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 DENSITY4 Competing Basal Area Per Unit Ground Area4 Growing Space (Area) Available to Tree Competitive Influence Zone Overlap11 Miscellaneous Methods  
10
24 26 29
SOURCE OF DATA            STATISTICAL DESIGN
POINT DENSITY EXPRESSIONS TESTED31 RESULTS AND DISCUSSION C row n Classes Method of Expressing
Growth

D ata se ts                             
34 35
36
37

PointDensity 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, fixedradius plot centered on the sample tree. Figure 1 and Appendix A.1. show how such a fixedradius 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 "anglecount" 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 = StenekerJarvis 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 StenekerJarvis 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 anglecount method being used with the same sample tree and surrounding stand depicted in Figure 1. As with the fixedradius 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 anglecount method of obtaining basal area per acre centered on the sample tree.
Spurr (26) originated a variant of the anglecount method, which he called the "anglesummation" 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 anglesummation 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 anglesummation 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 anglesummation 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 anglesummation 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 threedimensional. 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, freegrowing 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 crosssectional 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 crosssections of the right circular cylinders as a measure of competitive pressure. These horizontal crosssections 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 crosssections of the M.P.G. spaces, which probably would involve root extent rather than crown spread. Since root extent cannot be determined in a nondestructive 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 yintercept (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 wellreasoned 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 influencezone 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 LanePoole (15), that the C.I.Z. is closely approximated by the crownspread of opengrown trees and that this crownspread 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 opengrown 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 influencezone 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 influencezone 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 influencezone overlap using the FrittsGerrard, (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 FrittsGerrard 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 FrittsGerrard procedure. The magnitudes of the C.I. Zones in the Bella method are based on the relationship between the crown diameters of opengrown 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 opengrown 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 FrittsGerrard 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 OiS 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 (fixedradius plots, variableradius 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 anglecount 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 1yearold 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 secondgrowth 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 variablepoint density expressionspeciescrown classlevels 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).
(25). 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 anglecount, with basal area factors of 5, 10, 15, 20, 25, 30, and 40 square feet per acre. (7). Spurr's anglesummation, 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. (1015). 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. (1617). 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 FrittsGerrard 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 quarteracre 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 opengrown 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 opengrown. 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, pointdensity 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 1447. 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 threemember 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 124. 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 nonexistent. 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 slowtodevelop 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 1447. 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 growthpoint density relationship should be of more interest or utility than the d.b.h. growthpoint 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.
PointDensity 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 124. 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 StenekerJarvis 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 FrittsGerrard 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
. 6123 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 StenekerJarvis ISJ2 for basal area growth of codominant longleaf pines, was 0.6597, Appendix B, Table 4. Twentyeight 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 224, 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 StenekerJarvis 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. BiMonthly Research Notes 25:3:2425. 1971. A New Competition Model for Individual Trees. . Forest Science 17:364372. BITTERLICH, W. 1947. Die Winkelzahlmessung. Allg. Forst. u. Holzwirts. Ztg. 58:9496. 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 InfluenceZone Overlap:
(8)
Easy. J. For. 50:3237. (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. 42:519. 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. 7:3542. (15) LANEPOOLE, C. E. 1986. Crown Ratio. Austral. For. 1:2:511. (16) LATHAM, R. P. 1972. Competition Estimator for Forest Trees. Photogrammetric Engineering 38:4850. (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. 8:286249.  . 1962b. Stocking Density (18) Around Ponderosa Pine Trees. For. Sci. 8:397402. (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. 14:314323. (23) ROGERS, S. W. 1935. Soil Factors in Relation to Root Growth. Trans. 3rd Inter. Cong. Soil Sci. 1:249253.
(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. 8:8596. (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 SpruceTrembling Aspen Stand. For Chron. 39:334336. (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 110. 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
Blowup 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 StenekerJarvis 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)= i1
=
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 anglesummation 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)±12 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 FrittsGerrard index: The areas in the crosshatched 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
'
DominantsIntermediatesLoblolly 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
24 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 ..
92
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 .2I.
__ _ _
__
_
_
+.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
DominantsIntermediates5 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
DominantsI 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
GRWHFSOTER
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. 13. . 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."""" OvertoppedAllLongleaf 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
.3t
+.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
SUHRPNS7
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"
3F
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
ALBMGIULUAtXEIMN
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
nineP 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
OvertoppedAll
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
OOUHENPIES8
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
IntermediatesOvertoppedAll~
. 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 X20.4480 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.l800fn.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
VMXX MX
X2Large 156
plot
0.5210
X20.5183
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 ,II
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
X20.4474
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 0.65460.3326
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
VMXX 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 plot0.1658 32
10
0.2323n.s.
05470** 0.4884 0.5337
0.3512
plot0.5715*
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 STENEKERJARVIS
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 0.631700 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 0.24850.4509 0.5368 Large 12 0.4757 0.5897°° plot0.4849n.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 X2019,68 Large 39 plot
X20.2666 _
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
X0.2938
0.4029n.s.
plot
0.4743
0.5996n.s.
98 +0.0339
0.0160
plot
0.3510
VXX Large plot
X20.2458
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
STENEKERJARVIS
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 0.50740.4684
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 X0.1769 X Large 39 VX plot X20.3290
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.0.43460.4479 +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 X20.3005
_____
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 +01.2645t =40 + 0.2984tn. s. 4 +0.2l 1ltn.s. BAF +0.2,129140
10 46 32 101
+10.212910.2099
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
X0.7145
C I 0
All
BAF 84 =5 X20.3810 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 X20.4670
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 X20.5868 BAF 84 X =15 MX
X20.3483+0.2062t
33 60 42 15
150
+0.2787t +0.2598i
+0.3021tfn.s.
A0.2080tn.s. BAF +0.2072t =40
0.2187
0.2608
X MX X MX
BAF 10 X2 ____
BAF
0.5313 0.5190 0.5426* * __ ____ ____ X20.5716
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
X20.4884
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
X20.686.3
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 X20.0645
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
X20.4051
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
tn.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 +I0.1110tn.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 0.4733n.s.
20 14
65
36
0.3493
0.3726**
55
42
X2
16 trees X2
4 +]0.1368ttO.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
+0.2317
60 +0.2819n.s. +0,.2315n.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
+03368* +0.3196
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
0.0314t0.0627n.s.
+0,.0104
24
+01.0835
+0.0405
+0.1370n.s.
28
C I C
D O
X
60 42
Mx vx
x2
0O.084410.08861 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
0.0,97110.045310.1816tn.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 t001
+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


L1f
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 ±0.3112t' +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,* 0.5761**
aI
0.6202 n.s. ±0.50251'f ±0.49841' ±0.4829t'
K1.9
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
K1.9
K=2.8 ±0.14811' +±0.1492tn.s. ±0.14561' ± 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. 0.1324 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* +04782f"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
0.1568
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 0.4995* 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 +0.3592tn.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 10.2154tn.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 01376200 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. +0.0064t0.2486 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 1560.3988 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
+0.1598tn.s.
+0.0777t ±0.1613t
+ 0.1728tn. s.
K=2.2 26 0.4944 0.4649 0.5347 n.s. K=1.0 90 ±0.1406t +0.1203t±0.1895tn.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
0.2884
vx
x2
vx
0
All
K=1.6
39
0.3109*o 0.2425 0.4815 0.4931** 0.4338
K1.0
+0.1276t
60 +01.19501
+0,.2904
K=1.6
24
0.2231
0.2797
+0.3466n.s.
+0.2335n.s.
K1.0
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
K1.3
0.2938,n.s. 0.4586 0.4794 n.s.
* 0.4837
0.4960
0.5248n.s.
12
26
0.6365
~0.6222** 0.6089
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+0.1536fn.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
K2.8
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 0.6676* 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
+00180t' 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
06697 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
+±0.1420tn.
±0.3783t
+0.1028t
K=1.0 60 K=1.0 K=1.6 42 15
150
+0.3535t
0.1822
K=1.6 24 K=1.0 28 K=1.0 K=2.2 K=2.8 12 26 90
+0.4013tn.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 +±0.09251n.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
K1.0
K=1.9 K=2.8
K= 2.8
0.3641 0.4262* 0.2882
0.56,9014i
K=1.0 K1.0
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
K2.8
n. s.
10
+0.3142t
+t0.2911t 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 K1.0 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
0.3969* 0.3705 ±0.4622t +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
+0.1854tn.s.
K2.8
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 +0.4189tn.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 0.194440.2333*
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 FRITTSGERRARD
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
K1.3
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
K1.9
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
+ 0.1970tn.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
K1.0
±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
X1.1
K= 1.9 x= 1.4 K= 1.6 X0.5
X=1.7
K=2.2 33 x=1.4 K=2.8 60 x=2.0 K=1.0 42 x=1.4 K1.9 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 K2.8 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 K2.5 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
EI
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 X20.5595"" 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=1.6 260.4629
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 K1.0 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 K1.9 BAF 98 8.89 K 2.8 BAF=10 8.89 K2.8 BAF= 46 69.70 K1.0 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
0o
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
+0.0904tn.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 01.563611 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.