of trees in sample plot; Ds = d.b.h. of sample tree, in inches; GROWTH OF SOUTHERN PINES 25 G:i distance from sample tree to ith competitor, in feet. The sample tree itself was never allowed to contribute anything to these measures of competitive pressure. This appears logical since the pressure on the sample tree was being evaluated. Figure 1 and Appendix A.1. show examples of these indices. Opie (22) developed an index of competition that draws on both the overlapping C.I.Z. concept and the basal area per unit land area concept. The sizes of the C.I. Zones were defined in terms of d.b.h., with a separate multiplier (m) for each of three site classes: R= mD ___(26) Opie tested his procedure using data from stands of Eucalyptus spp. in Australia. For the best sites m was estimated to be 1.20, for medium sites it was set at 1.35, and for poor sites m was set at 1.45. These multipliers actually represent the radius of the C.I.Z. in feet per inch of d.b.h.o.b. Thus, the BAF (from the Bitterlich method) associated with each of the multipliers can be determined from the relationship expressed in equations (1), (29), and (30). With these multipliers, the corresponding BAF values are 52, 41, and 36 square feet per acre. Using an angle gauge with a BAF appropriate to the site, the C.I.Z. of the sample tree is determined, then the C.I. Zones of the competing trees are similarly derived. The index of competition, called by Opie the "Zone count," is computed as follows: BAF n Oi-S i S i=l where: Io = index of competition; BAF = basal area factor; Io S = 27) area of C.I.Z. of sample tree; O = overlap of the ith competition. In essence, the total amount of overlap is related to the area of the sample tree's C.I.Z. and the resulting quotient is considered to be the equivalent of an angle count. Thus, the angle count multiplied by the BAF yields an estimate of the basal area per unit land area centered on the sample tree. This procedure weights the effects of the competitors on a basis 26 ALABAMA AGRICULTURAL EXPERIMENT STATION which recognizes differences in tree size as well as differences in distance from the sample tree. Opie recognized that there would be practical difficulties in using the aforementioned procedure. As a result, he developed a field procedure which would yield estimates of values obtained by the formal procedure. Discussion of this field procedure is omitted here. Like Gerrard, Opie compared the effectiveness of his procedure with several others (fixed-radius plots, variable-radius plot proportional to tree d.b.h., Bitterlich's and Spurr's). The response variable used in these tests was basal area increment. The results indicated that Opie's method yielded results which were similar to the others. Latham (16) has proposed a competition index that is unusual in that it requires the use of stereoscopic pairs of large scale, vertical aerial photographs. A stereogram of an inverted cone is constructed on a transparent base. The image of the sample tree is viewed stereoscopically and the stereogram of the cone is superimposed on the stereopair in such a manner that the apex (bottom point) of the cone is at the foot of the sample tree. Trees whose crowns penetrate the cone are considered competitors. Latham did not elaborate on how the competition would be expressed beyond stating that the cone was acting as a vertically oriented angle gauge and made reference to Bitterlich's angle-count theory. The trees whose crowns penetrate the cone are in trees. In this case, the trees are sampled with probability proportional to height and the count of in trees has no direct connection with basal area. It is possible that Latham intended the simple count to be the measure of competitive pressure but, since he apparently was more concerned with the photogrammetric than the silvical and mensurational aspects of the problem, he left the latter unresolved. This approach is intriguing and someday might be developed to serve as the basis for a procedure that would be useful to foresters who use aerial photographs. SOURCE OF DATA To evaluate the effectiveness of a point density expression as a measure of competitive pressure, it is necessary to have data from a stand or stands of trees which have been measured periodically over a reasonable span of time. With such data, conditions found at the beginning of a growth period can be related to subsequent GROWTH OF SOUTHERN PINES 27 Forest Forest % Lobcily Pine Slash Pine 19.2 16 Slosh Pine 6 8 4 12 6 9.68 12 9.2 9.2 9.2 6 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 6 16 8 8 8 8 6 4 Long leaf Pine 6 16 12 Slosh Pine 6 16 Forest 12 83624 8 6 4 4 Open FIG. 11. Map of experimental area. Numbers in plots indicate spacing in feet. growth. Data of this type were available for this study from plantations of loblolly, longleaf, and slash pines established at Auburn, Alabama, for a spacing and thinning study by the Agricultural Experiment Station of Auburn University. The layout of these plantings is shown in Figure 11. Essentially, the individual plantation units were rectangular, /-acre plots grouped into two blocks, Block 31 on the north of the transverse road and Block 32 on the south side of the road. No statistical design formed the basis for the assignment of species or spacings to the plots. Since slash pine apparently was of more interest to the investigators than were the other two species, it was planted most extensively and occupies all the plots in Block 31 and onethird of the plots in Block 32. The original spacings of the trees varied from 4X4 feet to 19X19 feet, with 6X6 feet used more than any other spacing. The trees were precisely located within the plots. Those who conducted the planting were guided by wires stretched across the plots. This made it possible in this study to indicate tree position within a matrix and to use row number, column number, and original spacing to compute distances between trees. The plantations were established in 1932 with 1-year-old seedSMore detailed information about these plantations may be obtained from Livingston (19). 28 ALABAMA AGRICULTURAL EXPERIMENT STATION lings grown in the University's small, temporary tree nursery. Thinnings were made several times in subsequent years. The thinning policy apparently was uniform for all plots. It consisted primarily of thinning from below and salvaging trees that probably would otherwise have been naturally lost. Prior to each thinning, following the marking, a complete cut and leave inventory was made of all the plots. Usable data were obtained from the last four of these inventories (in 1945, 1950, 1955, and 1962) for slash pine and from the last three inventories for loblolly and longleaf pine. The primary data obtained in the course of these inventories were d.b.h.o.b. of all living trees, which were measured to the nearest 1/10 inch. In addition, crown class was recorded. Site index was estimated for each individual plot when the trees were 31 years old, using the site index curves from Volume, yield, and stand tables for second-growth southern pines (29). Four sample trees were chosen subjectively from each of the plots. Where possible, one of these was from each of the four crown classes: dominant, codominant, intermediate, and overtopped.4 These sample trees were chosen from trees that had survived to age 31 and were located deep enough within the plots so that the trees with which they were competing were plot companions. Consequently, no sample trees were chosen in the outer 7 rows in plots with 4X4 feet spacing, in the outer 4 rows in plots with 6X6 foot or 8X8 foot spacing, or in the outer 2 rows in plots with spacings greater than 8X8 feet. In some cases, not all crown classes were represented among the available sample trees. In such cases the deficits were made up by arbitrarily choosing substitutes. It was felt that subjective sampling would be acceptable since, at the time of selection, no knowledge was available concerning either the growth or the point density. Preliminary analyses of the data indicated that the slash pine in Block 31 responded in a much different way to point density than did the slash pine in Block 32. Therefore, the two sets of slash pine data were kept separate and were analyzed independently of one another. * block 32 sample trees were chosen from among the overtopped trees. This In was not done in Block 31. The preliminary work was done in Block 31 and in this phase it was thought that the growth response of overtopped pines to point density would be negligible and of little importance. Consequently overtopped trees were not used as sample trees. Later this opinion was changed but the decision was made to continue to use the original samples from Block 31 so as not to lose the time and effort invested in the analyses of those samples. GROWTH OF SOUTHERN PINES 29 STATISTICAL DESIGN Initially, the study plan called for the development of mathematical models that could be used to predict periodic annual increment in both d.b.h.o.b. and tree basal area. These models were to include, as independent variables, site index and age, d.b.h.o.b., crown class, and point density at the beginning of the period. The reduction in residual sum of squares attributable to the point density expression would be used as the measure of the expression's effectiveness, or power. A basic, theoretical model using these variables was devised but could not be fitted to the data by conventional regression procedures because of nonlinearity in the coefficients. Though iterative fitting procedures could have been used, the sheer magnitude of the required computations, even with the aid of a large computer, caused this approach to be rejected. An attempt was made to develop models amenable to linear regression fitting procedures. When this was done, however, the point density expressions often were eliminated in the fitting process and did not appear in the final equations. In the cases of one of the slash pine and one of the loblolly pine datasets not one of the point density expressions was retained. Consequently, the regression approach to evaluation of the effectiveness of the various point density expressions was abandoned. As a result of these experiences, it was decided that the degree of relationship between the growth and point density values would be measured in terms of simple correlation coefficients. It was further decided to retain the two original tree growth variables (periodic annual increment in tree basal area and periodic annual increment in d.b.h.o.b.) and to test the point density expressions with each of these two variables. The point density expressions that were tested are listed in the next section. Statistical significance of the correlation coefficients themselves were determined by standard procedures (24). However, since procedures for making multiple comparisons among correlation coefficients are not known, nothing could be done to determine the statistical significance of the differences between the large numbers of correlation coefficients generated in the course of the study. Individuals making use of the tables in this report will be obliged to draw their own conclusions with respect to the differences among coefficients. The relationship between growth of a sample tree and a meas- 30 ALABAMA AGRICULTURAL EXPERIMENT STATION 0A Growth Growth Point Density A Growth Growth Point Density B Point Density C Growth Growth Point Density D Point Density E Point Density F FIG. 12. Possible relationships between sample tree growth and point density. ure of competitive pressure against that tree may take on several conceivable forms, as shown in Figure 12. The correlation can be either positive or negative, depending on the nature of the point density expression. Furthermore, the relationship has a shape, which may be linear, as in Figure 12 A and B, or curvilinear, as GROWTH OF SOUTHERN PINES 31 in Figure 12 C, D, E, and F. Though the shape could be even more complex, that possibility was ignored in this study. To recognize possible curvilinearity, three coefficients were computed for each growth variable-point density expressionspecies-crown class-levels combination. With the first correlation coefficient, the relationship was assumed to be linear and no modifications were made to either the growth or the point density values. In the second, square roots of the point density values were used. This anamorphosis of the point density scale would tend to linearize the relationship in the event that it was of the Figure 12, C or D type. In the third computation, point density values were squared, with the effect that the relatoinship would tend to linearity if it were of the Figure 12, E or F type. It was assumed that the highest correlation coefficient would be associated with the procedure that most nearly linearized the relationship. POINT DENSITY EXPRESSIONS TESTED The following point density expressions were tested: (1). Basal area per acre from fixed radius plots centered on the sample tree. Two plot sizes were used, the first with a radius of 14.42 feet (0.015 acre) and the second with a radius of 26.33 feet (0.050 acre). (2-5). Steneker and Jarvis' expressions IsJ, IsJ2, ISJ3, and IsJ4 (Equations 22, 23, 24, and 25 respectively), in conjunction with the plots described above. (6). Bitterlich's angle-count, with basal area factors of 5, 10, 15, 20, 25, 30, and 40 square feet per acre. (7). Spurr's angle-summation, using the first 4, 6, 8, 10, 12, 14, and 16 trees subtending the largest angles. (8). Brown's growing space method. (9). A modification of Brown's method in which the relative sizes of the trees at the ends of each of the lines were taken into account. Following is a description of the algorithm used. (Also see Figure 11.) 6Level refers to the magnitude of a controlling variable, within a given point density expression, where that magnitude is arbitrarily assigned by the investigator. For example, in the Bitterlich method the person doing the work may decide to use several different BAF's. Each of these represents a level. Again, in the Spurr method, the number of competing trees that are to be considered can be controlled by the investigator. Each such number is a level. Many of the point density expressions have variables of this type. 32 ALABAMA AGRICULTURAL EXPERIMENT STATION (a). A map was constructed for each sample tree as in Figure 5. (b). The sample tree was connected to each of its competitors with a straight line. (c). The distance (Ti) between the sample tree and the ith competitor was measured. (d). The diameters d.b.h.o.b.) of the two trees were averaged: D = (Ds + Di)/2 (e). The difference between the larger of the two diameters (D) and D was computed: f -DD (f). The value q was computed: fTi q + Ti 2 2D (g). The distance q was laid off on the line connecting the two trees using the larger tree as the origin. (h). Perpendiculars were constructed through the points located in this manner, polygons were developed, and their areas were measured as in the Brown method. (10-15). Staebler's indices Is 1/F, IS2/F, Is3/F, and Is4/.F (See equations 6, 7, 8, 9, and 10). In addition, index Isi was used in its uncorrected form. Furthermore, a modification of the latter was used in which Isi was expressed as a percentage of the diameter of the sample tree's C.I.Z. This modification was labelled Iss55, see Figure 6 and Appendix A.4. (16-17). Newnham's index IN (see Equation 12). In addition, a modification of this index was used where the correction factor Ai/AS was deleted. This was labelled IN2. (18). The Fritts-Gerrard index IFG (see Equation 16). (19). Bella's index lB (see Equation 16). (20). Opie's index Jo (see Equation 27). (21). In addition, to provide a standard of comparison, conventional basal area per acre on an entire quarter-acre plot, not necessarily centered on the sample tree (SBA) was tested. In the case of the fixed plot, the Bitterlich, and the Spurr methods, separate basal areas per acre were computed with the sample tree both included and excluded. In the case of the methods based on the concept of the C.I.Z., a common definition of the C.I.Z. radius was used rather than GROWTH OF SOUTHERN PINES 33 each of those used by the individual investigators. Basically, the common relationship used was: 6 R = 1 + D(28) where: R = radius of the C.I.Z., in feet; D = d.b.h.o.b., in inches. The derived radius, R, was appropriate for open-grown trees. Since. both Newnham and Bella recognized that the C.I.Z. of a tree in a closed stand probably would be different from one in an open situation, they introduced correction factors into their C.I.Z. computations to compensate for this difference. Both investigators based their correction factors on empirical evidence. This policy was followed in this study. The effective C.I.Z. radius was defined as: R= (1 + D) K where: R = effective C.I.Z. radius, in feet; D = d.b.h.o.b., in inches; K = correction factor. (29) Values for K were arbitrarily set at 1.0, 1.3, 1.6, 1.9, 2.2, 2.5, 2.8. Note that when K = 1.0, the result is the same as when no correction value is used. As was previously described, the angles a used by Newnham as a measure of competitive pressure, Equation 12 and Figures 8 and 9, usually are consistent with theoretical considerations, though in some cases the angle decreases as the competitive pressure increases. Newnham recognized this and, in general, the procedures used in this study were in agreement with those he used. However, some changes were made. Whenever the situations shown in Figures 8E and 8F existed, the value assigned a 1 was set equal to that in Figure 8D, where a reaches a maximum for the given pair of circles. In contrast, Newnham assigned a a value of zero under these conditions. With Newnham's procedure, the measure of competitive pressure under certain situaD.b.h.o.b. and crown radius data were obtained in the Auburn area from 34 trees (24 loblolly, 5 longleaf, and 5 shortleaf pines) that apparently had always been open-grown. The diameter range was from 3.7 to 28.1 inches and the diameters were well distributed within this range. Apparently there were no appreciable species differences. The resulting equation was: R = 1.1 + 0.93 D. The correlation coefficient was 0.966. Thus, the relationship used (Equation 28) 6 seemed to be reasonable. 34 ALABAMA AGRICULTURAL EXPERIMENT STATION tions can decrease as the actual pressure increases. Since the procedure used in this study prevented that possibility, it appeared to be more logical. In the case of Bella's method, a series of exponents (x) were used with the weighting factor (Di/DS) x, as shown in Equation 21. The exponents tested were 0.5, 0.8, 1.0, 1.1, 1.4, 1.7, 2.0, 2.3, 2.6, 2.9, and 3.0. The basal area factor (BAF) used in Opie's method varied according to the correction factor (K) in Equation 80 7: BAF = 43560/(25 K) 2 (30) Consequently, the BAF's used were: 69.70, 41.24, 27.22, 19.31, 14.40, 11.15, and 8.89. RESULTS AND DISCUSSION After computation of the correlation coefficients, the printed output of the computer was searched for the highest correlation coefficient associated with each combination of growth variable, point-density expression, species, crown class, and level, regardless of the shape of the relationship. These correlation coefficient maxima were then plotted against crown class in the case of the point density expressions where level was not a factor, or against level by crown class in the case of the expressions where level was involved, Figures 14-47. From these Figures, one can obtain an idea of the effect of crown class and level differences on the efficiency of the several point density expressions. Each of the aforementioned maximum correlation coefficients was a member of a three-member set, or triplet, which showed the results using the original data and the two transformations of that data. These sets or triplets of correlation coefficients are shown in Appendix B, Tables 1-24. The statistical significance of SRefer to Equations 1 and 29. Cr2 Equation 1: BAF Equation 29: R = R When D Substituting C r = 1; and R BAF (1 + D) K 24 inches; when D == d.b.h.o.b. = = (1 + 24) K = 25K. = 24 inches, r = 12 inches or 1 foot. = 43560 = 25K in Equation 1 yields: 43560(1)2 (25K)2 =43560/(25K)2 GROWTH OF SOUTHERN PINES 35 each maximum is shown adjacent to that maximum but has nothing to, do with the other two members of the set. If one desires to find the significance of the latter two, he should use standard procedures (24). These tables also show which were the best levels in cases where levels were involved. This type of study does not lend itself well to a statistical analysis. Procedures have not yet been developed for making multiple comparisons of correlation coefficients. Furthermore, any procedure making use of regression analysis would be impractically massive. Therefore, the reader should keep in mind that most of the following discussion was based on the author's subjective judgment and reasoned interpretations of the results of this study. Datasets The most striking thing encountered in the course of the study was the behavior of the different groups of data. As might be expected, there were species differences, but the greatest difference, across the board, involved the two sets of slash pine data. The slash pine results from Block 31 (see the map in Figure 11 for relative location) are what one might expect. Point density was correlated significantly with growth in most cases and the results were consistent with theoretical considerations. In other words, when a point density expression indicated increasing competitive pressure the growth rate slowed. The slash pine results from Block 31, however, were highly erratic and the relationship between growth and the point density values were usually weak or non-existent. Often the growth rate increased as the point density increased, which, superficially anyway, is not logical. The reason for this divergence of behavior between the two blocks of slash pine is not clear. Both blocks were planted at the same time and, presumably, the genetic backgrounds of the trees were generally similar. Though there was a statistically significant difference between the mean site indices, the magnitude of the difference was not great.8 Furthermore, it is difficult to visualize the mechanism that would cause differences in site quality to have so much effect on the relationship between individual tree growth and point density. Both blocks had been thinned, and the thinning regime, rationale, and schedule apparently were the same for both blocks. 8 Mean site indices were: Block 31, 91.1; Block 32, 85.8. The difference was significant at the 0.01 level. The variances were homogeneous. 36 ALABAMA AGRICULTURAL EXPERIMENT STATION The two blocks, however, had different surroundings. As can be seen in Figure 11, the slash pine plots in Block 32 were bordered on the south by open fields and on the north by the longleaf pine plots. Since the longleaf pine stand was slow to develop, the slash pine stand, during much of its life, was essentially open on both sides. In Block 31, on the other hand, the slash pine plots were bordered on the south by the loblolly pine plots of Block 32 and on the north either by other planted pine stands of approximately the same age or by natural timber. Consequently, Block 31 more nearly represented closed forest condition while the slash pine in Block 32 probably had been influenced by openness on both sides of the single row of plots and represented an exaggerated edge situation, where substantially more light was available. With more light generally available the effect of point density conceivably could be greatly modified. This thesis receives added support when one examines the data from the longleaf and loblolly pine plots. Longleaf pine behaved as one would expect and was much like the Block 31 slash pine. It developed under conditions of competition for sunlight, and possibly for moisture, from the taller stands of loblolly and slash pine which bordered it to the north and south. Since the loblolly pine, which behaved somewhat more erratically than the Block 31 slash pine or the longleaf pine, was bordered on one side by the slow-to-develop longleaf for a substantial portion of its life, it had been reasonably free of competition for sunlight. Consequently, the edge effect probably influenced the loblolly pine results. These findings suggest that the effect of proximity to the edge of a stand may extend deeper into a stand than is generally recognized. Research workers involved with responses of individual trees to treatments of various kinds should be aware of this possibility and should locate their plots so that the treatment effects will not be confounded with edge effect. Crown Classes The behavior of the crown classes can best be visualized by a study of the graphs in Appendix B, Figures 14-47. In general, estimated point density had the greatest effect on growth in the case of the lower crown classes and, probably, the intermediate class showed the most consistent results. Only in the case of the slash pine in Block 31 did the dominants show consistently high cor- GROWTH OF SOUTHERN PINES 37 relations. Within the other groups the correlations for the dominant and codominant classes fluctuated widely and erratically. These results are not necessarily illogical. The dominants and codominants had been able to hold their positions in the canopy partly because they were more aggressive, while the intermediate and overtopped trees slipped to their positions because they were relatively susceptible to competition. The extremely erratic nature of the results from the dominant and codominant classes in both the slash pine of Block 32 and the loblolly pine probably was largely due to the edge effect previously discussed. The lower crown classes acted in a much more expectable manner than did the upper classes in these stands. The overtopped trees showed a weaker relationship between growth and point density than did the intermediates. This probably was due to the very small magnitudes of the growth increments. The d.b.h.'s were measured to 1/10 inch. It is possible that these measurements were too coarse, resulting in many trees showing the same increment over the period when actually there was a differential response to competitive pressure which could only be detected with measurements using units smaller than 1/10 inch. For a few of the point density expressions, the sign of the correlation coefficient for ALL trees was opposite to the correlation coefficients for each of the individual crown classes. This is demonstrated in Figure 13. Regression lines are shown since they are easier to comprehend than scattergrams. As can be seen, the individual crown class curves slope down toward the right while the overall curve slopes upward. When this occurs it indicates that the point density expression detects the fact that large trees (e.g., dominants), in general, regardless of competitive pressure, grow more than smaller trees (e.g., intermediates or overtopped). However, within a crown class, growth falls off as competitive pressure increases. This differential in growth response made it necessary to recognize crown class in this study. Method of Expressing Growth In general, the relationship between basal area growth and point density was similar to that between d.b.h. growth and point density. However, in the majority of cases, the correlation was somewhat better for the basal area data than for the d.b.h. data. No pattern emerged to support an argument that, under given cir- 38 ALABAMA AGRICULTURAL EXPERIMENT STATION 38 ALABAMA AGRICULTURLEPRMN P.A.I. (basal area) (sq.ft.) .I 1 TTO .05 .03 .02 F LA .0.7 7000 .007 .006 .005 .004 .003 .002 "1 0007 .00069 .0005 .0004 .0003 °- Dominants 0002 """Codominants -- Intermediates .0001 IC I 20 -------304050 I "--Overtopped ""All 7090 200 300 500 700 1000 Point density FIG. 13. Relationship between periodic annual increment in basal area and the point density values obtained using Staebler's competition index Isi with longleaf pine. GROWTH OF SOUTHERN PINES 39 cumstances, one of the growth variables would correlate better than the other with a selected point density expression. Theoretically, the basal area growth-point density relationship should be of more interest or utility than the d.b.h. growth-point density relationship because basal area partially accounts for size of the tree. For example, any unit of d.b.h. growth on a small tree is the same as that same unit of d.b.h. growth on a large tree as far as d.b.h. growth is concerned. When the identical units d.b.h. increments are converted into basal area increments, however, the larger tree exhibits more basal area growth than does the small tree. The somewhat higher correlation encountered when basal area growth was the dependent variable may result from the partial accounting for tree size. Point-Density Expressions Examination of the correlation coefficients in the tables and figures of Appendix B will reveal that, in general, the relationships between individual tree d.b.h. or basal area growth and point density were weak. The correlation coefficients ranged in magnitude from a high of 0.8448 (Bella's index IB, basal area growth, dominant trees, loblolly pine) to a low that was essentially zero. Most of the correlation coefficients were in the range from 0.3 to 0.6. Since a substantial proportion of the correlations were not significant (0.05 level of probability), serious doubts of the utility of the point density expressions arise. Tables 1 and 2 show the rankings of the 24 different point density expressions tested using the results from the basal area growth of the slash pine in Block 31 and the longleaf pine in Block 32. These two sets of results were chosen because they represent the conditions under which the point density expressions appeared to be most effective. Rankings for the other groups can be developed from the information in Appendix B, Tables 1-24. As can be seen, no single point density expression is clearly superior to the others. However, one can generalize to the extent that the expressions based on C.I.Z. overlaps usually ranked high and that the Steneker-Jarvis and the Brown expressions usually ranked low. In addition, stand basal area was about as reliable a predictor of individual tree growth as any point density expression tested. Furthermore, stand basal area ranked highest with the dominants. That the Fritts-Gerrard and Opie indices (IFG and almost exactly the same result appears logical because, in essence lo) yield TABLE 1. RANKING OF POINT DENSITY WHEN THE GROWTH EXPRESSION WAS~ PERIODIC ANNUAL INCREMENT IN BASAL AREA, SLASH PINE, BLOCK EXPRE~SSIONS 31' A Rank 12 3. 4 5 6 7 8 9 10 11. 12 13 14 15. 16 17_ 18 19 Dominant Expr. SBA r Codominant Expr. r Crown Classes Intermediate Expr. r Overtoppe d Expr. r All Expr. '---B'---N -7 r 7 5 3 -. 612-3 SBA -. 8146 -5 860 'B -. 6028 -. 8105 733. IN 'N -. 57~ 'S4/F -. 5176 Spurrw/o -. 8066 'B 'EG -5 621 -. 5174 612 -. 8041 JFG -. 5125 -. 7924 476 '0 'N2 -. 4914 -. 7886 Fixed w/o 462 'N2 -. 4816 -. 7841 Bitt. w/o 449 Bitt. w/o -. 4796 -. 7774 Bitt. w/ 449 S53 -. 7728 Fixed w/ -. 4548 439 -. 4509 -. 7665 -. 52 436 Fixedw 'S5 -. 4379 -. 7665 -. 51 420 'Si '2FG 153/F -. 4229 -. 7565 413 Isi/F IS2/F Fixed w/o -. 7527 Brown mod. +.38101 262 Fixed w/ -. 7431 -. 3475 221 'Si Spurr w/ -.7391 Brown ±.343,0 123 S3 F -. 5 724 Spurr w/o -. 3423 SBA -. 7336 -. 3013 -. 7327 705 'si/F 'SJi -. 7158 -. 2874 659 'SJ2 'Si -. 5] 568 'SJ2 F -. 26.72 -. 7147 Spurr w/o 20 -.7118 -. 2587 Bitt. wo.+2 377 'SJ4 'S4/F 21. -. 2.569 -. 6914 294 '5J3 'SJ2 22 Brown mod. +.6765 -.. 2346 154 Spurr w/ 23Brown -. 1604 736 + .6481 'SJ3 24Bitt. w/ -. 1528 -. 6409 123 '5J4 1 There were no overtopped trees in this set. For an explanation see Footnote 4. O- ----------- 'FG jo N2 -. 6205 -. 6188 -. 6,094 -. 5853 ----- Fixed w/o ----- rown mod. B ----- Bitt. w/o Bitt. w/ SBA Fixed w/ 'S3/F +.-5655 r -. 5541 ---- -. 55,11 -. 5481 -. 53.91 -. 5880 ----------- =-- ----- purr w/o S ------- -. 5344 -. 5262 -. 5231 '55 ----Spurr w/ ---- Brown ----- 5 2 /F -----5J2 'sJi 'S4/F 1 5 1 /F -.49,95 +.4952 -. 4338 -. 4284 -. 4122 -. 3861 m m -------- z ------- 'Si-.3192 ---- ISJ4-.3066 ---IsJ3 -. 2628 z TABLE 2. RANKING OF POINT DENSITY WHEN THE GROWTH INCREMENT IN BASAL AREA, LONGLEAF PINE EXPRE~SSIONS EXPRESSION WAS PERIODIC ANNUAL 0 Overtopped Crown Classes Rank Dominant Expr. -. -. -. -. -. -. -. -. -. -. _ .... - Codominant r 5492 4898 4485 4466 4427 4400 4390 4381 4336 4313 Expr. Spurr Intermediate r Expr. Spurr w/ Spunr All r Expr. IN 'B 0 r 0 C r o Expr. Bitt. w/ Bitt. w/o SBA 1- - - - - - - - - 2 -- - - - - - - - - Bitt. w/o 3- - - - - - - - - 'S3/ F 4- - - - - - - - - 'N2 5 --- - - - - - 'Si 6 -- -- -- -- 'S4/F 7 '52/F &- - - - - - - - - - Bitt. w/ 9 -- - - - - - - - IM1 -- - - - - - - - IS F 11 - - - - - - - - - 'N 12 - - - - - - - - 'o 1 3 -- - - - - - - - 'FG 1 4 -- - - - - - - - - Spurr w/ 1 5 -- - - - - - - - 'B 1 6 - - - - - - - - - - Spurr w/o 1 7-- - - - - - - - - Fixed w/o 1 8 1- - - - - - - - - Fixed w/ 1 9 - - - - - - - - - - Brown mod. 'SJ3 20 -- - - - - - - - 21 -- - - - - - - - 'SJi 22 --------- Brown 0 -. 4262 -. 4254 -. 42.53 -. 4210 -. 4178 -. 4160 -. 4127 -. 4123 +.4055 -. 3947 23 -- - - - - - - - - '5J4 '5J2 24 -- - - - - - - - - -. 3778 +.3629 -. 2822 --.2735 -. 7930 -. 7924 -. 7214 'SJi -. 7134 'SJ3 -. 7119 'S2 /F -. 6970 Fixed w/o -. 6836 '54/F -. 6271 'Si/F -. 6694 '0 -. 6694 'FG -. 6616 -. 6597 '5J2 -. 6576 'S5 -. 6518 'B -;6441 Fixed w/ -. 6441 '5J4 + .6430 Brown -. 6271 'Si -. 6183 Bitt. "w -. 6104 Bitt. W/o -. 5916 'N2 Brown mod. +.5890 -. 56.90 'N -.5493 SBA Spurr w/ w/o -. 7828 -. 7606 -. 6917 'N -. 6715 'N2 -. 6676 IS4 /F -. 6624 'S2/F -. 6514 Fixed w/ -. 6405 Fixed w/o -. 6369 -. 6320 'B -. 6290, 'FG -. 6290 -. 6278 SBA -. 6158 'Si -. 6121 'S5 -. 6067 'Si/F -. 5450 'SJ3 -. 5250 'SJ4 -. 5063 'SJi -. 4849 '5J2 Bitt. w/ -. 4535 Bitt. w/o -. 4497 Brown +.3329 Brown mod. +.2441 w/ 'S5 'N2 Fixed w/ Fixed w/o 'Si/F 'B 'Si -. 6516 -. 6487 -. 6340 -. 6340 -. 6228 -. 6222 -. 6194 -. 6111 -. 6090 -. 5900 -. 5881 -. 5793 -. 5761 -. 8027 -. 7941 Brown mod. ±+.7455 -. 6259 '.N2 'FG z z Fn -.564.2 -.5642 -. 5603 -. 5390 -. 5381 ±.4571 -. 4406 -.4319 -. 4155 ±.4131 +38,53 -. 3676 -. 3,36,6 -. 3296 +.2854 -. 2802 -. 1853 -. 1321 +.120,1 -. 0948 Spurr w/ Spurr w/o Fixed w/o Brown 'S3/F Bitt. w/o Bitt. w/ 'SJ3 'Si -. 5692 SBA -. 5479 Spurr w/o -. 5475 Brown mod. -. 5227 Brown ±.5141 -. 4789 IN -. 4726 Spurr w/ -. 3762 'SJ 1 -. 3454 'SJ3 -. 3092 'SJ2 -. 2749 'SJ4 'sl/F '5 SBA 'SJ4 Fixed w/ 'S4/F 'SJi 'SJ2 42 ALABAMA AGRICULTURAL EXPERIMENT STATION they differ only in the: choice of a constant multiplier, the basal area factor (BAF). If one should compute the 95 per cent confidence interval for any one of the correlation coefficients that are close to the average value, that interval would include virtually all of the other coefficients. For example, the correlation coefficient for the Steneker-Jarvis ISJ2 for basal area growth of codominant longleaf pines, was -0.6597, Appendix B, Table 4. Twenty-eight trees were in that sample. The 0.95 confidence limits were -0.3800 and 0.8287. As can be seen in Table 2, this interval includes the correlation coefficients for every point density expression tested with that same set of data. This suggests that, with the sample sizes used here, few significant differences between correlation coefficients would be shown if suitable multiple range tests were available. Since differences between the various point density expressions are relatively small, more intensive sampling would be needed to confirm those differences if they really exist. It is doubtful that making such intensive tests would be of much practical value because there is no clear evidence that any specific expression would prove more useful than any other in a similar situation. Shape of Relationship More often than not, the square root of the point density expression yielded a stronger correlation than either the unweighted point density expression or its square. However, as can be seen in Appendix B, Tables 2-24, in most instances the differences between the three correlation coefficients associated with different ways of expressing point density were small. It is doubtful that any of the differences were real. There may be a tendency toward curvilinearity of the relationship, but it is not strong. Linearity could probably be assumed in most cases without much loss of information. CONCLUSIONS 1. It appears that in general point density is not closely correlated with individual tree growth in either d.b.h. or basal area. 2. It appears that no point density expression is clearly better than the others as a predictor of tree growth. However, those based on overlapping C.I. Zones appear to perform generally better than the others while the Steneker-Jarvis and Brown expres- GROWTH OF SOUTHERN PINES 43 sions appear to be less effective. The range in performance, however, is not great. 3. It appears that crown class must be recognized whenever point density is to be a factor in a study. 4. It appears that, at least in the case of the pine species studied here, edge effect penetrates deep into the stand. This can cause confounding in statistical studies involving the growth of individual trees. 5. It appears that the relationship between growth and point density may be curvilinear. However, this tendency is so slight that it probably can be ignored. 6. It appears that average stand density, measured in terms of basal area per acre, is just about as good a predictor of individual tree growth as is point density, especially in the case of the dominant and codominant crown classes. This indicates that the existing point density expressions are not functioning as expected and that, perhaps, a new approach to the problem of evaluation of competitive pressure on individual trees will have to be developed. 44 ALABAMA AGRICULTURAL EXPERIMENT STATION LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) A Competition Model for Individual Trees. Canada Dept. of Fisheries & Forestry. Bi-Monthly Research Notes 25:3:24-25. 1971. A New Competition Model for Individual Trees. -----------------. Forest Science 17:364-372. BITTERLICH, W. 1947. Die Winkelzahlmessung. Allg. Forst. u. Holzwirts. Ztg. 58:94-96. BROWN, G. S. 1965. Point Density in Stems Per Acre. New Zealand Forest Service, Forestry Research Inst., For. Res. Note 38. FRITTs, H. C. 1956. Relations of Radial Growth of Beech to Some Environmental Factors in a Central Ohio Forest. Unpublished Ph.D. Dissertation. Ohio State Univ. 128 pp. GERRARD, D. J. 1969a. Competition Quotient: An Index of the Competitive Stress Affecting Individual Forest Trees. Unpublished Ph.D. Dissertation. Mich State Univ. 64 pp. . 1969b. Competition Quotient: A New Measure of the Competition Affecting Individual Forest Trees. Mich. State Univ. Agr. Exp. Sta. Res. Bull. 20. GROSENBAUGH, L. R. 1952. Plotless Timber Estimates - New, Fast, BELLA, I. E. 1969. Competitive Influence-Zone Overlap: (8) Easy. J. For. 50:32-37. (9) --------------------------. 1958. Point Sampling and Line Sampling: Probability Theory, Geometric Implications, Synthesis. USDA, Forest Service, Southern Forest Exp. Sta., Occas. Pap. 160. (10) HILEY, W. E. 1948. Craib's Thinning Prescriptions for Conifers in South Africa. Quat. J. For. 42:5-19. 1954. Woodland Management. Faber & Faber. Ltd., ..-------------(11) London. 463 pp. (12) KEISTER, T. D. 1971. A Measure of the Intraspecific Competition Experienced by an Individual Tree in a Planted Stand. La. State Univ. Agr. Exp. Sta. Bull. No. 652. (13) KRAJICEK, J. E. AND K. A. BRINKMAN. 1957. Crown Development: An Index of Stand Density. USDA, Forest Service, Central States Forest Exp. Sta., Note 108. 1961. AND S. F. GINGRICH. (14) -------------------------------------------------------Crown Competition - A Measure of Density. For. Sci. 7:35-42. (15) LANE-POOLE, C. E. 1986. Crown Ratio. Austral. For. 1:2:5-11. (16) LATHAM, R. P. 1972. Competition Estimator for Forest Trees. Photogrammetric Engineering 38:48-50. (17) LEMMON, P. E. AND F. X. SCHUMACHER. 1962a. Volume and Diameter Growth of Ponderosa Pine Trees as Influenced by Site Index, Density, Age, and Size. For. Sci. 8:286-249. --------------------------------- . 1962b. Stocking Density (18) -------------------------Around Ponderosa Pine Trees. For. Sci. 8:397-402. (19) LIVINGSTON, K. W. 1964. Slash Pine at Auburn, a Case History. Auburn Univ. (Ala.) Agr. Exp. Sta., Forestry Dept. Series No. 1. GROWTH OF SOUTHERN PINES 45 (20) NEWNHAM, R. M. 1964. The Development of a Stand Model for Douglas Fir. Unpublished Ph.D. Dissertation. Univ. B.C. 201 pp. (21) NICHOLs, N. G. 1958. Some Factors Affecting Lateral Root Development in Longleaf Pine in Southwest Alabama. Unpublished M.S. Thesis. Auburn Univ. (22) OPIE, J. E. 1968. Predictability of Individual Tree Growth Using Various Definitions of Competing Basal Area. For. Sci. 14:314-323. (23) ROGERS, S. W. 1935. Soil Factors in Relation to Root Growth. Trans. 3rd Inter. Cong. Soil Sci. 1:249-253. (24) SNEDECOR, G. W. AND W. G. COCHRAN. 1969. Statistical Methods. (Sixth Ed.). Iowa State Univ. Press, Ames, Iowa. 591 pp. (25) SPURR, S. H. 1952. Forest Inventory. Ronald Press Co., New York. 476 pp. 1962. A Measure of Point Density. For. Sci. 8:85-96. (26) ---------.---(27) STAEBLER, G. R. 1951. Growth and Spacing in an Unevenaged Stand of Douglas Fir. Unpublished M.F. Thesis. Univ. Mich. 46 pp. (28) STENEKER, G. A. AND J. M. JARvIS. 1963. A Preliminary Study to Assess Competition in a White Spruce-Trembling Aspen Stand. For Chron. 39:334-336. (29) U.S. FOREST SERVICE. 1929. Volume, Yield, and Stand Tables for Second Growth Southern Pines. USDA Misc. Publ. 50. APPENDIX A Computations for examples in Figures 1-10. A.1. For Figure 1, basal area per acre, from fixed radius plots: Plot area = r2 = 3.1416(15)2 = 706.86 sq. ft. or 0.016227 acre. Trees inside plot: 1 2 3 4 D.b.h. In. - -r Basal area Sq. ft. 0.545 0.442 0.136 0.098 1.221 Remarks 10 9 5 6 S Half in and half out. Sq. ft., excluding sample tree. Sample tree. Sq. ft., including sample tree. S 7 0.267 1.488 Blow-up factor: 1/0.016227 -- 61.625686 Basal area/acre, excluding sample tree - 61.625686 (1.221) = 75.2 sq. ft. Basal area/acre, including sample tree -= 61.625686 (1.488) = 91.7 sq. ft. 46 ALABAMA AGRICULTURAL EXPERIMENT STATION A.2. For Figure 1, the Steneker-Jarvis competition indices: Trees inside plot: Gi Gi2 Ft. 1 2 3 4 13.75 6.0 8.0 15.0 2 203.1 36.0 64.0 225.0 Half in and half out. DS = 7.0 inches; DS = 49.0 n IsJ1= I (DS/Gi)= i-1 = n (7/13.75)+(7/6.0)+(7/8.0)+(7/15.0) 3.017 IsJ2 = Y (D,/G 2 ) = (7/203.1)+(7/36.0)+(7/64.0)+(7/225.0) i=1 = n 0.369 ISJ3 = I n 2 (DS /Gi) = (49.0/13.75)+(49.0/6.0)+(49.0/8.0)+ 21.122 i-= (49.0/15.0) = IsJ4 = . (D, 2 /Gi 2 )= i=l +(49.0/225.0) (49.0/203.1)+(49.0/36.0)+(49.0/64.0) = 2.586 A.3. For Figure 3, basal area per acre, using Spurr's angle-summation method: Four trees will be used, the ones subtending the four largest angles (angle ranks 1 to 4). Ranking the trees requires the computation of the sine of half of the subtended angle: Tree d.b.h. In. A B C-....... D E..... F G H I 6.0 10.0 6.0 8.0 5.0 8.0 9.0 9.0 5.0 Distance Sine 2 ( 24 )d.b.h.)/Dist. Rank Ft. 15 13.75 36 28 8 19 6 20 24 (6/24)/15 (10/24)/13.75 (6/24)/36 (8/24)/28 (5/24)/8 (8/24)/19 (9/24)/6 (9/24)/20 (5/24)/24 = = = = = = = = -= 0.01667 0.03030 0.00694 0.01191 0.02604 0.01754 0.06250 0.01875 0.00868 6 2 9 7 3 5 1 4 8 GROWTH OF SOUTHERN PINES 47 Excluding the sample tree : 0.5(43560)(9.0/24)2 0.5 Cr 2 BG R2 62 =85.06 sq. ft./acre = 60,.00=73.85 53.59 272.50 BB_ BE EE 1.5 C r 2 B R2 1.5(43560)(10.0/24)2 2.5(43560)(5.0/24)2 .13.752 = 2.5 C r 2 R282 3.5 C r 2 B11 - 3.5(43560)(9.0/24)2 - R2202 272.50/4 Basal area/acre Including the sample tree: BG= 1.5 C r2 R2 62 68.12 sq. ft. 1.5(43560)(9.0/24)2 255.19 sq. ft/acre B BE - 2.5 C r2 = 2.5(43560)(10.0/24)2 B R2 13.752 =99.991 103.39 - 3.5 C r2 _ R2 3.5(43560)(5.0/24)2 82 68.90 B11 = 4.5 C r2 _ 4.5(43560)(9.0/24)2 527.47 R2 202 131.87 sq. ft. Basal area/acre= 527.47/4= A.4. For Figure 6, the Staebler indices: -S 7.0"? 10 7.3" d.b.h. of average tree in stand. Di/10= Da = i A - 1 73/10= a D F = 2= diameter of C.I.Z. in feet. ± k =2D [(2/2)(7.0 + 7.3) + 2] 2/10 [(a'2)(Ds + Da) + k] 2 /10 =26.57 which rounds to 27. + dA=-5.2' dB - 12.0' d6 = Is _ .0' 3 di=-5.2 + 6.0 + 12.0 -23.2 feet i=1 Is/F i=1 di/F =23.2/27 =0.86 n I/F= ~dig/F i=1 =207.04/27 =7.67 48 48 ALABAMA AGRICULTURAL EXPERIMENT STATION n Is3/F= (dDc)/F - [5.2(10) + 6.0(5) + 12.0(9)] 27=7.15 i=i n _ =S4/F (d 1Dc)/F = [(5.2)2(10) ± (6.0)2(5) + (12.0)2(9)] /27 i=i 65.05 n - IS5 = I di/A, = 23.2/16 = 1.45 or 145%. i=i A.5. For Figure 7, the Newnham indices: A - 2D ± 2 - diameter of C.I.Z. in feet A5 - 2 (7.0) 2 = 16 AA=2(10.0)±1-2 22 AB = 2 (9.0) + 2 - 20 Ac 2(5.0)±2 12 aA = aB = ac = 1050 1770 88° 1 IN = 60 3 1[a 1 (A/A,)] 1 + 177(20/16) + -=_1__-[105(22/16) 360 - 88(12/16)] 431.625 1.20 or 120% 1 I (a ) =1.03 360 or (105 + 177 ± 88) 370 360 103%. A.6. For Figure 10, the Fritts-Gerrard index: The areas in the cross-hatched overlaps could be measured using a planimeter or a dot grid, or they could be computed using conventional mensurational formulae. The latter procedure was used in this study and is described below. Angles from the sample tree, as were used in Newnham's method: aA= aB = 1050 177' or 1.8326 radians or 3.0892 or 1.5359 ac= 880 Equivalent angles measured from the centers of the competing trees: 16A = 72' 1190 or 1.2566 radians PB = Pc=1350 or 2.0769 or 2.3562 GROWTH OF SOUTHERN PINES 49 GROWVTH Radii As/2 OF SOUTHERNd PINES 8.0 feet 11.0 10.0 4 of C. I. Zones: - 16/2 = AA/2 = 22/2 = AB/ 2 =20/2 = Ac/2 - 12/2 =6.0 Areas of segments of C. I. Zones on sides of overlap areas toward the sample tree: USA = aA(AS/22 / (S As/2)) 2)cs(a)sn(aA) 2 2 () 82. o s( 2 s n 1.8326(8.0)2 = 10 5 2 27.73 sq. ft. 2 97.18 sq. ft. 0 ( 10 50 (8.0)2 [COS( 17 ) 2 sin ( 2 )]7 ] US$ =3.0892(8.0)2 = usc 1.5359(8.0)2 2 =17.17 sq. ft. (8.0)2 [cos (88 2 ) sin (88 )] 2 Areas of segments of C. I. Zones on sides of overlap areas away from UA the sample tree: 3609(1.0)272 AiA/2)2 (AA/2)2 /3A(Q [cos ( A) sin ( A ) 72 2 S1.25( 2 2 - (11.0)2 [ cos (2 2 ) sin (7 2 )] 119° 2 2 = 18.48 sq. ft. 2.0769(10.0)2 UB _ 2 = 02 -(10.0)2 [cos ( 119° 2 ) si ( )sin(1 in )] 60.12 sq. ft. 2.3562 (6.0)2 2 29.68 sq. ft. - j = (6.0)2 [cos(1 )] 2 2 Total: 250.36 sq. ft. overlap Area of sample tree C.I.Z. 3.1416 (8.0)2 S =IT(AS/2)2 100 n JFG 100 - 201.06 sq. ft. 250.33=124.52% (I O j) 100 Si=1 S201.06 A7. For Figure 10, the Bella index: K was arbitrarily set equal to 1. Therefore, the C. I. Zones were equal in size to those used for the previous calculations. 50 ALABAMA AGRICULTURAL EXPERIMENT STATION X was arbitrarily set equal to 2. The overlapped areas in sq. ft.: Between A and the sample tree = 27.73 + 18.48 = 46.21 B C = = 97.18 + 60.12 = 17.17 + 29.68 = 157.30 46.85 The Oi(Di/Ds)x values: 46.21 (10.0/7.0)2 = 94.31 157.30 ( 9.0/7.0)2 = 260.03 46.85 ( 5.0/7.0)2 = 23.90 378.24 IB -= I n S [Oi(Di/Ds)x] Si= = 378.24/201.06 = 1.88 or 188%. A.8. For Figure 10, the Opie index: Opie's "m" is equivalent to "k" above. Opie did not use an additive term when defining his C. I. Zones but the + 1 used here should not invalidate the procedure. The BAF, using Equation (30). BAF = 43560/(25k) 2 = 43560/ [(25)(1)]2 - 69.70 o-= BAF S (1 n (1 Oi)= 69.70 201.06 (250.36) 86.79 sq. ft./acre of basal area. GROWTH OF SOUTHERN PINES 51 GROWTH OF SOUTHERN PINES 51 APPENDIX B Figures i.HjJ J Loblolly pine D C I 0 Al I.W D 1 Al Cown classes Crown classes FIG. 14. Correlation coefficients associated with basal areas per acre from fixed radius plots, with sample tree. 52 52 ALABAMA AGRICULTURAL EXPERIMENT STATION i_ 1__ ___~-. Slosh pine , Block 31 Slash pine, Block 32 Basolarea0.015 ocri Boo Qoe0.050 ocr 5 43 S+ Bas -. Loblolly pine -- Longleof pine .I -. ;2 - 2 3-; 4 5 4 7 -4i 7 8 -. f -I u k I --. u vAll 9 n v I I I 0 Crown closses L C I 0 Crown classes All I FIG. 15. Correlation coefficients associated with basal areas per acre from fixed radius plots, without sample tree. GROWTH OF SOUTHERN PINES GSP 53 Slash pine, Block 31 *21 5 4. Slash pine, Block 32 3 2 3 -. 6. 4j 7. 8. -. 9. Basal area Labially pine El0.0150acr( _. ._ '. plot ce aDBH re +. -. -. 5 Longleaf pinel 1 + +. . D C I 0 Crown classes All D C 1 0 Crown classes All FIG. 16. Correlation coefficients associated with the Steneker and Jarvis petition index com- IS jT1 plo 54 54 ALABAMA AGRICULTURAL EXPERIMENT ~I~C ~~l~ ~A~ A STATION Slash pine, Black 31 Slash pine, Block 32 ICrown FIG. 17. Correlation petition index IS J2. D C 0 All D C 1 0 All classes Crown classesJ associated with the Steneker and Jarvis com- coefficients GROWTH GROWTHIOF SH OF SOUTHERN PINES I 55 55 Slash pine, Block 31 Slash pine, Block 32 0 0.015 Baa ara~0.050 D I 0 DCw classes All- D C Crown I 0 classes All FIG. 18. Correlation coefficients associated with the Steneker and Jarvis competition index IS J3. 56 ALABAMA AGRICULTURAL EXPERIMENT STATION Crown classes Crown classes FIG. 19. Correlation coefficients associated with the Steneker and Jarvis competition index ISJ 4 . GROWTH OF SOUTHERN PINES 57 GROWTH OF SOUTHERN PINES 57 Slash pine, Block 32 +.2 +.3 -. 2 -. 3I -. 5I --.6 -. 7 -. 8 -. 9 -1.0 Codominants .... Overtopped "--"--"All %b % Slosh pine, Block 31 +. 4 +.3 -. 2 -. 3 -. 4 --. 5 -. 6 -. 7 -. 8 -. 9 -I.0 Dominants intermediates ----Loblolly pine +. 3 +. +. 4 +. 3 Longleaf pine +.2 r O -.2 --.3 -. 4 -. 5 -. 6 -. 7 (r +.2-.I " . 00 -. 8 -. 9 -. l -. 7 -. 9 5 10 15 20 25 30 40 Basal area factors -1 0 5 10 1520 25 30 Basal area factor 40 terlich method, with sample tree. FIG Coreltinwith hasal area growth and the Bit20 ceffcietsassociated 58 58 ALABAMA ALABAA AGRICULTURAL AL EXPERIMENT STATION E +. ~ $.. Slash pineBok3 +.5 -.2 +.3 +.42 -. 5 -. 6I r Slash pine, Block 32 +.5 -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 -1.0 -. 7 -. 8 -. 9 -1 .0 Codominants.""" mnnsIntermediates - Overtopped ".-"-" All "- Long leaf pine +.3 rO 9 . - .... )d.:** . ... 5 10 15202530 Basal area factor FIG. 21. -. I -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -.9 -1.040 0 5 10 15202530 Basal area factor I I 1 I I I i method, with sample tree. Correlation coefficients associated with d.b.h. growth and the Bitterlich GROWTH OF SOUTHERN PINES 59 +.5 -. 2 -.3 -. 4 +.5 -. 6 -. 7 -. 8 -.9 -. 0 r ~ GROWH O SOUHER PINS Skcsh pine, tClock 32 5 Slosh pnBok3 .5 -. 2 -. 3 -. 4 +.5 -. 6 -. 72 -. 8 -. 9 ' DominantsIntermediates--Loblolly pine +.5-. 2+.3-.4 +.5 -. 6 -. 7 -. 8 -. 9 5 10 15 202530 40 Basal. area factor i__1 I 1 -1.0 I Codominants""". Overtopped--- AII"-" u 1 I' -Longleaf pine \ ... , .5 -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 3 i '_.i _-. r a; r. ," ' ' ... -. 9 -I.0 )L I I I I v*0 5 10 15 20 25 30 II Basal area factor 40 FIG. 22. Correlation coefficients associated with basal area growth and the Bitterlich method, without sample tree. 60 ALABAMA AGRICULTURAL EXPERIMENT STATION 60 ALABAMA AGRICULTURAL EXPERIMENT STATION Slash pine, Block 31 Slash pine) Block 32 +4 +.2 rO0 -. 1 -. 2 -. 3 -. 4 - +. 5 +. 2 +.I -. 2 -. 3 .4 -. 5 -. 6 -. 7 .i I ~j _L -. 5 -. 6 -. 7 -. 8 -. 8 -. 9 -I.0 --.9 -1.0 DominantsIntermediates - Codominants."""" Overtopped "-"-"- " +. 5 +.43 All " Longleaf pine +.3-. 2-. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 5 1Q 15 20 25 30 Basal area factor FIG. 23. Correlation N -. .. '. * --- x2 1 5 10 15 1 1 I I 20 25 30 40 Basal area factor associated with d.b.h. growth and the Bitterlich method, without sample tree. coefficients GROWTH OF SOUTHERN PINES 61 GROWH PINS O SOUHER 6 _ +. 4 +.2 Slash pine, Block 32 Slosh pine) Block 31 +.2 +.3 +.2 -. 3 .4 -. 5 -.6 .7 -. 8 -. 9 -I.0 rO0 -.I -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 Dominants Intermediates ---5 Loblolly pine - -. 8 -. 9 -1.0 I I- I I I I I I I Codominants.""" Overtopped "-"-"+.53 +. 3 -. 2 -. 3 All "-" Long leaf pine 4 +I. 3 2 r ( 2 -. 5I I -.6 -. 1 4 -.8 2-4 6 1 1 11 -. Number of trees -.9 )2 4 6 8 10 12 14 16 Number of trees FIG. 24. Correlation coefficients associated with basal area growth and the Spurr method, with sample tree. 62 62 ALABAMA AGRICULTURAL EXPERIMENT STATION Slash pine, Block 31 +.5 +.4 +.3 Slash pine, Block 32 +.5I +.3 -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 -1.0 L I +.2 +.I " . . .r"I. -. 3 -. 4 -. 5 -. 9 1.0I I , 1 1 1 1 I DominaintsIntermediates - --- Codominonts.""" Overtopped--+. c AllI--" +.5 +.4-. 3- Loblolly pine 5F Longleaf pine e +. 4I +. 3i '+'. +. 2t 3 r ( r -. 5 -. 8 -. 9 0 2 4 6 8 10 12 14 16 Number of trees .I 0 -. - F -I .( 0 2 4 6 8 10 12 14 16 Number of trees associated with d.b.h. growth and the Spurr FIG. 25. Correlation method, with sample tree. coefficients GROWTH OF SOUTHERN PINES 63 GROWTH OF SOUTHERN PINES Slash pine, Block 31 +. +.42 63 Slash pine, Block 32 +. .5 .4 5 -I-. .3 .2 r +.3 +.2 .5- ... .. ... ... .2 .3 .4 .5 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 -1I.0 Overtopped . I -I +.5 low I I .9 +. Codominants."""" "-"-"- All Longleaf pine +.4 +.3 +.2 Donat +. +. +. -E-. I r rv -. 2 r 0 -. 1 -. 2 -. 3 -.4 -. 8 -. 9 rlJ0 2 4 6 8 10 12 14 16 Number of trees 0 2 4 6 8 10 12 14 16 Number of trees FIG. 26. Correlation coefficients associated with basal area growth and the Spurr method, without sample tree. 64 64 ALABAMA AGRICULTURAL EXPERIMENT STATION i i I~rir I Slash pine, Block +.52 31 5 Slash pine, Block 32 +.3 -. 2 -.3 -. 5 -. 6 ~... ". 4 3 2l r 0 +4 2 _.' -. 7 -. 8 -1I I I 6 7 8 9 0 IL DominantsIntermediates Loblolly pine - Codominants."""" Overtopped---"All "-" 5 Longleaf pine 4I +.5 -. 2 3k -. 3 -. 4 -.5 -. 6 -. 7 -. 8 -.9 -l.0 ... -. ,,, 9 - r(. I I II I 234 .. 9---2 -c I )lI 1 I I I I I I I II - I FIG. 27. 24 6 810 12 14 16 Number of trees Correlation I - I .( 0 with 2 4 6 8 10 12 14 16 . ,I associated Number of trees assciaed growth and the Spurr ithd.b.h. method, without sample tree. coefficients GROWTH OF SOUTHERN GROWTH OF SOUTHERN PINES PINES 65 65 -F~. .4 .5 Slash pine, Block 31 " " . +..3 .2 r. .2- +.52 . " M" " +.3 -. 2 -. 3I -. 51 r r 3 .4- 5 -. 6 -. 73 r 6 7 .89 .0 I I -1. -. 8 -. 9 Slash pine, Block 32 DominantsIntermediates---_ Codominants """" Overtopped "-"-"All- 4.3. 3 .2-I. __ _ _ __ _ _ +.5 +.3 Longleaf pine 10 +.2I -.I -. 2 -. 3 -. 4 -. 5 4. 5n vo .. -. 7 -. 8 1.0 1.6 K 2.2 2.8 -.9 -. 0 1.0 1.6 2.2 K 2..8 FIG. 28. Correlation coefficients 'Si. ler competition index associated with basal area growth and the Staeb- 66 ALABAMA AGRICULTURAL EXPERIMENT STATION 66 - AABAM AGICULURALEXPRIMET STTIO Slash pine, Block 31 + .4 +. 3 +5 Slash pine, 81c ock 32 _._. rO0 -.l -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 -I. r"0 -. 2 -. 6 -. 7 -. 8 -I I I DominantsIntermediates--5 Loblolly pine Codominants .... Overtopped "-""-"-Al"" +5 Longleaf pine +. 4 .3 r 0 2 .l 02- rO -. 2 -. 3 -. 4 .34 .5o7- .8 -I. '9 .W0 1.0 1.6 2.2 K 2.8 -. 8 -. 9 -. 0 1.0 1.6 2.2 2.8 FIG Coreltinwith d.b.h. growth and the Staebler 29 ceffcietsassociated competition index 'is. GROWTH OF SOUTHERN PINES 67 GROWTH OF SOUTHERN PINES 67 Slash pine, Block 32 4-. 5 +. 3 Slash pine , Block 31 +.45 +.34 +5 +. I rO -.2 -. 3 -.4 -. 5 -. 2 -. 3 -. 6 -. 7 -. 8 -. 9 -. -. -. -. 5 6 7 8 -1.0 DominantsIntermediates -Lobially pine +.53 - Codominants.... Longleaf pine +.-4 +.4 +.3+.4 -. 5 ... .......... .... : +.3-. 2- -. 6 -4 -.7 -. 8 -.9 I -1.C0 .0 1.0 -. 8 I I I I I I -. .9 0 1.6 2.2 2.8 1.0 1.6 2.2 2.8 FIG. 30. Correlation ler competition index I1 1 /F. coefficients associated with basal area growth and the Staeb- 68 68 ALABAMA AGRICULTURAL EXPERIMENT STATION +. 5 - Slash pine, Block 31 +.43 gInch nino AIn,4 7IOCK ' 7 JL +.3 -. 2 -. 4 -. 2 -. -. -. -. 6 7 8 9 +.3-. 2 -. 3 -. 4 -. 6 -. 7 _.8 -. 9 -1I.0 Codominants """" Overtopped "-"-- .. rssr - -_. 1r tI 1 I Dominants- I I I Intermediates + . All Loblally pine 412 r( : i'ce +5 Longleaf pine - r -. 2 " " " ............ -. 2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 8 L -- O 0 W 3 "f' . ........... - .2 -. 7 _ I I I 1.6 I 2.2 I I 2.8 I -.9 I0 1.0 1.0 1.6 2.2 2.8 FIG. 31. Correlation coefficients associated with d.b.h. growth and the Staebler competition index S 1 /F. GROWTH OF SOUTHERN PINES 69 GRWHO SUHR1PNS6 Slash pine, Block 31 + .3 + .2 +,1 .2 -.3 -4 -.6 -. 7 .8' I _ I n , I I I I 1 I I I DominntsIntermediates - - -- Codominants."" Overtopped--- Al+5 +.43 +.32 +5 Loblolly pine +.l4 -~ Longleaf pine -.3 -. 2 +.2-. 2 -. 3 ".7 -. 8 -.9 .0 -. 9 1.0 1.6 2.2 2.8 -1I.00 1.0 1.6 2.2 2.8 FIG. 32. Correlation coefficients associated with basal area growth and the Staebler competition index IS, 2 /F. 70 70 ALABAMA AGRICULTURAL EXPERIMENT STATION Slash pine, Block 31 +.3 + 3. 5 4 T..3 2 r i o. Slash pine, Block 32 rO0 -. I -. 2 -. 3 -. 4 -. 5 2 " " " .............. ... . /- 3456-~ 7- -. 6 -. 7 -. 8 -. 9 I I I -. 189Codominants"""""" +5 +4Longleaf pine +.5 Dominants-I ntermediates -Loblolly pine +.1 -. 2 -. 6 -. 7 -. 8 -. 9 I001.0 +.3+.2- -. 3 -. 4 -. 5 -. 8 -. 9 2.8 ' 1.6 2.2 110 1.0 __1 1.6 2.2 2.8 K FIG. 33. Correlation competition index Ise /F. coefficients associated with d.b.h. growth and the Staebler GROWTH OF SOUTHERN PINES 71 GRWH-FSOTER INS7 Slosh pine, Block 31 532 3 2 3 5 -- 5 Slosh PineBlock 32 4 3 2 r ( ,6 7-. 4 0 ,8 - f. 6 7 8 9 0 Dominonts Intermediates -Overtopped "-"-" +5 +. 4 +. 3 Codominonts."""" All- +5 +.2 Loblolly pine +.2-. I .2 Lon gleof pine -. 6 * -. 7 -.8 .9 0 1:0 1.6 K FIG. 34. Correlation 2.2 2.8 -8 -9 0 10 1.6 K 2.2 2.8 ler competition index 1S /F. 3 coefficients associated with basal area growth and the Staeb- 72 ALABAMA AGRICULTURAL EXPERIMENT STATION 72 AAAAARCLUAEXEIETSTI Slosh pine, Block 31 Slosh pine, Block 32 --. +I. r( ,3 2 5. - + 4. 1-3. . r ( C) 3 .. ... 4.- .... " 67 8 9 3456- 7 9 Dominonts Intermediates +'5 Loblolly pine Codominonts.""" Overtopped "-"-"45 ----- All Longleof pine -. 3- +.3-. 2-. 3I -. 7 +.25 -. 7 -. 9 -'0 1.0 1.6 2.2 2.8 -. 8 y-.9 .0 1.0 1.6 2.2 2.8 --.6 FIG. 35. Correlation coefficients associated with d.b.h. growth and the Staebler competition index 1S /F. 3 GROWTH OF. SOUTHERN PINES GROWH PINS O SOUHER 73 7 Slash pine, Block 31 -. Slosh pine, Block 32 5 .4 +4 +. . F.2 r F.I _.2 .3 .6 -.4 -.5 2 -.36 -.4 -.8 -.9 -1.0 Dominants Intermediates -.5 Lablally pine Codominants."""" Overtopped--AllLongleaf pine +. 3 +. 2 -. 4 \ r 0 -. 2 -. 3 0+ .0 r 1.222". K -. 4 -. 5 -. 6 -. 7 -. 8 -. 9 -I.e 0 1.0 1.6 K 2.2 2.8 FIG. 36. Correlation coefficients associated with basal area growth and the Staebler competition index 1S4 /F. ,74 74 ALABAMA AGRICULTURAL EXPERIMENT _ i ~ STATION I _~~~ +. 5 Slosh pine, Block 31 Slash pine, Block 32 +.44-.3 -. 4 -. 5 -. 6 -.2 -. 3 -. 4 . . . . . . . +.5 3-. -. 2 -. 3 -. 41 -.I +.I r -. 6I -. 7 -. 8 -. 9 -1.0 Dominants Intermediates Codominants." Overtopped ""--All "- -1.0 +.4 0. +.5 +.I _.2 L .3-t +.5 +.2 -. 7 -. 2 0i~t1.0-. 2 Longleaf pine _. 4 " \ll 1.6 222. -. 4 -. 5 -. 8 -. 9 -1.0 ., I FIG. 37. Correlation coefficients associated with d.b.h. growth and the Staebler competition index IS4 /F. GROWTH OF SOUTHERN PINES 75 GROWTH OF SOUTHERN PINES Slosh pine, Block 75 Slash pine, Block 32 +.5 -. 2 +.3 -. 42 +.5 -. 6 -. 72 -. 3 -. 9 31 +.5 +.2 +.3 +.4 -.5I -.1 -. 7 -. 8 r ' r I r lop 00 1 -. 9 _1.0I1 1 1 1 1 _ 1 Dominants Intermediates--+.5 +.43 Loblolly pine -1.0 Codominants""". 1 1 1 1 l L Overtopped--+. All- Longleaf pine -1-. 2 r. 2 .3 .................... \ .45 i - rO0 -. 1 -. 4 .80 -0 IL 1.0 1.6 K 2.2 2.8 -.9 -. 0 1.0 1.6 2.2 2.8 FIG. 38. Correlation coefficients associated with basal area growth and the Staebler competition index 'S5' 76 ALABAMA AGRICULTURAL EXPERIMENT STATION +5 Slash pine, Block 31 +.3 +. +.3 Slash pine, Block 32 -. 4 -.- "4..,-" .8 -1-.3 -. 2 Dominants Intermediates-----+.5 Lablally pine Codominants. Overtopped "-"-"+.5 All .- Longleaf pine r 0 ~rO0 -"3.1- -,3 -I0 1. 1. .2. -I.60 <1. . 6 . . K K FIG. 39. Correlation coefficients associated with d.b.h. growth and the Staebler competition index 'S5. GROWTH OF SOUTHERN PINES 77 GRWHO SUHR-PNS7 5 Slosh pine, Block 32 Slash pine, Block 31 +'.3 +.2 .Flj ~1-. 2 -1.. .1 . . 4 3 -.2 -. 3 -.4 -. 5 -. 6 -. 7 2 46 .7 8 9 .r.-."- -.8 -.9 W L_ 1 _I I 1 I Dom.nunt 1 1 .0 Codominants.""" Intermediates -----Loblolly pine Overtopped-----+.5 +'.3 +. 2 4.. I All-" 3-F -e 4- Longleaf pine 2F C) .c~ rO0 -. I *-.E .. .. -. 2 -. 3 3 -. 1 0 1.0 1.6 2.2 2.8 -. 5 -I.8 0 1.0 1.6 2.2 2.8 FIG. Newnham competition index IN. 40. Correlation coefficients associated with basal area growth and the 78 ALABAMA AGRICULTURAL EXPERIMENT STATION 78 ALBM-GIULUAtXEIMN TTO Slash pine, Block 31 5 4 3 Slash pine, Block 32 +.4 -. 2 -.3I -. 5 ... . '". ... ,..."" 2 r ( 2 - . 3 -.62 -. 73 -.8 -1.I -1.0 Dominants - -. 9 Intermediates---- - Codominants. Overtopped--- """" All Loblolly pine .5-. 3-. 6I -. 7I Longleaf pine +. 3. +2 r0 -. I .4. -. 5. -. 6 -. 7 -. 8 -. 9 -1.C -. 8 -. 9 1.0 1.6 2.2 2.8 0 1.0 1.6 2.2 2.8 FIG. 41. CorreJlation competition index IN. coefficients associated with d.b.h. growth and the -Newnham " rr GROWTH OF SOUTHERN PINES 79 GROWTH OF SOUTHERN PINES nine-P Block 3 I iIv%, .. 79 Slas~h Slosh pine, Block 31 +.3 4 +.3 +.2r. +.3 -. 5 ". '". .. "". ". " " r r L -.3-. 4- -. 6 -. 7 -.8 -.9 -. 0 I I ' \ -. 6 -. 7 -.8 -1.0 -. 9 Dominants Intermediates - Codominonts"""" Overtopped "-"-"+l.5 +.4 +.3 +.2 -. 1 All- +.5 +.4 L Loblolly pine Longleaf pine +.2 i -. 2 .36 -. 7 -. 8- 0 1.0 1.6 2.2 2.8 0 1.0 1.6 2.2 2.8 ceffcietsassociated FIG42 Coreltin with basal area growth and the Newnham competition index 'N2' 80 80 ALABAMA AABAM AGRICULTURAL AGICULURALEXPRIMET EXPERIMENT STATION STTIO t'.5 'Slash pine, Block 32 +.3 -. 2 +.I -. 5 -.6 -.7 -. 8 K..... DominantsIntermediates -t.5 +.-3 +1.2I Lobiolly pine -. 9i -I.0' Codominants. "" --- Overtopped---+. 4 All- . Longleaf pine 1-. I rC0 -. 2 -. -. -. -. 3 4 5 6 ............ -. 3 -. 8 -. 9 -. 0 1.0 -. 7 -. 8 -. 9 1.6 2.2 - I L I I 1 1 I I 2.8 0 1.0 1.6 2.2 2.8 FIG. 43. Correlation coefficients associated with d.b.h. growth and the Newnham competition index 'N2 " GROWTH OF SOUTHERN GROWTH OF SOUTHERN r PINES PINES 81 81 9 +.5+.4+.3+. 2 1-. I Slash pine, Block 31 +.5 Slosh pine, Block 32 r 0 ' -. 1 .,2 4-.5- -..6 -. 7 -. 8 -.7 -.8 1.9 Dominants Intermediates - -. 9 -. 0 Codomirnants."" "" Overtopped --+. +. 3 +. 2 AII"-" +.5' +4 Loblolly pine Longleaf pine +2 -. 2I~ 3 -.4 ....... . '. +. I rO0 -. I -. 2 . -. 53 -. 7 - ~ -. 9 o 1.0 1.6 2.2 2.8 -. 8 -. 9 0 1.0 1.6 2.2 2.8 FIG. 44. Correlation Gerrard competition index coefficients associated 'FG* with basal area growth' and the Fritts- 82 82 ALABAMA AGRICULTURAL EXPERIMENT STATION I -I +. 5 Slash pine, Block 31 +5 Slash pine, Block 32 -. 2 +.3 -. 42 -. 5 -. 6 -. 7 -. 8 -. 9 -. DominantsInterm p +5 -. 3- -. 4 -. 5 -. 7 -. 8 -. 9 1-__l ly Codominants.. n ediatesLo +'.5 +4 +. 3 l Overtopped---All Longleaf pine +4 +.3 -. 2 +,I -. 4 -. 5 -. 6 -. 7 -. 8 -N9c I I I I I I I +.2I rO0 -.2 --.3 -. 4 -. 5 -.6 -.7 -. 8 -. 9 -1.0 '...0 r . 0 1.0 1.6 2.2 2.8 1.0 1.6 2.2 2.8 FIG. 45. Correlation Gerrard competition index coefficients 'FG. associated with d.b.h. growth and the Fritts- GROWTH OF SOUTHERN PINES 83 GRWT O-OUHENPIES8 Slash pine, Block 31 +.52 Slash pine, Block 32 +.5 -.2 -. 3 -. 4 -. 5 -. 6 -. 7 -. 4 -. 5 -1.0 +.3. -.2-.3I . . . . . "". '"".. 'v . _ '""". ""-.ri" -. 7 -.5 -.6 _-- .... . .. . 1 -. 8 S I t i -. 9 -1.0 Codominonts."" " -. 73 Dominants Loblolly pine Intermediates--Overtopped----All~- -. 8 -. 2 -1.3 +.5 -. 6 -. 7 +.5 Longleaf pine -. 8I -. 2 +.3 -. 2 +.3 -. 4f -. 52 -. 63 -. 7 -. 8 . -. 9 _ 1 I 1 1 1 0 1.0 1.6 K 2.2 2.8 -. 0 1.0 1.6 2.2 2.8 FIG. 46. Correlation coefficients associated with basal area growth and the Opie competition index I0. 84 84 ALABAMA AGRICULTURAL EXPERIMENT STATION -% I Slash pine, Block 31 +. 3 Slash pine, Block 32 +.2 -. I -. 2 -. 3 -. 4 -. 5 -. 6 +.4-.2 -.3I -.5 -.6 --. 7 -.9 -1.0 Dominants Intermediates ---- .: ... ..... -. 8 -. 9 -1.0 L t I I I Codominants."""" Overtopped --- All Loblolly pine +.+.4-. 2-. 3 -. 4 -.7 -. 8 Longleaf pine +.5 -. 2 -. 3 -. 4 -. 5 -. 6I -. 2 -. 8 -. 9 -. 5 -1 0 I I I l 2.8 O 1.0 1.6 K 2.2 2.8 1.0 1.6 K 2.2 FIG. 47. Correlation petition index I~. coefficients associated with d.b.h. growth and the Opie com- GROWTH OF SOUTHERN -PIN!ES. 85 GROWTH OF SOUTHERN PINES 85 APPENDIX B Tables APPENDIX B, TABLE 1. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING BASAL AREA PER ACRE FROM FIXED RADIUS PLOTS, WITH SAMPLE TREE C~rown class Curve form Slash pine, block 81 Best No. of level ohs. r 33 84 89 -0.7381 -0.7431** -0.6931 -0.4449 -0.454840 -0.4106 -0.5360 -0.5268 -0.5462** -----------------------0.5264 -0.539140 -0.4833 -0.6777 -0.7121°° -0.6000 0.4835 Slash pine, block 82 Best No. of level ohs. r Large plot Small plot Large plot Small plot Small plot 33 60 42 15 150 Loblolly pine Best No. of level ohs. r 10 46 32 10 98 -0.2986 -0.3099n.s. -0.2741 -0.2752 -0.2489 -0.3198° Longleaf pine Best No. of level ohs. r Large plot Small plot Large plot P.A.I. in basal area D X Large VX plot X2 C X Large MX plot X2 -0.1573 Small -0.1495 plot -0.1690n.s. +0.06761 Large ±0.0708tn.s. plot 24 28 12 26 90 +0.0628t -0.3902 -0.4123° -0.3458 -0.6238 -0.6441°° -0.5577 I O X X X2 Large plot X VX X2 X All VX X2 P.A.I. in d.b.h.o.b. D X MX X2 C X -------- ---Large plot 156 -0.2149 -0.1898 -0.2572n.s. -0.3989 -0.4049n.s. -0.3737 -0.1734 -0.1570 -0.1924' Small plot Large plot Small plot -0.6649* -0.6503 -0.6405 -0.6405° -0.6380 -0.6402 > -0.5670 -0.5767n.s. -0.5505 -0.2338° -0.2336 -0.2238 -0.5720 -0.5837n. -0.5463 -- Large plot Large plot -0.6012 -0.5862 -0.6111°° -0.2615 -0.2802°° -0.2257 -0.3122 -0.3268n.s. -0.2784 -0.5878 Large plot Large 33 84 Small plot Small 33 60 VMx X VMx X X2 I o All plot X2-0.4480 Large 39 plot ----- -0.4925 ° -0.5471 -0.5392 0.555604 ---- plot Small plot Large 42 15 ±0.1423t Small ±0.1686fui.s. plot ±0.0879t Large ±0.1683t plot +0.l800-fn.s. +0.1489f --0.1592 Small plot -0.0894 10 46 Large plot Small 24 28 4 0.1739 32 10 0.2576n.s. -0.1510 -0.2162n.s. -0.5625°° -0.5391 -0.5592 plot Large plot Large 12 26 0.6261°° -0.5052 -0.6592 -0.6510M -0.6689° Mx 00 z VMX--X MX X2---Large 156 plot -0.5210 X2-0.5183 plot -0.5614 -0.5748 ° Large 150 plot -0.5152 0.5234 -0.1491 -0.1355 -0.1705 Large plot -0.3676 -0.3533 Small plot 98 -0.3975n.s. -0.2600 -0.2504 -0.2676** plot -0.5365 Large plot 90 -0.5251 0.5446** -0.3563 -0.3686°° -0.3242 0 at 0.05. ~''Significant at 0.01. n.s. Not significant. *Significant RADIUS LOTS, WITHOUT SAMPLE IBEE Crown class Curve form Slash pine, block 31 Best No. of level obs. r 33 84 39 -0.7452 -0.7527*0 Slash pine, bloci 32 Best No. of level obs. Loblolly pine r r of Best ohs. level No. Small plot Small plot Small plot Large plot Small plot Small plot 10 46 32 10 98 r r -0.6533 Longleaf pine r Best No. of r level ohs. 24 28 12 26 90 -0.3831 -0.4127 0 ,I-I P.A.I. in basal area D X Large plot X= C X Large VX plot 2 X I X Large plot X2 o X -------- M -0.1991 -0.2676n.s. -0.1678 -0.0988 -0.1279n.s. 0.0988 -0.2216 -0.1958 VX VX VX -_-X2 X VX . Large 156 plot Large plot Large plot X2-0.4474 0.6949 -0.4860 -0.4914** 0.4494 -0.5325 -0.5220 -0.543940 ---------------0.5740 -0.5853*° -0.5238 ------ Small plot Small plot Large plot Small plot Small plot Large plot Large plot Small plot Large 33 60 42 15 150 -0.6509 Large plot -0.6546-0.3326 -0.3857 -0.3673* -0.3331 _0.6629* -0.6186 0 .In 0 C m Small plot Large plot -0.6223 -0.6970** -0.5050 -0.6337 -0.6287 All -0.2648n.s. -0.4358 -0.4483n.s. -0.3988 -0.3572 -0.373100 -0.3281 -0.1255 -0.1174 -0.1377n.s. + -0.6188 -0.5595 -0.5696n.s. Large plot -0.6369 -0.6010 -0.5872 z z fn -0.5430 -0.4267 -0.3646 -0.4527** Small plot Large plot Small -0.6090** -0.4772 -0.5384** -0.3610 P.A.I. in d.b.h.o.b. D X VMX X2 X C X I X VMX X X '----- 33 84 39 -- -0.6329 -0.6674°° -0.5617 -0.4782 -0.4812"" 33 60 42 15 10 +0.0951t 0.0896t -0.5169 -0.6401 -0.64440 -0.6284 24 28 -0.2678 -0.2788n.s. -0.2387 -0.5112 -0.4148 Large plot X2 o All VMX---X VX ---156 -0.5344 -0.5244 -0.545700 ---- ±f0.1962t n.s. -0.1624 Small -0.0844 plot -0.2673n.s. -0.5106 0.52064 Large 46 -0.1896 plot-0.1658 32 10 -0.2323n.s. -05470** -0.4884 -0.5337 -0.3512 plot-0.5715* 12 26 Large plot Large -0.6431 -0.6314 -0.6581* -0.5309 Large plot Small plot 150 plot Small plot 98 -0.3365 -0.3822 n.s. plot Small plot 90 -0.5202 Large plot X°-0.5270 -0.5678 -0.5769*0 -0.2320 -0.1963 0.2694** -0.4029 -0.3257 -0.4483* -0.4874 -0.5186* -0.3943 -0.53820* at 0.05. *0Significant at 0.01. n.s. Not significant., j The sign of the correlation coefficient is reversed from what would be expected from theory. 0Significant APPENDIX B, TABLE 3. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING THE STENEKER-JARVIS COMPETITION INDEX I.J. Slash pine, block 31 class form Best No. of level obs. 33 r -0.6779 -0.7147** Slash pine, block 32 Best No. of level obs. r Small plot Small plot Small plot Loblolly pine Best No. of level ohs. r Small plot Small plot Small plot Longleaf pine Best No. of level obs. r Large 24 28 -0.31600.3778n.s. P.A.I. in basal area X Large D vx plot 2 C I O All 33 60 42 15 x x vx x2 X vx 2 X x Large plot Large plot 84 39 -0.5461 -0.2676 -0.3O1304 -0.2066 -0.4043 -01.429411 -0.3250 -0.1437 -0.2514n.s. -0.0847 -0.0107 -0.0601n.s. ±0.01094 -0.0957 10 46 -0.2020 -0.2616n.s. -0.0913. -0.3453 -0.37901* plot Small plot Large plot Small plot Large -0.230,1 -0.6457 -0.72.140* -0.5597 -0.5063n.s. -0.2747 32 -0.0425 vx Large plot x. X vx vx x2 X vx 2 X X vx x Small plot 156 -0.3388 -0.41220* -0.2572 -0.4643 Large 150 plot -0. 1398 n.s. Large +0.1425 plot ±0.0982 +10.1984n.s. ±0.0856n.s. Large 10 98 -0.6075 -0..6243** -0.5324 -0.4669 -0.3905 -0.5520n.s. ±01.0454 -0.0039 12 -0.4999 -0.4706 26 -0.3762n.s. -0.3760 -0.3685 ±0.1179 ±0.1022, ±0.1201 n.s. -0.1139 -0.1523 n.s. -0.0632 -0.5947 -0.6-31700 -0.5379 -0.4361 n.s. -0.4119 -0.4335 -0.4830 -0.4339 -0.0458 -01.1311 n.s. ±0.0110 tG) +0.0779 90 plot plot Large plot Small plot Large plot Large 12 26 90 + 0.0815 Small plot Large ±0. 1444 n.s. Large plot Small 10 P.A.I. in d.b.h.o.b. D X C I 0 All Large plot Large 33 84 -0.5139* -0.3693 33 60 ±0.1297 ±0.1302n.s. ±0.0469 ±0.2304 +01.1803 ±0.2181 ±0.1778 n. +±0.2844 s. 24 28 M F r- -0.2404 -0.2604* -0.1923 -0.3451 46 32 -0.1678 -0.1718,n.s. -0.1343 -0.5402 -01.524500 plot plot ± 0.2489 n.s. -0.0582 plot plot m Large plot 39 -01.35454 -0.2861 Small plot 42 15 +0.0,010 Small Small plot x m vx x2 Small plot Large 156 -0.3132 -0.3532°* VX X2 plot X Large 150 plot -0.2409 -0.1164 n.s. -0.3162 -0.3686n.s. -0.2362 ±0.2037 ± 0.2176* * ±0.1499 -0.4991 10 -0.5843 Large a 98 plot -0.5086 -0.6872* ±0.0868 plot Small plot ~0.5068** z CA aI 0I ±0.0389 -f±0.1808n.s. Significant at 0.05. Significant at 0.01. n.s. Not significant. *: Crown class Curve form Slash pine, block 31 Best No. of level ohs. r Large clot Small plot Large plot 33 84 Slash pine, block 32 Best No. of level ohs. r Small plot Small plot Small plot 33 601 42 -0.1072 -0.2183n.s. -0.0818 -0.0417 -0.0940n.s. -0.0055 -0.1065 -0.0579 -0.1308n.s. +0.0674 +0.0370 +.0752n.s. ±0.0115 -0.0981 n.s. +0.0485 +0.1142 +0.1379n.s. +0.0124 +0.1987 +0.2080n.s. ±0.1590 -0.0646 -0.0054 -0.1088n.s. -0.3548 Loblolly pine Best No. of level ohs. r Small plot Small plot Small plot Small plot Small plot Large plot Small plot Large plot Small Longleaf pine Best No. of level ohs. r Large plot Small 0 0 .-I ,-El P.A.I. in basal area D X VX X2 C X VX X2 I X VX X2 o X All X VX -0.6572 -0.7158*° -0.5272 -0.2072 10 46 -0.0913 -0.1887n.s. +0.0528 -0.3324 24 28 -0.1962 -0.2735n.s. -0.1481 -0.5486 0 on 39 __-_ -------- Large 15 -------VX -------plot X±0--__--Small plot 156 -0.3488 -0.2638 33 -0.2569° -0.1914 -0.3878 -0.4154*0 -0.3045 32 10 -0.3846°° plot -0.6597*0 -0.2485-0.4509 -0.5368 Large 12 -0.4757 -0.5897°° plot-0.4849n.s. -0.4418 -0.4288 -0.4024 0 C m z -0.3121 Large plot 26 -0.2946 -0.3092n.s. 'O X2 P.A.I. in d.b.h.o.b. D X Large VX plot X2 -0.4284*0 Small plot Small plot Large plot Small plot Small 150 98 -0.4961n.s. -0.0640 -0.1430n.s. +0.0216 +0.2424 +0.1850 Small plot 90 -0.2768 -0.0033 -0.0948n.s. sm +0.0385 Large plot Small plot Large plot Large 3H -0.4433 -0.4981°° -0.3586 33 60 42 15 10 46 32 10 24 28 12 26 C I VX VX X X +0.3213n.s. -0.1728 -0.1854n.s. -0.1305 -0.4789 -0.4915*0 -0.4276 -0.5436 -0.0143 -0.0606n.s. +0.0024 Large 84 plot X2-019,68 Large 39 plot X2-0.2666 -_ -0.2137 -0.2212° -0.3305 -0.3423 -0.5344 -0.5986°° -0.4632 -0.4126n.s. -0.4015 -0.3967 -0.4026 -0.4359° 00 o All X VX ---- ------plot X------0.2938 -0.4029n.s. plot -0.4743 -0.5996n.s. 98 +0.0339 -0.0160 plot -0.3510 VXX Large plot X2-0.2458 155 -0.3146 -0.355100 Large 150 plot +0.1557 +0.lSS8n.s. +0.1130 Large plot Small plot 90 -0.0624 -0.1456n.s. -0.0089 +0.1116n.s. at 0.05. at 0.01. n.s. Not significant. t The sign of the correlation coefficient is reversed from what would be expected from theory. *Significant *0Significant wO APPENDIX B, TABLE 5. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING THE STENEKER-JARVIS COMPETITION INDEX I Crown class Curve form Slash pine, block 31 Best No. of level obs. 33 84 39 ---- Slash pine, block 32 Best No. of level obs. Small plot Large plot Small plot Large plot 33 60 42 15 -0.0986 -02203n.s. -0.0450 +.12688 ±0.1872n.s. +0.0558 -0.0132 +0.0445 -0.0814n.s. +0.4510 +0.3408 +0.5915° +0.3120 +0.3838°° +0.1852 +0.1262n.s. ±0.1140 +0.0651 +0.2861 +0.3340*0 +0.2067 -0.0289 +0.0270 -0.0904n.s. Loblolly pine Best No. of level ohs. Large plot Small plot Small plot Large plot Large plot 10 46 32 10 98 r Longleaf pine Best No. of level ohs. 24 28 12 26 r -0.6822 -0.6914°° -0.6011 -0.0780 -0.1604n.s. -0.0622 -0.4281 -0.4568** -0.3523 --------0.1715 -0'.26280° -0.1333 r -0.3331 -O.3947n.s. 0.6312 -0.7134** -0.5414 0.5304 -0.5450n.s. -0.3283 -0.3114 o P.A.I. in basal area Large D X VX plot X2 C X Small VX plot I X VX X2 X VX Large plot -------- o All X2 X VX X2 X VX X2 --------------Large 150 plot Large +0.0556 -0.0053 plot ±0.1535n.s.-0.2441 Small -0.3006 -0.3380° plot -0.2379 Large -0.5672 -0.5804*0 plot -0.5074-0.4684 -0.4586 -0.3541 Large plot W Small plot 156 -0.5930n.s. ±0.3198 +0.2970 ±0.3521* ±0.2852 +0.2472 +0.3467n.s. Large plot 90 -0.3454n.s. ±0.3672 ±0.4131*0 +0.2845 0.1795 -0.2130n.s. -0.1251 P.A.I. in d.b.h.o.b. D C I Large plot 33 -0.5420 -0.5876°° -0.4513 Small plot Large plot Small plot Small 33 60 42 15 Large plot Small plot Small plot Large 10 46 32 10 Large plot Large plot Large plot Large 24 28 12 26 -j C X VX o All Large 84 plot X-0.1769 X Large 39 VX plot X2-0.3290 X __ -0.2072 -0.2333° -0.4030 -0.4282°° VX ---Large ----plot ----0.2218 -0.0598 -0.1457 -0.1532n.s. -0.1075 -0.5217°° -0.4999 -0.4922 -0.7087 -0.6281n -0.674944 -0.5486 -0.5318n.s. -0.5195 -0.5079 -0.4609Z mn M -0.1717n.s. plot Large -0.6214 98 X2------+0.0970 -0-.798844 plot Large 90 -0.48390 VX X2 X plot 156 0.262444 -0.1780 Large plot 150 +0.3669 +0.3387 +0.4368*0 +0.2208 plot +0.3072 +0.3724°° plot +0.2260 -]-0.2532* -0.4195 +0.1742 *Significant *0Significant at 0.05. at 0.01. . . ._ z n.s. Not significnt. I u I-/I I~rrr~ _I I,-/ ~r I . 111C . Crown class Curve form Slash pine, block 31 Best No. of level obs. r -0.6756 -0.7118°° -0.5783 84 -0.0861 -0.1528n.s. -0.0832 39 -0.4089 -0.4377"" -. 0 3278 ________ ____ ________ Small plot Large plot Large plot 156 -0.2239 33 Slash pine, block 32 Best No. of level ohs. r Small plot Large plot Small plot Large plot 33 60 42 15 Loblolly pine Best No. of level obs. r ±0.0615 -0.0241 +0.1791n.s. -0.3074 -0.3533° -0.2361 -0.5242 -0.5663** -0.4440 -0.3309 -0.5722n.s. Longleaf pine Best No. of level ohs. r Large plot Small plot Large plot Large plot 0 P.A.I. in basal area D X Large VX plot X2 C X Small VX plot X2 I X Large plot VX 0 All X VX 2 X --------------Large 150 plot Small plot Large plot Small plot Small plot -0.0696 Large 10 -0.1875n.s. plot -0.0579 +0.0474 Small 46 +0.0882n.s. plot +0.0157 Small 32 -0.0460 plot +0.0122 -0.1002n.s.-0.4346-0.4479 +0.4243 Large 10 +01.3163 plot +0.5419* 24 28 12 26 90 -0.2031 -0.2822n.s. -0.1411 -0.5216 -0.64411 -0.4188 0.5075 -05250n s -0.2708 -0.2710 -0.2749n.s. = c Z m X VX X2 -0.1756 -0.3066°° -01.5623°° +0.2259 +0.2807°° +0.1253 +0.1150 +0.1246n.s. +0.0255 +0.2339 +0.2733 n.s. +0.1740 Large plot Large plot Small plot Large plot Small plot 98 +0.2288 +0.1955 ±0.2809*0 +0.2973 +0.2447 +0.3690n.s. -0.1590 -0.1703n.s. 0.1167 Large plot Large plot Small plot Large plot Large plot +0.2445 +0.2854°° +0.1837 -0.0579 -0.1024n.s. -0.0348 0.5417 -0.6162** 0.4621 P.A.I. in d.b.h.o.b. D X VX X2 2 33 84 -0.5029 -0.4191 -0.1727 -0.1935n.s. -0.3783 -0.4026* 33 60 42 15 10 46 32 10 98 24 28 12 26 90 C I X VX X VX X VX -0.1622 o All Large 39 plot X2-0.3005 _____ X2 __ ----------0.2371 -0.2910** -0.1897 -0.0442 +0.0145 -0.0960n.s. -0.0757 -0.1963n.s. +0.0853 -0.4727 -0.4847*0 -0.4254 -0.6732 -0.5708 -0.772044 -0.5042n.s. -0.4904 -0.4854 -0.4020 -0.4375* -0.3522 VXX Small plot X2________ 156 Large 150 plot +0.2.979 +0.3632** +0.1622 Large plot +0.2614 +0.2223 +0.311414 Large plot +0.1393 +0.1570n.s. +0.1068 at 0.05. at 0.01. '~Significant n.s-. Not significant. t The sign of the correlation coefficient is reversed from what would be expected from theory. *Significant APPENDIX B, TABLE 7. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING BITTERLIGH'S METHOD, WITH SAMPLE TREE class Con Cre form Slash pine, block 81 Best No. of level ohs. r Best level Slash pine, block 32 No. of ohs. r Loblolly pine Best level No. of ohs. r Longleaf pine Best No. of level ohs. r P.A.L. in basal area D X BAF VMX 25 2 X 33 84 -0.6366 -01.6409"1 -0.6246. BAF 5 -0.4524 -0.4796* BAF =5 BAF =15 BAF =20 33 60 42 15 150 -0.1962 -0.1912 -0.2036 n.s,. BAF =40 BAFP -40 BAF 25 10 46 32 10 98 -0.5669n.s. -0.56.68. -0.566.9 BAF 10 BAF =40 BAF =5 24 28 12 26 90 -0.4031 -0.43810 -0.3549 C X VMX 2 X I O All X MX BAF =10 X2 ---- 39 -- -01.3837 -0.4895 -0.4724 -------- -0.1293 -0.1331n.s. -0.1163 -0.1797 -0.1260 -0.3606 -0.3749** -03215 -0.5509 -0.5514** -0.6104 -0.6183** -0.5749 -0.448.1 -0.4535n.s. -0.4356 X2 P.A.I. in d.b.h.o.b. D X VMX x X x VMX VMx -0.5113* -0.2627n.s. -0.5268 BAF =15 -0.6400 -0.66370" -0.5895 BAF =5 -0.5191 -0.5276n.s. -0.4988 BAF -5 -0.6516** -0.6446 -0.64.80' 2 ---BAF 156 5 BAF 15 -0.5268 -0.55,11** -0.4689 33 84 39 -- BAF =20 -0.2279 -0.2007 BAF =30 -0.3381 -0.3128 BAF -10 -0.3901 -0.4155** c- -0.2663** -0.36280" -0.3440 BAF -15 BAF =30 -0.6697 C I O X2 X BAF MX =15 X2 X BAF MX =10 -0.6020 -0.3987 -0.4168*0 -0.3567 -0.5313 -0.5202 ---- -01.699,711 BAF =20 BAF =5 BAF 33 60 42 15 +0.27871BAF +01.2645-t =40 + 0.2984t-n. s. 4 +0.2l 1ltn.s. BAF +0.2,129140 10 46 32 101 +10.21291-0.2099 -0.6237 -0.2418 -0.7035 -0.7034 -0.70,36* -0.3217 -0.33170 -0.2833 25 28 12 26 90 -0.2848 -0.29,38 n.s. C -0.2431 -0.6236 -0.6460 " -0.5555 -0.5431 n.s. -0.5400 -0.5263 m x .x X X2 -0.542200 =30 =15 BAF BAF =30 =5 -0.4415 -0.4105 -0.4371 BAF =40 x -0.2871 n.s. -0.4702 *0 -v m m -- -- BAF BAF X2 All 156 -0.5349 -- Mx *Significant **Significant =15 -0.4968 -0.5468 * BAF 150 =40 -0.6447** -0.5779 -0.2903 -0.2612 -0.332444 BAF =30 98 -0.4360 -0.4383 n.s. -0.3507 -0.3232 -0.3802 BAF =5 -0.6130* -0.6058 z BAF =10 -0.6121 -0.4345 -0.4495** -0.3976 * at 0.05. at 0.01. z n.s. Not significant. Curve Crown form class Slash pine, block 31 Best No. of level ohs. r 33 -0.7778 -0.7841"" Slash pine, bloc]k 32 Best No. of r level ohs. BAF =30 level BAF Loblolly pine Best No. of ohs. 10 r level Longleaf pine Best No. of ohs. r 0 P.A.I. in basal area BAF D X Sx X MX X MX X MX X 33 -5 X-0.7145 C I 0 All BAF 84 =5 X2-0.3810 39 BAF =10 X2 ____ __ X2____ BAF 156 -0.4533 -0.48161* -0.4895 -0.4705 0.5127** ____ BAF =15 BAF =20 BAF BAF 60 42 15 +h0.1581t -0.1293 +0.1782- +0.1940fn.s. =40 -0.5669n.s. -0.5668 -0.5669 BAF 10 24 28 12 26 90 -0.4109 -0.48984 -0.3498 0 0 C -I ____ 15 -0.1334n.s. -0.1139 -0.1797 -0.1116 -0.2754n.s. -0.6400 BAF =40 BAF =25 BAF =5 46 32 10 98 -0.3606 -0.6668** 0.5826 -0.3940** -0.2980 -0.5509* -0.5495 -0.5185 -0.5191 -0.5280n.s. BAF =40 BAF =40 BAF =10 -0.6104" -0.6100 -0.5367 -0.4347 -0.3770 -0.4497n.s. -0.6388 -0.648704 z z m Hn -0.4977 BAF -0.3381 BAF -0.6057 -0.3909 -0.5283 150 -0.2971 -0.2358 -0.34004* MX P.A.I. D C I 0 All in d.b.h.o.b. X MX =5 X2-0.4670 0.554144 -0.6697 -0.70674" -0.3987 -0.42661" =40 BAF =20 BAF =5 BAF -40 BAF 15 BAF =40 =30 BAF 40 10 46 32 10 98 -0.2948 -0:.3657** -0.7035 -0.7035 -0.7036* -0.3217 -0.3310" =10 BAF =10 BAF =30 BAF =40 BAF =5 BAF =5 24 28 12 26 90 -0.4319** -0.3391 -0.2610 -0.3250n.s. -0.2147 -0.6236 -0.638444 -0.5174 -0.5431 n.s. -0.5292 -0.5116 -0.6082*~ -0.6030 -0.5970 -0.4435 -0.46360* -0.3890 BAF 33 =15 X2-0.5868 BAF 84 X =15 MX X2-0.3483-+0.2062t- 33 60 42 15 150 +0.2787t +0.2598i- +0.3021tfn.s. A-0.2080tn.s. BAF +0.2072t =40 -0.2187 -0.2608 X MX X MX BAF 10 X2 ____ BAF 0.5313 -0.5190 0.5426* * __ ____ ____ X2-0.5716 156 -0.5350 39 -0.1000 -0.3052* -0.6237 -0.6474** -0.2903 BAF =30 BAF =5 BAF =30 -0.4415 -0.3965 -0.4730 0 -0.4371 -0.4359 -0.4382n.s. -0.3507 VMx X X2-0.4884 15 -0.5483 * -0.2158 0.3471** -0.3035 -0.3843*~ Significant at 0.05. Significant at 0.01. n.s. Not significant. fj The sign of the correlation coefficient is reversed from what would be expected from theory. APPENDIX B, TABLE 9. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING SPUR.i's METHOD, WITH SAMPLE TREE Con Cre formclass Slash pine, block 31 Best No. of r obs. level Slash pine, block 32 Best No. of r obs. level Loblolly pine Best No. of obs. level r Best level Longleaf pine No. of obs. 20 14 10 22 r -0.3639 -0.4210,n.s. -0.2,638 -0.7510 -0.7924** -0.6706 -01.7807 -0.7828*'* P.A.I. in basal area X 12 D trees VMX X2-0.686.3 33 80 36 -0.7387 -0.7391** -0.1739 -0.2346* 16 trees 4 trees 30 60 10 ±0.0754f +f0.0872tn.s. trees ±0.0537t -0.0553 -0.0528 4 trees 10 46 28 10 90 -0.5866 -0.5901 n.s. -0.5791 -0.3283 -0.33870 -0.2952 -0.5204 12 trees 16 trees 14 trees C I 0 All X M X vMx 16 trees x X2-0.0645 trees 12 -0.0573 n.s. 42 -0.2178 -0.1736 -0.5436** -0.5414 4 trees 14 trees -0.5420,0* X2 X M x Mx vx 2 X x -0.5400 --------------- 8 trees 15 149 -0.2850n.s. -0.5464 -0.56f3063 16 trees X2 0.5022 12 trees 151 -0.4874 -0.5231* 10 trees -0.3569 -0.3384 14 trees -0.4743 -0.4498 -0.4657ns. -0.4212 -0.3009 -0.2958 -0.30160* 14 trees 4 trees -0.7714 -01.47260 -0.4703 -0.4606 90 -0.5369 -0.560,3** -0.4640 X2-0.4051 14 trees -0.3800** 10 P.A.L. in d.b.h.o.b. D 29 C I 0 All X X M/X -0.7506 -0.7856*0 -0.6541 -0.3061 -0.334100 -0.2499 10 trees 33 +0.1850t 93 10 -0.3474 -0.3476,n.s . 12 trees 16 20 -0.2931 -0.3556n.s. C X VMX X2 ---X VMX 2 16 trees X2 16 trees 65 36 -139 16 trees 55 42 -0.5851 -0.5854** -0.5774 -------0.5153 4 trees 16 trees 8 14 150 X VMX X2 *Significant **Significant x 14 trees -0.5429* -0.4578 trees t-n.s. trees +0.18 + 0.1780t +0.1220t 4 ±0.1230fn.s. trees -+0.121714 -0.2504 trees -0.2084 -0.3,153* 16 -0.5575 trees -0Q559.9* -0.5357 14 -0.3446 trees -0.3219 -0.3462 46 -0.2636 14 -0.1865 trees 12 11 -0.2781 n.s. -0.2242 28 -06445 -0.6624** -.0.6059 m m -0.4206 -0.4302* -0.3988 -0.1939 -0.1988n.s. -0.18,63 -0.2682 -0.2604 -0.8220, -0.832:7* -0.79801 -0.4775 _0.4795* x -o z -1 trees 14 trees 4 trees 22 90 10 90 _0.3742*4 -0.2762** -0.4574 -0.5606 -0.5,839** -0.4753. at 0.05. at 0.01. n.s. Not significant. ------ z _____1_1 Con Cre form class Slash pine, block 31 Best No. of level obs. r 12 33 Slash pine, block 32 Best No. of r level ohs. 16 Loblolly pine Best No. of level ohs. r Longleaf pine Best No. of level ohs. r -0.3645 -0.4160n.s. -0.2682 -0.7506 -0.7930** -0.6715 -0.7505 -0.7427 -0.7606* -0.54754* 0 0I P.A.I. in basal area D X 1/ X X 2 trees 12 trees X2 16 trees X2 80 36 -0.7265 -~0.7336** 30 -0.6931 trees 16 trees 4 trees 55 +0.10088 +I0.1110-tn.s. trees +10.0825t 10 46 -0.6873 -0.6779 -0.7045* 12 trees 20 14 10 0 0 C 177 C I X VX X VX -0.2154 -0.2.672* -0.1214 -0.5621** -0.5591 -0.5600 +0,.0555t +0.0606txn.s. 4 -0.3169 -0.3264 -0.2871 16 trees 14 trees 14 trees 16 trees 8 28 +0.0466t 42 15 O All X 1VX X ---12 trees -151 --------0.5044 -0.4321 8 trees 8 -0.2450 -0. 1972 -0.32210 -0.5475 -0.5591* -0.5340 -0.4854 -0.5566 * trees 14 trees z z 10 98 -0.4752 -0.4887n.s. 22 90 -0.5096 150 -0.4515 -0.3194 -0.5443 -0.5321 -0.5225 m VX X2 -0.5344"-* trees 8 trees 16 trees 4 trees -0.3481 -0.3292 -0.3707** -0.3204** -0.3075 4 trees trees 12 trees -0.5390** -0.4740 -0.2885 -0.3464n.s. -0.1872 -0.6482 -0.6677** P.A.I. in d.b.h.o.b. D X VX C I X VX X VX 14 trees X2 16 trees 29 -0.7578 -0.7845* -0.6708 33 +0.2298t +0:.2272t +10.2349t'n.s. 8 trees 10 46 28 -0.4481 -0.4351 -0.4733-n.s. 20 14 65 36 -0.3493 -0.3726** 55 42 X2 16 trees X2 4 +]0.1368t-tO.1383tn.s. trees +10.1351t -0.2867 -0.2404 14 trees -0.2588 -0.2734n.s. -0.2214 -0.4446' 16 trees 12 -0.3017 -0.5996** -0.5992 -0.5935 0 All X VX ---14 -139 ------- 16 trees 4 14 150 v x X 2 x -0.5350i -0.5582** trees trees -0.4847 -0.36190 -0.58420 -0.5827 -0.5691 -0.3615 -0.3414 -0.3764 16 trees 8 trees 10 98 -0.4563* -0.4183 -0.2278 -0.2330n.s. 11 22 90 -0.6089 -0.7864 -0.7893* -0.7751 trees 14 trees 4 -0.2203 -0.5232 -0.5243* -0.5005 -. 553.0 -0.2954** -0.2935 trees -0.2860 -0.5667** -0.5014 U' * Significant at 0.05. Significant at 0.01. n.s. Not significant. f The sign of the correlation coefficient is reversed from what would be expected from theory. 00 APPENDIX B, TABLE 11. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING BROWN'S METHOD r r Longleaf pine Best No. of level _ohs. %0 Crown Curve Slash pine, block 31 Best No. of level ohs. 33 r r Slash pine, block 32 Best No. of level ohs. r ±0.2543 class form Loblolly pine Best No. of level ohs. 10 + 0.4108 P.A.L. in basal area D X ---- vx +0.5795 +0.6481*2 +0.4743 33 24 +0-.23-17 60 +0.2819n.s. +0,.2315-n.s. +0-.2290 ±0,.20:72 46 +0.3735 +0.4440n.s. +0!.32,79 +0.2,849 +0.362.9n.s. x C 84 +0.3297 +0.34302 o All vx x2 X Mx x2 vx 2 X vx x- X ---39 + 0.2838 +0.2116 + 0.2736,n. s. +0.3671 +0.3932*1 +0.2861 28 42 +01.0016, +0.0530 -0.0880 n.s. + 0.1655 +0.2134n.s. +0,.1030 32 +0.5279, +0.534012* +0.4902 12 26 +0.6346 +0.6430* +0.5801 +0.2892 +0.3329n.s. +0. 1629 +0.0828 ---156 15 10 +0.16,80 +0.1710n.s. +0.1586 +0.4.801 +0.5141* +0.3990 +0.4534 +0.4952*12 +0.3530 + 0.4675 + 0.4765~1 +0.4547 s. + 0.1958 n. +0.1949 150 +0!.3351 +0-3368* +0.3-196 98 +01.3474 +0.3610**2 90 +0.2905 10 +0.4492 ±0.4571*0 +0.3732 33 ---84 39 33 -0.180,01 -0.2016tn.s. -0. 1253- -0.0314t-0.0627-n.s. +0,.0104 24 +01.0835 +0.0405 +0.1370n.s. 28 C -I C D O X 60 42 Mx vx x2 0O.08441-0.08861- n.s. -0.01863f- 46 +0.1760 +0.1107 +0.2007n.s. +0.5124 +0.5159* +0,.1861 +0.4818 12 x ± 0.0796 +0.1411 -0.0251t- n. s. 15 -0.0,9711-0.04531-0.1816tn.s. 32 +0.3909 +0.1449 +0,.1698 +0.2072n.s. +0.0,592 +0.40274 +0.3524 10 m All o X vx ---156 +01.2313 +0.1562. +0.1773 n.s. 26 +0.4401 +0.4676* .5 xinfcnta +0.2789n.s. + 0.16,68 z -I m xignficnt -t-001 +0.3330 +035691 150 +0.1125 +0.01907 98 +0.1296n.s. +0,.265,6 90 +0!.2781 n.,*Significant .05 I1,-- +0.2805 4 + 0.2162 +0.3739 +0.3569 +03902"1 +0.2559 z £12 - -- L1--f- 1_. .r.. .. t .1 _...... S1ach Crown Curve )d1 Best form class ______________level P.A.I. in basal area D X j~~7 No. of nine FJni1 Uluuls, R1 V'1 obs. r r +0.6210 +0.6765** +0.5178 ±0.3559 +0.3810** +0.2889 +0.1846 +0.2123n.s. +0.1406 Slash pine, block 32 Best No. of r level ohs. 33 60 Loblolly pine Best No. of r level obs. 10 46 Longleaf pine Best No. of level obs. 24 r 0) 4 ----33 ----- C I 0 All X2 x 84 + 0.2365 n.s. +0-.2342 +01.2344 x2 X +0!.3837 +0.4079 +0.3137 +0.4821 +01.4616 +0.4870n.s. +0.35,91 +01.58.28 +0.3195 +0.405,5-* 28 0 C +0.4286 +0.4372** +0.3752 32 + 0.5890'* +0.5430 12 --------- 39 -- 42 +0.0,674 X x X +0.1250n.s. -0.0400t +0-.3441 10 +0.5675 +0,.0383 +0.2:044 +0.5760** +0.510,8 26 90 + 0.2441 n.s. +0.1197 + 0.5227'* +0.5201 +0.4699 -f m z Il 15 x MX ---156 ---X2+0.4798** + 0.4135n.s. +0.1701 +0.5107 +0.5655'** +0.3693 +0.4773 +0.4772 +0.2021 n.s. +0.2,018 ---------150 +0.5336 + 0.57011 + 0.4412 33 60 42 *" 98 -0.0067+ 0.0709n.s. +0.5048 +0.524500 + 0.4417 +0.0592 +0.0443 +0.0705n.s. +0.6.474 +0.74550* +0.43,61 ---24 28 12 P.A.I. in d.b.h.o.b. X D VX 33 84 39 ----0.2238t -0. 2 3 0 2 ftn.s. +0.0538 +O.0810n.s. +0.0175 C I X VMX X ------- -01965t 10 46 32 +0.1284 +0.0860 +0.1896n.s. ------- X2+0.1882 X2+0.0090 ------ VMX X VMX +0.0852n.s. +0.0515 -0.0440t +0.0123 o ---------- ---- 15 X20.0375f 98 ---150 +0.2932 ---156 +0.3640 X ---All +0.3619** +0.3929** VMX +0.1968 X2+0.2864 *Significant at 0.05. **Significant at 0.01. n.s. Not significant. f The sign of the correlation coefficient is reversed from what would be expected from theory. -0.1421ftn.s. ---+0.0819 +0.1283 n.s. 10 ---+0.2105 +0.2221 n.s. +0.1679 ---±0.4259 +0.4419 +0.3664 ----0.3250 -0.3914tfn.s. -0.2438 ---+0.4023 +0.4346** +0.3270 +0.4236 +0.4276* +0.3989 +0.0165 +0.3044 +0.0900 +0.1253n.s. +0.3076,n.s. +0.2593 +0.4783 +0.5878** +0.2855 26 90 APPENDIX B, TABLE 13. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING STAEBLER'S COMPETITION INDEX is Crown class Curve form Slash pine, block 81 Best No. of level obs. r 33 84 39 -0.7390, -0.7665* -0.6517 -0.2793 -0.2874** -0.2592 -0.5262,** -0.5226 -0.5213 Slash pine, block 32 Best No. of level obs. r K=1.0 33 Loblolly pine Best No. of level ohs. r Longleaf pine Best No. of level ohs. r P.A.I. in basal area D X K=2.8 x C I 2 vx x2 x K=2.8 K=1.3 K=1.0 K=1.0 K=2.8 60 o All P.A.I. in vx x2 x vx 2 42 15 x X vx 2 X K=2.8 156 -0.3045 -0.3192* -0.2697 -0.7285 K=1.6 150 ±0.18471' ±0.19791'n.s. ±0.156,7t ±0.3-112t' +0.3552t * ±0.2288,t -0.0642 +0.015,31 -0.1689n.s. ±0.27561' ± 0.2326,t ±0.35181'u.s. +0.486.91' +0.5241t'* +0.388,61' K=1.0 K=1.0 K=1.3 K=1.6 K=1.6 10 +0.20521' 46 32 10 98 ± 0.1856 ±0.24201n.s. -0.1595 K=1.0 -0.1547 -0.1737 n.s. -0.5365 K=1.0 -0.5473** K=1.3 24 28 -0.3872 -0.3022 -0.4427* -0.6179 -0.627144 -0.5588 12 -0.6109 -0.5986 -0.5514 -0.5116 -0.5772 -0.5503 K=1.6 26 -0.6158,* -0.576-1** aI -0.6202 n.s. ±0.50251'f ±0.49841' ±0.4829t' K-1.9 90 .- 0.5418 ±0.34831' ±0.38531t'0 ± 0.26391' W d.b.h.o.b. vx x2 vx 2 X X K=1.0 33 K=2.2 K=1.3 84 39 -0.6383 -0.3257 D C I 0 All ~0.7633*A K=1.0 33 K= 2.2 60 X X x -0.3549** vx x2 vx 2 -0.2781 0.5775 -0.5801*" -0.5604 K=1.0 K=1.0 42 15 150 x vx x K=2.8 156 -0.3422 -0.3694*4 -0.2894 K-1.9 K=2.8 ±0.14811' +±0.1492-tn.s. ±0.14-561' ± 0.29961' ±01.33241'* ±0.23851' -0.1352 K=1.3 -0.0600 -0.2297 n.s. -0.4132 K=1.6 -0.4309,n.s. -0.3524 ±0.43341' K=1.6 +0.4647t'** +0.3,516t I 10 46 K=1.0 32 10 98 K=1.6 +0.45131' ± 0.440,81' +0.4562,-'n.s. -0.13-24 K=1.0 -0.1382 n.s. -0.1264 -0.4853 K=1.0 -0.4708 -0.7129 24 28 12 26 -0.4903** -0.6899 K=2.2 -0.74791* +0-4-782f"0 ±0.46'821' ± 0.466,81' K=2.2 90 -0.3216 -0.3617n.s. -0.2357 -0.6734 -0.7076*0 -0.5844 -0.6638 -0.6447 -0.6778* -0.6282* -0.6268 -0.5802 ±0.15801' +0.1757f'00 C -I C -o z m -I ±0. 12181' at 0.05. **Significant at 0.01. n.s. Not significant. *Significant z Crown class C urve form Slash pine, hlock 31 Best No. of level obs. r 33 84 39 -0.6905 -0.7327** -0.5692 -0.3752 -0.2585 -0.4443 -0.4659 -0.3714 Slash pine, hiock 32 Best No. of r level ohs. K=1.9 33 -0.1948 -0.2362 n.s. -0.1214 -0.1115 -0. 1578 n.s. -0.0456, Lohlolly pine Best No. of r level ohs. K=1.0 10 K=1.0 46 K=1.3 32 -0.1209 -0.1806 n.s. -0.0154 -0.3398 -0.2956 -0.5730 -0.5991*' -0.5046 -0.4439 -0.4596n.s. -0.4156 -0.1280 -0.170$8n.s. -0.0389 Longleaf pine Best No. of r level ohs. K=1.3 24 -0.3719 -0.4313* -0.2807 0 0 on P.A.I. in basal area D X K=1.9 vx x2 X C I K=2.5 K=1.3 O All x2 X vx x vx x2 X vx 2 X vx X -0.4229 K=2.8 60 ~0.35584 K=1.0 K=1.0 K= 2.2 K=2.8 28 -0.6452 0 C K=1.0 * 42 -0.15-68 -0.0933 -0.1981 12 26 90 n.s. K=1.6 10 K=2.5 98 K=1.0 15 K=2.5 156 -0.4437 -0.49-95* -0.3257 -0.5063 -0.5842* -0.3954 -0.2656 -0.2993** -0.2044 -0.3885 -0.39,684 -0.3334 K=2.8 150 -0.3551 -0.3590 -0.1466 -0.1949* -- 0.3877n.s. -0.0654 -0.6802** -0.5547 -0.5867 -0.5565 -0.6067k -0.5808 -0.5881* -0.5376 -0.3391 -0.3676** -0.2840 -0.1769 -0.2179n.s. -0.1194 -0.5769 -0.6227 -0.4928 -0.5533 -0.5048 -0.6,035* -0.5983 -0.615111- z P.A.I. in d.b.h.o.b. D X C I 0 K=1.0 K=1.3 K=1.3 33 84 39 K=1.0 33 + ±0.1877t -0.2087tn.s. +i0.1178t K=2.8 10 +10.3058t +0.3592-tn.s. -0.1810 -0.1917n.s. -0.1570 -0.4954 -0.5034** +0.33721 K=1.3 K=1.0 K=1.0 24 28 12 vx 2 X X vx X K=1.0 60 K=1.0 K=1.3 42 15 150 +0.1945f K=1.0 46 -1-0.2154tn.s. +10.1580t -0.1239 K=1.3 32 -0.0563 -0.1760n.s. K=1.9 10 -0.5438 vx All vx X K=1.0 156 -0.3845 -0.4239114 K=1.9 +]0.0428t +0.0367- -0.4736 ~0.5587* K=1.0 98 -0.4585 K=2.2 26 -0.4001 -0.3959 -0.4063 n.s. -0.0987 K=2.8 90 -0.3144 + -0.0521 n.s. -0.1131n.s. -0.0772 -0.5440 -0.3567 -01-376200 -0.3109 *Significant at 0.05. Significant at 0.01. n.s. Not significant. t The sign of the correlation coefficient is reversed from what would be expected from theory. APPENDIX B, TABLE 15. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING STAEBLER'S COMPETITION INDEX IS2/F Con Cre form class P.A.I. in basal area X D vx x2 C I o All Slash pine, block 31 Best No. of level ohs. r Slash pine, block 32 Best No. of level ohs. r Loblolly pine Best No. of level ohs. r Longleaf pine Best No. of level ohs. r K=1.6 K=1.0 24 28 12 O 0 K= 2.5 33 -0.7263 X vx K=2.8 K=1.6 84 39 xv X vx x2 x vx x2 -O.7565** -0.6341 -0.3206 -O.3475,* -0.2613 -0.4987 -0.5.123* -0.4503 K=2.8 K=1.0 K=1.0 K=1.0 33 -0.1228 -0.1474.n. s. -0.0731 60 K=1.0 K=1.0 10 -0.0505 -0.1099 n.s. ±0.0524t 46 +0.0498t -0.2964 -0.30854 42 15 -l0.lOS3tn.s. +0.0064-t-0.2486 -0.1700 K=1.6 -0.0795 32 10 98 -0.5472 - 0.2597 n.s. -0.5035 K=2.5 K= 2.2 -0.5629* 0 K=1.0 -0.3656 -0.4390 -0.2519 -0.6657 -0.7119** -0.5478 -0.66010 vx 2 X x K 156-0.3988 2. -0.433804 -0.3264 K=1.0 33 K= 2.5 84 K=1.9 150 K=1.0 33 -0.3006 -0.2647 -0.3223 n.s. + 0.1255- +0.1598t-n.s. +0.0777t ±0.1613t + 0.1728-tn. s. K=2.2 26 -0.4944 -0.4649 -0.5347 n.s. K=1.0 90 ±0.1406t +0.1203t±0.1895-tn.s. -0.6,624* -0.60561 -0.5692** -0.5603 -0.5270 -0.1307 -0. 1321 n.s. - 0.015,93 r- P.A.I. in d.b.h.o.b. D X vx x2 m -0.5777 -0.6796* -0.4532 K=2.8 10 +0.3136 C x -0.28-84 vx x2 vx 0 All K=1.6 39 -0.3109*o -0.2425 -0.4815 -0.4931** -0.4338 K-1.0 +0.1276t 60 +01.19501- +0,.2904 K=1.6 24 -0.2231 -0.2797 +0.3466n.s. +0.2335-n.s. K-1.0 K=1.6 K=2.5 K= 2.2 46 -0.1825 -0.19,75n.s. -0.1387 K=1.0 28 K=1.0, 12 K=2.5 26 K=1.0 90 +0.1495t K=1.0 42 K=1.0 15 x vx x2 -0.1725 -0.0872 -0.2612n.s. -0.5946* -0.5617 -0.5639 32 10 98 -0.4667 -0.4700* -0.4463 -0.5582 -0.5301 -0. 1314 -0.613,50 -0.6998 -0.5193. -0.698,7* -0.6757 -0.6717 n.s. x m vx 2 X x K=1.6 156 at 0.05. at 0.01. I . -0.3774 -0.4131* -0.3145 K= 2.2 150 +0.2153t -0.5988n.s. + 0.1797-- -0.6154. -0.6369o* -0.5440 -0.2276, -0.2547'* z +0.2431t'* +0.1695t- +0.15761 0 +0.2273t * -0. 1189 *Significant SSignificant n.s,. Not significant. m II , i r Crown class Curve form Slash pine, block 31 r -0.7492 -0.7728** -0.6688 -0.4050 Slash pine, block 32 Loblolly pine Longleaf pine level Best No. of ohs. 33 84 39 level Best No. of ohs. 33 60 42 15 r -0.1512 -0.1602n.s. level Best No. of ohs. 10 46 32 10 r -0.1834 -0.2057 -0. level Best No. of ohs. r -0.3876 -0.44854 -0.2.804 0.6616'* -0.6607 -0.6051 -0.6514* -0.6417 0 P.A.I. in basal area X D K=1.9 vx 2 X X C K=2.8 vx x 2.r I X K=1.3 vx o x x K=1.9 K=2.8 K=1.0 K=1.6 K=1.0 K=1.3 K=1.9 -0.4379"0 -0.3243 -0.5393 -0.5413** -0.1275 -0.1066 -0.1233 n.s. -0.5155 -0.0844 -0.1879 -0.1050~ -0.4743 13,69 -0.3136 -0.31670 -0.2973 -0.5275 -0.545,6* s. n. K=1.6 24 K=1.0 28 K=1.0 K=2.2 0 'I 0 C zI K-1.3 -0.2938,n.s. -0.4586 -0.4794 n.s. * -0.4837 -0.4960 -0.5248n.s. 12 26 -0.6365 -~0.6222** -0.6-089 z All vx P.A.I. in d.b.h.o.b. D X K=1.0 ,x C I 0 All K=2.5 156 -0.4982 -0.5380* -0.4128 K=2.8 150 -0.1165 -0.1512n.s. K=2.8 98 -0.4443 -0.1441 -0.1643 -0.6055 K=2.8 90 -0.0570 K=1.0 33 60 -0.0984 n.s. -0.4172 -0.4406"0 -0.3664 -0.2370 -0.2882 n.s. 33 84 39 -0.6475 -0.7109** +0.1914t +10.19961tn. x vx X vx x vx vx K=1.9 K=1.3 -0.5332 -0.3270 -0.349700 -0.2800 -0.5373 -0.5389** -0..5,118 K=1.0 K=1.0 K=1.6 42 + 0.1740 K=1.0 ±0.1070+0.1536f-n.s. +--.0481t K=1.3 -0.1933 -0. 1144 -0.2:985n.s. S. K=2.8 10 46 32 10 98 K=1.6 +-0.3411t -+-0.3175t + 0.3691't~s -0.2085 K=1.0 -0.2188n.s. -0. 18916 -0.4308 K=1.0 -0.4362* 24 28 12 -0.1495 -0.6271 -0.6505** -0.5576 -0.6581 -0.6781 -0.67900 an -0.4124 -0.3302 15 -0.6108 x K =1.3 156 -0.4898** -0.4106 -0.4649 -0.6017 K=1.0 150 ~0.6114* K=2.2 K-2.8 K=2.5 K=2.8 26 90 -0.3342 n.s. -0.3239 -0.07461 -0.0871 n.s. -0.0584 n.s. -0.0317 -0.0502 -0.0442 -0.6223 -- 0.62690* -0.5864 -0.4515 -0.4664** -0.4118 0 n.s. Not significant. 14Significant Significant at 0.05. at 0.01. t The sign of the correlation coefficient is reversed from what would he expected from theory. APPENDIX B, TABLE 17. HIGHEST COERELATION COEFFICIENTS OBTAINED, USING STAEBLEE'S COMPETITION INDEX I 5 4 /F Con Cre form class Slash pine, block 31 Best No. of r level ohs. -0.7442 Slash pine, block 32 Best No. of r level obs. Loblolly pine Best No. of r level ohs. K=1.3 10 Longleaf pine level Best No. of obs. r -0.3585 -0.4400 -0.2330 -0.0794 -0.6836 -0.6001 -0.6-676* -0.6648 -0.6381 -0.59000* -0.5737 -0.5581 - 0.1853 n.s. -0.16,93. -0. 1111 -0.2706 -0.3337n.s. -0.1591 -0.6827 -0.7142** -0.5918 -0.728600 -0.7198 -0.7073 -0.6343 -0.6426** -0.5709 -0.2978 _0.3052** -0.1846 r P.A.L. in basal area K=2.8 33 X D ,vx vx vx vx x vx x2 vx x vx vx X X x X X K=2.8 K=2.2 84 39 -0.6645 -0.2440 -0.7665* ~0.2587* K==1.6 K=1.0 33 +0.10161' +0.1250'n.s. +0o.0562-' +0.0667t' + 0.0518-' + 0.0971-' n. s. -0.2205 -0.2298n.s. -0.1790 -0.4022 -0.4131' -0.3815 -0.5549 -0.5508 -0.5619n.s. +0.33281' +0.32891' +0.3377'** K=1.6 24 K=1.0 28 K=1.0 12 K=2.5 26 K=1.0 90 60 +0.03261' K=1.0 46 32 10 I O -0.2230 -0.5624 -0.5508 -0.5733* K=1.0 K=1.0 42 15 +0. 12381'n.s. -0.0673 K=1.6 -0.2010 -0.0936 -0.3257* D Cll K=2.8 156 -0.3675 -0.3861** -0.3266 -0.7316 -0.7743* -0.6290 -0.3245 -0.3490** -0.2812 -0.6243 -0.6181 -0.62674 K=2.5 150 -0.3653 -0.3093 -0.3797n.s. +0.1116' +0.2015'* +0.0176-' K=2.5 K=2.2 98 x K=1.9 K= 2.8 33 84 39 K=1.0 33 +0.08541' +0.09431' 0.1131- n.s. +f +0.0385t' +0.15751'n.s. K=2.8 10 +0.30241' +0.29441' K=1.6 24 +0.3187t'n.s. K- 1.0 46 K=2.8 K=2.8 K=2.2 32 10 98 -0.1922 -0.2.081 n.s. -0.1373 -0.3236 -0.3179 -0.3289n.s. -0.5680 -0.5539 -0.5925n.s. +0.3259' K=1.0 K 28 1.0i 12 26 90 C rI C 7m -v m m K=1.0 K=1.0 K=1.0 60 0 All K=1.9 42 15 K=2.8 156 at 0.05. -0.4335 -0.4620 * -0.3754 K=2.8 150 +0-0180t' -0.2423 -0.1423. -0.3619' -0.6107* -0.5583 -0.5874 +0.15441' +0.222,01'00 +0.017291' K=2.5 K=1.0 z +0.33371' + 0.3446'*4 0 *Significant SSignificant at 0.01. n.s. Not significant. r I , , , .. i r _ . _ _ Con Cre form class Slash pine, block 31 Best No. of os. rlevel b. lee 33 84 39 -0.7542 -0.7774*'* Slash pine, block 32 Best No. of level obs. r K=2.2 K=2.8 K=1.0 K=1.3 33 60 42 15 -0.1404 -0.1574 n.s. -0. 1003 -0.0913 -0. 1113 n.s. -0.0566 -0.1499 -0.0674 -0.2561 n.s. -0.4627 -0.4354 -0.4985n.s. Loblolly pine r Best No. of level ohs. r Longleaf pine r BevelNoh. o K=1.3 24 -0.3764 -0.2850 -0.6388 0 P.A.I. in basal area X D K=2.2 K=2.8 K=1.0 K=1.3 K=1.9 10 vx c I ±0.0391t -0.0121 Mx x2 X x K=2.8 K=1.3 -066-97 -0.4153 -0.4509,11 -0.3340 -0.5199 -0.522111 +0.11311 46 32 10 98 n.s. 0 0 C -I O All Mx Mx x2 Mx X2 x -0.4969 x K=2.8 156 -0.4850 0.5262*~ -0.3977 K=2.8 150 -0.1181 - 0.1482 n.s. -0.0541 K=-1.6 K=1.0 28 -0.3035 -0.3030 -0.2978 K=1.0 12 -0.5780 -0.5981*' -. 5261 K=2.2 26 -0.5870 -0.5998 n.s. -0.5628 K=2.8 90 ±0-.0545t +0.0275t -0.657644 -0.5695 -0.6008 -0.5774. -0.61210 -0.6228~ -0.6,128, 0.6100 -0.3143 Z z +0.ll4Ofxn.s. K=2.8 s. 10 0.36'-0.2583 P.A.I. in d.b.h.o.b. D X K=1.0 K=1.9 K=1.3 33 C Mx x2 M x vx x x x -0.713700 -0.5418 -0.3599 -0.3887*4 -0.6540 K=2.8 33 +0.1289t +±0.1420-tn. ±0.3-783t +0.1028t K=1.0 60 K=1.0 K=1.6 42 15 150 +0.3535t -0.18-22 K=1.6 24 K=1.0 28 K=1.0 K=2.2 K=2.8 12 26 90 +0.4013-tn.s. 84 39 o -0.3018 -0.5055 0.5067*~ -0.4832 K=1.0 ±0.2253f ±0.2497tn.s. ± 0.1880K=1.3 -0.1635 -0.0835 -0.2681 n.s. 46 32 10 98 -0.1896 -0.1949n.s. -0.4904 -0.49801~ -0.2362 0.2788n.s. -0. 1576 -0.6221 -0.6625,44 r -0.53,84 -0.4628 -0.4523 -0.4459 -0.5909 -0.5833 -0.5957 K=1.9 All x Mx K=1.3 156 -0.4822 -0.3838 -0.4488 -0.4654n.s. K=1.6 +0.0905t +0.0634t -+0.1471tn.s. K=:1.9 +0.0896t +0.0,912t +±0.09251-n.s. -0.6097 -0.5738 -0.6388* --0.5856"~ -0.5782 -0.5734 -0.3625 -0.3811~ -0.3105 O *Significant at 0.05. W Significant at 0.01. n.s. Not significant. f The sign of the correlation coefficient is reversed from what would be expected from theory. APPENDIX B, TABLE 19. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING NEWNHAM'S COMPETITION INDEX IN class Curve Crown form Slash pine, block 31 Best No. of level ohs. r 33 84 39 -0.7909 -0.8105* -0.7216 -0.5912 -0.6028** -0.5444 -0.5285 -0.5135 -0.5476 Slash pine, block 32 Best No. of r r level ohs. K=1.6 33 60 Loblolly pin( e Best No. of r level ohs. K=1.3 K=1.6 10 46i 32 Longleaf pine Best No. of level ohs. r K=1.3 24 28 0 P.A.L. in basal area K=1.6 X D vx 2 x x x x C I o All x vx 2 X vx 2 x vx 2 vx K=2.2 K=1.6 K=2.8 K=1.0 K=1.6 -0.2259 -0.2157 -0.2450n.s. -0.2473 42 15 * x K=1.9 156 x2 K=1.0 K=1.6 K=1.3 33 84 39 -0.7130 -0.7337** -0.6432 -0.6792 -0.7216 * -0.5966 -0.4447 -0.4477** -0.4303 -0.5314 -0.5187 -0.5472* K=2.8 150 -0.3121* -0.1546 -0.2333 -0.1595 -0.3364 -0.4795 -0.5302* -0.3821 -0.4765 -0.5420** -0.3520 +0.1988t -0.4410 -0.4337 -0.4556n.s. -0.3815 -0.3713 -0.394600 K-1.0 K=1.9 K=2.8 K= 2.8 -0.3641 -0.4262* -0.2882 -0.56,9014i K=1.0 K-1.0 K=2.8 -0.4946 -0.518100 -0.4419 10 12 26 90 +0.0655t 98 -0.0249 +0.2099fn.s. -0.4517 -0.494500 -0.3462 -0.5539 -0.5527 -0.6770 -0.6670 -0.69174 -0.4494 -0.4789' -0.3855 -0.7284 -0.5502 K=1.3 K=1.0 K=1.9 K=1.0 24 28 12 26 -0.802714 W P.A.I. in d.b.h.o.b. X D K=2.8 33 K=2.8 60 K=1.0 42 K=1.3 15 I 0 Ml vx x2 X ,vx x2 X vx x vx x2 +0.2031t K-2.8 n. s. 10 +0.3142t +t-0.2911t -0.2851 -0.2831 -0.29230 -0.3905 K=1.3 156 -0.6134 -0.62.05** -0.5873 K=2.8 150 + -0.1855 K=1.0 46 -0.0597 -0.01819n.s. -0.0219 K-1.0 32 -0.2301 -0.1576 -0.3364* K=1.0 10 -0.1308 -0.2173 n.s. -0.0175 K=1.0 98 -0.3813 -0.4,11444 -0.2978 +0.34281'n.s. -0.2289 -0.2782n.s. -0.1676 -0.5200 -0.4840 -0.6398 -0.6251 0 -O±1ei33. -0.3556 -0.4331* -0.2415 -0.6385 -0.6830** -0.4987 C C -0.5252** m -0.396-9* -0.3705 ±0.4622-t +0.3819t' m z +0.5775t'n.s. K=2.8 90 -0.4462 -0.3894 -I -0.45500*4 at 0.05. Significant at 0.01. n.s. Not sierificant. *Significant z Slash nine. bloci k31 Curve&-v Best No. of form r level obs. P.A.I. in basal area D X K=1.6 33 -0.7724 -0.78860 0 vx 2 x -0.6963 C X K= 2.2 84 -0.48013 Crown class Slash pine, block 32 Best No. of level obs. r K=1.9 K=2.8 K=1.0 33 60 42 15 Loblolly pine Best No. of level obs. r Longleaf pine Best No. of level obs. K=1.3 K=1.0 K=1.9 K=2.8 K=2.8 24 28 12 26 90 -0.3935 -0.4466* -0.3146 0.5916 * -0.59018 -0.5592 -0.6715* -0.6713 -0.6595 -0.6194-" -0.6162 -0.6020 -0.5971 -0.5297 24 28 12 26 90 0 -I o All vx x2 vx x vx vx vx X -0.5125"'0 K=1.0 39 -0.3980 -0.5420** -0.5393 -0.5332 -0.1791 -0.1863 n.s. -0. 1579 -0.1895 -0.2299n.s. -0.1216 -0.14501 -0.0675 -0.2573n.s. K=1.6 10 K=1.0 K=1.0 K=1.6 K=2.8 46 32 10 98 -0. 1792 n.s. -0.0982 -0.1514 -0.3197 2 0 on -0.3280 0.3138 C 0 m K=1.3 K=2.2 156 -0.5349 -0.3337 -0.5477 -0.5527* -0.5738 -0.60304* -0.5047 -0.5224 -0.5469n.s. -0.4767 z 17 Hf x -0.5701 -0.6094* -0.4803 -0.6676 -0.5756 -0.3910 -0.4217** -0.3282 -0.70,970* K=2.8 150 K=1.0 -0.3660** -0.2588 -0.2913 -0.2665 -0.3026** -0.625900 P.A.I. in d.b.h.o.b. D X C I K=1.0 K=1.3 K=1.0 33 84 39 33. +0.1765t +0.1854t-n.s. K-2.8 10 +0.3983 vx 2 K=1.0 60 K=1.0 42 K=1.6 15 o All X X vx x2 x vx X +0.1844t -0.1537 -0.0767 -+0.16141 +0.21121 K=1.0 46 ±0.2301tn.s. K=1.0 32 10 98 K=1.3 +01.8699 +0.4189t-n.s. -0.2074 K=1.0 -0.2076 -0.5372'** -0.5322 -0.5315 -0.2142 -0.4864 n.s. K=1.6 K=2.2 K=2.8 -0.5010'44 v2 X x K =1.3 156 -0.4394 -0.5030 -0.5305** K=1.0 150 -0.2675n.s. -0.5790* K=2.2 -0.5741 -0.5790 -0.1295 K=2.8 -0.0804 0.19444-0.2333* -0.4450 -0.2935 -0.2920 -0.3002n.s. -0.2311 -0.2269 -0.2616 -0.3053n.s. -0.1935 -0.5726 -0.5935 -0.5186 -0.6543, -0.6405 -0.66590 -0.5674* -0.5589 -0.5577 -0.5814 -0.58761* -0.5505 at 0.05. SSignificant at 0.01. n.s. Not significant. *Significant VI O j- The sign of the correlation coefficient is reversed from what would be expected from theory. APPENDIX B, TABLE form 21. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING THE FRITTS-GERRARD COMPETITION INDEX Longleaf pine T FG Con Cre class Slash pine, block 31 Best No. of r level obs. 33 84 39 -0.7849 -0.8041* -0.7041 -0.4870 Slash pine, block 32 Best No. of r level obs. K=2.2 K=2.8 33 60 -0.1785 -0.1815n.s. -0.1674 -0.1481 -0.2066 -0.1122 -0.3298* Loblolly pine Best No. of r level ohs. K=1.0 K=1.3 10 46 Best No. of level ohs. 24 r r -0.3633 -0.4253* -0.2634 -01.5833 -0.6290* -0.6178, 0 0O P.A.I. in basal area K=2.2 X D vx 2 X x -0.2749 K=1.6 .3045n.s. -0.2125 c I K=2.8 K=1.6 vx vx x2 x -0.4098 -0.5176* -0. 1711 n.s. -0.1061 x -0.5413 -0.5332 -0.5449* K=1.0 42 K=1.6 32 -O.3375* -0.3348 -0.3370 -0.5594 -0.5169 -0.5265 K=1.0 28 K=1.0 12 K=2.5 K=2.8 26 90 -0.6563 -0.6694 " ~0.5767** a o All P.A.I. in vx K-1.3 K=2.5 156 -0.5862 -0.620544 -0.5046 -0.6540 -0.7241** -0.5380 -0.4202** -0.3482 -0.5309 -0.5226 - 0.5350* 15 -0.52,83 -0.5439 K-1.9 K=2.8 -0.6058 -0.6192 10 x vx d.b.h.o.b. vx 2 V X ~0.5439* K=1.0 150 -0.2651 -0.2064 -0.323644 + 0.19031- 98 -0.5447n.s. -0.4949 -0.2757 -0.2796,* -0'.6340** -0.6297 -0.5383 -0.5,6421* a -0.2658, -0.4791 49 D C K=1.0 33 K=1.0 33 vx x, I 0 All X X + 0.1970-tn.s. + 0.1791t K= 2.8 10 +0.2956t K=1.9 84 K=1.6 39 -0.3980 K=1.0 60 K=1.0 K=1.9 42 15 150 +[0.1599 K=1.0 46 vx vx x2 vx x2 Not x x K=1.6 156 -0.5368 -0.55894 -0.4840 K-1.0 ±0.1802t n.s. +0.1295t -0.2173 K=1.6 32 -0. 1271 -0.34054 -0.60734 K=2.5 10 -0.6058 -0.6035 -0.2295 K=2.8 98 -0.1672 -0.3026* +10.2776t ±0.3191t n. s. -0.2,229 -0.2247n.s. -0.2160 -0.4515 -0.4570** -0.4332 -0.3148 -0.3127 -0.3231 n.s. -0.2156 -0.2085 -0.2263* K=1.6 24 K=1.0 28 K=1.0 12 -0.1465 -0.6098 -0.2310 -0.2,820n.s. Im -0!.6509*0 -0.5219 -0.65394 -0.6432 -0.5705* -0.5644 -0.6313 m K=2.5 26 K=2.8 90 z -I -0.56,34 -0.5454 -0.555010 -0.5122 Significant at 0.05. **Significant at 0.01. n '. z sicoiflcpnt Crown class Curve form Slash pine, block 31 level Best No. obs. 33 84 of Slash pine, block 32 level Best No. of Loblolly pine level Best No. of Best Longleaf pine No. of r -0.7854 -0.80664 " -0.7174 ohs. r -0.2265 -0.2209 -0.2392n.s. -0.4323 -0.466444 -0.3650 -0.2891 ohs. 10 46 r -0.8448 -0.86424" -0.8019 -0.4189"" -0.4104 -01.4238 -0.5035 -0.5193"" -0.4669 -0.3259 -0.3596n.s. -0.2648 -0.4598 -0.5131" -0.3406 -0.7949 -0.7892 level ohs. r -0.3523 -0.4178* 0 P.A.I. in basal area D X vx vx X X-1.1 K= 1.9 x= 1.4 K= 1.6 X-0.5 X=1.7 K=2.2 33 x=1.4 K=2.8 60 x=2.0 K=1.0 42 x=1.4 K-1.9 15 X=0.5 K=1.0 x=1.7 K=1.6 K=1.6 24 x=0.5 K=1.0 x=0.5 K 2.2 x=0.5 K=2.8 x=0.5 K-2.8 x=1.1 28 12 26 90 C I 0 All x2 x -0.2527 0 on 0 C m K=2.8 -0.6045 vx 2 X X vx vx 39 -0.6123*4 -0.5709 -0.5449 -0.5315 -0.5612"" x=1.4 K=1.6 x=0.5 K=2.8 x=0.5 K-2.5 X=1.1 K=1.3 x=3.0 32 10 98 X2 X K=2.5 156 K=1.0 x=0.5 -0.7308 -0.7550"" K=2.5] 150 V, P.A.I. in d.b.h.o.b. X D X X2 C X -0.6525 33 -0.6,516 -0.7203" -0.2065 -0.3737* -0.5893 -0.60574 -0.5493 -0.5379 -0.5912"" -0.4187 +0.18551 +0.1964'n.s. -0.6507 -0.6518"" -0.5910 -0.6173 -0.6068 -0.63204 -0.5705 -0.5793"" -0.5422 -0.7142 -0.7941"" -0.5246 -0.2190 -0.2721n.s. z E-I z m V K=1.0 33 x= 0.5 K=1.9 x=3.0 K=1.0 x 1.1 x=0.5 10 K=1.6 x=0.5 24 VX X' X_ K 1.9 84 x=0.5 -0.5410 -0.4209 60 42 15 +I0.1630t -0.3228 -0.3431" -0.4330*" K=1.3 46 x=2.0 K=2.2 x=0.5 K=1.0 x=1.7 K1.0 98 -0.7950"" -0.3046 -0.3092 -0.1365 -0.5913 K=1.0 28 x=0.5 -0.6228* I 0 All K=1.6 39 X x=0.5 VX X2-0.5595"" X ____ VX X -01.3895 -0.5439 -0.5309 ________ K=1.9 _______ -0.6138 ----K=1.9 150 -0.2839 -0.2764 -0.1936 -0.3742 -0.3848 -0.3933n.s. 32 10 -0.2812 -0.3822 -0.3721 -03957" +0.5650+0.4870f -0.5133 K=1.0 12 -0.6394 -0.6307 x=0.5 -0.6022 K=1.6 26-0.4629 x=0.5 K=2.8 90 -0.4683" x=1.7 -0.4654"" -0.5146"" -0.6209"" x=1.4 x=1.0 VX -0.2630 -0.3605 -0.5876 X2 "Significant at 0.05. SSignificant at 0.01. n.s. Not significant. ' The sign of the correlation coefficient is reversed from what would he expected from theory. K=1.6 156 -0.3600 -0.4686 -0.6353t -0.4019 -0.4225 -0.6581 x=0.8 -0.6859"" -0.5511 O APPENDIX B, TABLE 23. HIGHEST CORRELATION COEFFICIENTS OBTAINED, USING OPIE'S COMPETITION INDEX Jo Crown class Curve form Slash pine, block 31 Best No. of level ohs. r BAF= 33 14.40 K=2.2 BAF= 84 8.89 K 2.8 BAF= 39 27.22 K 1.6 ________ ____ -0.7735 -0.7924** -0.6961 -0.4870 -0.5174** -0.4098 -0.5413 -0.5333 -0.5449 * ________ -0.5842 -0.5027 -0.6540 -0.72420" -0.5380 -0.3979 -0.420004 -0.3482 -0.5309 -0.5226 Slash pine, block 32 Best No. of level ohs. r BAF= 33 14.40 K=2.2 BAF= 60 8.89 K=2.8 BAF42 69.70 K-1.0 BAF= 15 41.24 K =1.3 BAF= 150 69.70 K 1.0 -0.1785 -0.1815n.s. -0.1674 -0.1481 -0.1710n.s. -0.1061 -0.2066 -0.1122 -0.32984 -0.5283 -0.5102 -0.5439* Loblolly pine Best No. of level ohs. r BAF10 69.70 K=1.0 BAF=46 41.24 K 1.3 BAF 32 27.22 K=1.6 BAF 10 19.31 K-1.9 BAF 98 8.89 K 2.8 BAF=10 8.89 K2.8 BAF= 46 69.70 K-1.0 BAF= 32 K=1.6 BAF= 11.15 10 27.22 Longleaf pine Best No. of level ohs. BAF 27.22 K 1.6 BAF 69.70 K=1.0 BAF r -0.3633 -0.4254* 0.2634 -0.6563 -0.6694* -0.5833 0.6290* -0.6178 bs.r 0 P.A.I. in basal area D X v'X X2 C X VX X2 I X VX X2 O X V -0.2750 -0.3046n.s. -0.2126 -0.3375* -0.3348 -0.3370 -0.5595 -0.5766114 24 28 12 X 2 X X BAF= 156 MX 11.15 2 X K=2.5 P.A.L. in d.b.h.o.b. D X BAF- 33 MX 69.70 X2 K 1.0 C X BAF= 84 VMX 14.40 2 X K=1.9 I X BAF= 39 MX 2 All -------------BAF= 33 41.24 K 1.3 BAF= 60 69.70 K=1.0 BAF= 42 K=1.0 BAF= 19.31 15 69.70 -0.5169 -0.5265 -0.5447n.s. -0.4949 -0.2758 -0.2796** 69.70 K=1.0 BAF=26 11.15 K=2.5 BAF 90 -0.6057 -0.6340* -0.6297 -0.6192 r- -0'.618844 -0.2651 -0.2064 -0.3236** -0.2658 ±0.2955t-+0.27751' ±0.3191n.s. -0.2229 -0.2246n.s. -0.2160 -0.4515 -0.4332 -0.3148 -0.3127 8.89 K=2.8 BAF 24 27.22 K=1.6 BAF= 28 69.70 K=1.0 BAF= 12 69.70 K=1.0 BAF= 11.15 26 -0.5383 -0.5642* -0.4791 -0.2310 -0.2822n.s. -0.1465 -0.6098 -0.6509** -0.5218 -0.6539* -0.6312 -0.6432 -0.5705n.s. -0.5645 3I- +0.1405±0.15941'tn.s. +0.10621t+10.1598-' -10.1802tn.s. ±0,.1295t -0.2174 37v C -I C r- -0-o m m ZI X X K=1.6 27.22 O All ----___ -0.5350** ____ -0.1272 -0.6058 -0.3405 -0.6073* -0.4570** VMX 2----- ---0.5368 -0.5588** -0.4840 BAF= 156 27.22 K=1.6 *Significant at 0.05. SSignificant at 0.01. u.s. Not significant. X VMX X2 K=1.9 BAF= 150 69.70 K=1.0 -0.6035 -0.2295 -0.1672 -0.3026 * K=2.5 BAF= 98 8.89 K=2.8 -0.3231n.s. -0.2156 -0.2085 -0.2263° K=2.5 BAF= 8.89 K=2.8 90 -0.5634 -0.5454 -0.5550* -0.5122 ZI z Con Cre class form Slash pine, Best No. of obs. level block 31 r Slash pine, block 32 Best level No. of ohs. 33 60 r -0.2249 -0.2176 -0.2385n.s. ±0.0856t +0j.0,895- n.s. +0.0782f -0.2497 Loblolly pine Best level No. of ohs. r Best level Longleaf pine No. of ohs. 24 r r -0.5287 -. 549240 -0.4838 0 P.A.I. in basal area X DI 33 84 39 -0.814604 -0.8091 -0.7627 -0.3190 -0.3423,44 -0.2755 -0.5860 -0.5851 10 46 32 10 98 -0.1962 -0.2263n.s. vx 2 x 0 'TI C I o x Mx x2 X Mx -0.3238 -0.3113 -0.3459* -0.5525 28 -0.549,341 -0.5424 -0.5470 -0.6230, 0 C 42 15 12 26 x x vx x2 156 -0.5816 -0.2197 -0.3U,3U* -0.4246 -0.4293n.s. -0.4090 -0.5449 -01.5639** -0.4858 -0.6012 ~0.6278,* z z -0.4849 -0.4903n.s. -0. 1546 -0.5391 -0.5243 -0.5292 -0.5481** -0.4745 150 -0.2306 -0.22,73 -0.2348 * 90 -0.1486 -0.16,50n.s. 10 -+0.0741- -0.547944* -0.3209 -0.32,96** -0.3016. -0.3417 -0.3552 n.s. P.AI. in d.b.h.o.b. X D 33 Mx X -0.7238 -0.6405 84 39 -0.7529* 4 33 60 -0.0573 -0.0372 - 0.0j992,n. s. 24 28 C I o All Mx x2 X Mx x Mx x2 Mx at 0.05. -0.3512 -0.3702** -0.3113 -0.5962 -0.5958 -0.5917 +0.2734t -0.2023 46 32 42 15 +0.2793t* +0.2606t -0.1684 -0.2649n.s. -0.5209 +0.0904-tn.s. +10.0427t -0.1640 -0.1458 -0.2002n.s. -0.4710 -0.4584 12 26 -0.52314 10 98 -0.4936** -01.4263 -0.4128 -0.4547n.s. -0.3149 -0.5.931 -0.60404* -0.5625 -0.6073 -0.6118* -0.5890 -0.5822** -0.5754 -0.5757 O -0.5093 x 156 -0.5474 -01.563-611 -0.5002 150 -0.1749 -0.1386 90 -0.1602 -01.2018.* -0.1291 -0.1568n.s. -0.4334 -0.4422* -0.4103 0* *Significant Significant at 0.01. n.s. Not significant. tThe sign of the correlation coefficient is reversed from what would be expected from theory. F AL AANA'S LAnD -GRANT UNIVERSITY With an agricultural research unit in every major soil area, Auburn University serves the needs of field crop, live5 stock, forestry, and horticultural producers in each region in Ala- bama. Every citizen of the State has a stake in this research program, 3 7 1zn ri u '; since any advantage from new and more of 17 economical ways producing and handling farm products directly benefits the consuming O s pulblic. Research Unit Identification SMe;, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Agricui~turc E Hrpcrm. ' tan'tiom Auburn. Tennessee Valley Substation, Belle Mina. Sand Mountain Substation, Crossville. North Alabama Horticulture Substation, Cullmar Upper Coastal Plain Substation, Winfield. Forestry Unit, Fayette County. Thorsby Foundation Seed Stocks Farm, Thorsby. Chilton Area Horticulture Substation, Clanton. Forestry Unit, Coosa County. Piedmont Substation, Camp Hill. Plant Breeding Unit, Tallassee. Forestry Unit, Autniga County. Prattville Experiment Field, Prattville. Black Belt Substation, Marion Junction. Tuskegee Experiment Field, Tuskegee. Lower Coastal Plain Substation, Camden. Forestry Unit, Barbour County. Monroeville Experiment Field, Monroeville. Wiregrass Substation, Headland. Brewton Experiment Field, Brewton. Ornamental Horticulture Field Station, Spring Hill. Gulf Coast Substation, Fairhope.