INTERNATIONAL CENTER FOR AQUACULTURE
AGRICULTURAL EXPERIMENT STATION AUBURN UNIVERSITY
R. DENNIS ROUSE, DIRECTOR AUBURN UNIVERSITY. ALABAMA
RESEARCH AND DEVELOPMENT SERIES NO. 27 PROJECT: AID/LA-C-1176 SEPTEMBER 1980
Catch
Assessment
zurvey
Design for Monitoring the
Upper Meta River Fishery,
Colombia, South
i4 ' r Ai
--..
" . .'
Stratum I
Upper Meto River Study Area
Stratum I - Main Meta River
Stratum 2- Upper Tributaries
Stratum 3 - Lower Southern Tributaries
Stratum 4 - Lower Northern Tributaries
Inset shows location
of study area within
Colombia
FIG. 1. The Upper Meta River area, showing the 10 zones of the 1977 frame survey (zones IX and X are lagoons to the north and south of the
Meta River, respectively) and the four strata of the 1978 catch assessment survey.
Stratum 3
SUMMARY
Catch and fishing effort in the Upper Meta River System for
the hydrological year April 10, 1978 - April 9, 1979, were
estimated using a statistically designed catch assessment survey
(CAS). The design was based on CAS methods used at Auburn
University and incorporated results from a frame survey
conducted during the 1977 hydrological year on the Upper Meta
River.
Total catch in 1978 was 1,071,366 kilograms from 126,334
Fishing Economic Unit (FEU)-days where 1 FEU-day was
equivalent to 1.8 fisherman-days. Average catch per FEU-day
was 8.1 kilograms. Ninety-one percent of the catch came from the
main river and upper tributaries (70 percent and 21 percent,
respectively). Similarly, 88 percent of fishing effort (FEU-days)
was expended in the main river and upper tributaries (70 percent
and 18 percent, respectively). Catch and fishing effort in lower
tributaries, especially those on the southern side of the Meta
River, were relatively insignificant.
The annual harvest was evenly distributed between the high
and low water seasons. However, because the low water season
was 71 percent as long as the high water season, daily catch was
actually higher during low water. This was due primarily to
increased daily fishing effort within the main river stratum
during the low water period. Catch per unit effort changed only
slightly from the high water season (7.9 kilograms per FEU-day)
to the low water season (8.4 kilograms per FEU-day).
The relative standard error (RSE) for fishing effort (9.9
percent) indicated that samples were providing relatively
precise estimates of this variable on an annual basis. Variation in
fishing effort was inherently low because artisanal fishermen
live near the river and their frequency of fishing changes little
within seasons. Catch estimates were more variable, however,
giving a RSE of 25.1 percent for the year; greatest variation was
encountered in the low water season (RSE = 44.4 percent).
Further seasonal stratification is recommended to reduce
variation in catch estimates.
Future catch assessment surveys on the Upper Meta River are
outlined and sampling schedules within time strata are defined.
The number of time strata will be increased from two to four
with the addition of one stratum for the rising and one stratum
for the falling water season. It is recommended that six samples
be taken within each time stratum; due to the logistics of
sampling, two or three samples will be taken during a single field
trip and trips will be systematically scheduled. The Upper Meta
River will be divided into two geographical strata, one
composed of all tributaries and the other composed of-the main
river only. Sample sections will be chosen with nonuniform
probability, with twice as many samples coming from the main
river stratum as from the tributary stratum (four samples and
two samples, respectively).
Application of nonuniform probability sampling is
recommended for initial surveys of all river fisheries within
Colombia's Orinoco System. A pre-survey overflight will
provide initial sampling probabilities based on number of
canoes counted per section, and initial time strata will be the
same as defined for the Upper Meta River. Strata definition and
sampling probabilities for later surveys can be amended based
on information gathered during the initial survey.
A 10-year CAS sampling program for Colombia's Orinoco
System is proposed. Sampling will be conducted on the Upper
Meta River in alternate years (from 1978). Six other Orinocian
rivers will be sampled, one each year, during successive
alternate years beginning in 1979. These other rivers have much
less potential for immediate fisheries development than does the
Upper Meta River and thus merit less sampling effort. After
1989, consolidation of sampling to include two or more river
fisheries in 1 year may be feasible, thereby allowing comple-
tion of data collection necessary for a Schaefer surplus yield
model in all fisheries of the Colombian Orinoco System
within 15-20 years from 1978. Methods for obtaining estimates of
maximum sustainable yield and optimum fishing effort at the
community level based on the Schaefer surplus yield model are
discussed.
CO0N T ENT S
Page
SUMMARY................................................ 2
INTRODUCTION...........................................
5
BACKGROUND OF THE PROJECT.............................. 5
ANALYSIS OF RESULTS FROM THE 1978 CATICH ASSESSMENT
SURVEY (CAS) ON THE UPPER META RIVER.................
5
Calculation of Total Fishing Effort.................
6
Calculation of Average Daily Catch per Unit Effort
. 7
Calculation of Total Annual Catch..................
8
Final Calculations of E and C for 1978..............
9
Verification of Estimate of Annual Harvest (C) ... 9
Precision Associated with Estimates of E, C, and U..
9
CAS DESIGN FOR CONTINUED MONITORING OF THE
UPPER META RIVER FISHERY.............................. 9
Division of the System into Time Blocks and
Geographical Strata ............................ 10
Sampling within Time Blocks......................
11
Sampling within Geographical Strata................
11
Choosing River Sections and Tributaries for
Sampling Purposes .............................
11
PROPOSED METHOD OF CONDUCTING INITIAL SURVEYS OF
OTHER MAJOR RIVERS IN LLANOS REGION................... 13
Initial Surveys..................................
13
Follow-up Surveys ...............................
13
USE OF THE GRAHAM-SCHAEFER SURPLUS PRODUCTION
MODEL
FOR MANAGEMENT OF THE UPPER META RIVER FISHERY........
13
REFERENCES............................................ 15
PUBLISHED SEPTEMBER 1980 - IM
COVER PHOTO. INDERENA biologist interviews successful
artisanal fisherman to acquire data on catch and fishing
effort.
Information contained herein is available to all
Catch Assessment Survey Design for Monitoring
the Upper Meta River Fishery, Colombia, South America
STEPHEN P. MALVESTUTO, RICHARD J. SCULLY, and
FERNANDO GARZdN FI
INTRODUCTION
T 1 IIM)EREN S It1) At Fit RN I NI\ P1151 cooperative'
fisheries project in C olomibia requested D~r. Stepheii \alx estuti)
to consult in Colombia with the Llanos ()rientales Fisheries
Project (hiring April 15-28, 1979. 'Hie specific, purpose and
expectedl outcoines ot the v isit wxere to bring an expe'rt in surx ex
anaix s to \ illax icencio to proxvide aditional input into) analx sis
of the accumulated 2 x'ears of data from the \leta Ri'ver
fishery catch assessmnt surveyv (CAS). Special effort wxas
employed in the estimation of catch and fishing effort from the
food fish fishery . Specifically , assistance was gixven to:
1. Imnproxve experimental design, i.e., deveClop methods to
minimize variance estiimates of catch, fishing effort, and catch
per unit effort.
2. Plan and implemient the analysxis and p)resentation of
project results.
BACKGROUND OF THE PROJECT
Thbe plrinciple plroject goal xwas to present a rational approach
to fisheries management based on knowxledge of fishing
effort,
catch per unit effort, and total catch from the fishery.
Ultimately , the present dlata are to be incorpoiratedl into a surpluos
yield mnodel (6, Chapter 13) to proxide an estimate of maximum
sustainable y ield and optimuilm fishing effort. Catch statistics o~f
length frequency by species, relative abundance
oif each species,
and length frequency of the spaxxning p~opulatioins haxve been re-
corded as further aids to future management decisions (7).
D)uring the first 12 months of the program, data on catch and
effort xvere collected xvia a frame siirxvex xvhere each of the i10
zones5 comprising the selected study area (the uipper 316
navigable kilometers of the Nieta Rixver and its associated
'Respectixvely, Assistant Professor, I)epartmnent of Fisheries and Allied
Aquacutmires; Research Associate, l)epari ient of Fisheries and Allied
Aquacmitures; and Field Biologist, IN I)EFRENA, ( olonmibia, South
Amnerica.
tributaries) xwas survexyed once (hirinig the high xx ater p~hase
(April 1)) N oxember 9), and again (hliriing the loss x% ater p)hase
(Noxvember it)-April 9), figure 1. D~uring the second 12-mionth
perioid, eiiding April 9, 1979, the studx area xwas dixvided into
sampling strata aeccordhing to the characteristics of (1) saimplle
v ariation in catch per unit (of fishing effort, (2) cost of saimipling
each stratum, and (:3) intensity of fishing effort. Areas that had
little need for studs , or that return(( little intormation in relation
to samnpiig cost, xwere gix en little or no sampling effort.
'[his report suggests a more appIrop~riate saimiple siirx c
dlesign xx hich should be amenable to co~ntinuemi'ionito~ring of
the tUpper Mecta fix er Sx stem) Also, the design lends itself wxell
to saiiliiig of other fisheries in the ( rinoco Sxysteiii Detamls of
these iiipuiits are p resenlted, along \% i th a biblio1graphNli
ANALYSIS OF RESULTS FROM THE 1978 CATCH
ASSESSMENT SURVEY (CAS) ON THE
UPPER META RIVER
i'le 1978 C.AS oil the I. pper Mleta Rixver xxas based on
stratification in tiiie and space. Specifically , the lixdrological
year (April 10, 1978-April 9, 1979) wxas dixvided into txxo tiii
strata (henceforth called time blocks) xwhere 'lone Block A
referred to the high wxater period (April 10, 1978-Novemnber 9,
1978) andl limne Block B referred to the lowx xwater period
(Noxvember if), 1 978-April 9, 1979). 'Ilhe riv er audi its assoiciated(
tributaries xxerc dixvidd into three' geograp)hical (area) strata
xx,,here Stratumn I encomipassed the iiain U..pper Nleta Rixer
channel, Stratum 2 encompassed the uipper tributaries, and
Stratum :3 enc'omp~assed the loxx er southern tributaries, figure 1.
T he lowxer northern tributaries, the Rio (hisiana and Rio Crax i
Sur (labeled as Stratum -4 in figure 1), xxere not includedi in the
1978 C:AS because they contributed little to catch and effort in
1977 and wxerc extreiiielx' difficult to sample (hliring the lowx
Isolated and meandering tributaries (left) and extensive sandbars
(right) made access to, and travel on, the water difficult and time
consuming.
4,'
TABLE 1. NUMBER OF SAMPLES TAKEN WITHIN EACH GEOGRAPHICAL
STRATUM (1, 2, AND 3) DURING EACI TIME BLOCK
(A AND B) DURING THE 1978 CAS
Number of samples taken
Time block Stratum Stratum Stratum Total
1 2
3 Total
A ............. 5 5 2 12
B ......................... 3 3 2 8
TOTAL ................... . 8 8 4 20
water period; however, 1978 catch and effort estimates were
adjusted upward to include the expected contribution from
these tributaries.
The main Meta River channel in Stratum 1 was divided into
three sections, which were given equal probabilities (0.33) of
being chosen for any given sample; likewise, the individual
tributaries within Stratum 2 were given equal probabilities of
being chosen (six tributaries with probability of 0.167 each), as
were the individual tributaries in Stratum 3 (two tributaries with
probability of 0.50 each). Table 1 gives the number of samples
taken within each geographical stratum during time blocks A
and B. Because of cost considerations, two main river sections or
three tributaries were sampled during each survey trip.
Calculation of Total Fishing Effort
Within any sampled river section or tributary (henceforth
referred to as sampling units = SU), a count of the total number
of active fishing canoes (fishing economic units or FEU)
provided an estimate of fishing effort. The steps involved in
expanding this estimate of effort per SU to an estimate of total
annual effort for the whole system are as follows:
(1) For each time block, expand the number of FEU
counted within each SU (Esu) to a total daily number of FEU for
the entire geographical stratum (Edaily) by dividing E.u by the
sampling probability associated with the particular SU. Thus,
for any given geographical stratum within any given time block,
Edaily is calculated as
Edaily = Esu/Psu
where Pu = the probability associated with the particular SU.
These calculations are shown in table 2.
(2) Calculate the average daily fishing effort per stratum
(Edaily) within each time block by averaging the sample
totals
(Edaily) calculated in table 2. Thus, for any given stratum within
any given time block, Edaily is calculated as:
E _1
Edaily = IZ Edaily
where n = the number of SU sampled in the particular stratum
within the particular time block. These calculations are shown in
table 3.
(3) Calculate a variance for each Edaily, i.e., a variance of the
mean, as
Vi = n(n-1) [I E
2
daily - ( Edaily)
2
/n]
Values of VI (with intermediate sums) are also given in table 3.
(4) Calculate the total daily effort for each time block (Edaily
total) by summing the Edaily for each geographical stratum. Thus,
Edaily total = 1 Edaily.
For Time Block A:
Edaily total = 198.80 + 52.60 + 14.00 = 265.40 FEU
TABLE 2. EXPANSION OF FISHING EFFORT PER SU (Esu) TO AN ESTIMATE OF
DAILY EFFORT FOR AN ENTIRE GEOGRAPHICAL STRATUM (Edaily) WITHIN
EACH TIME BLOCK USING APPROPRIATE SAMPLING PROBABILITIES (Psu)
TIME BLOCK A: HIGH WATER
Stratum 1 Stratum 2 Stratum 3
Esu + Psu = Edaily Esu* + Psu = Edaily Esu* + Psu = Edaily
76 0.33 = 230 6.5 + 0.167 = 39 8.7 + 0.5 = 17
59 0.33 = 179 19.1 + 0.167-= 115 5.7 + 0.5 = 11
62 0.33 = 188 4.0 + 0.167 = 24
73 0.33 = 221 0.8 + 0.167 = 5
58 + 0.33 = 176 13.3 + 0.167 = 80
TIME BLOCK B: LOW WATER
Stratum 1 Stratum 2 Stratum 3
Esu + Psu = Edaily Esu* + Psu = Edaily Esu* -Psu = Edaily
139 0.33-421 6.9+0.167=41 4.9+0.5 = 10
106 0.33=321 12.2+0.167 = 73 3.1+0.5 = 6
63 + 0.33 = 191 13.9 + 0.167 = 83
*Decimal Esu values were generated as a result of multiplying the total
number of canoes counted by the proportion of canoes actively fishing
on a daily basis; this proportion was estimated by questioning fishermen
on canoe use. Larger Esu values were rounded to the nearest whole
number.
and for Time Block B:
Edaily total = 311.00 + 65.67 + 8.00 = 384.67 FEU.
(5) Calculate the variance of Edaily total for each time block
(VE daily total) by summing the Vf for each geographical stratum.
Thus,
VE daily total = I VE.
For Time Block A:
VE daily total =-- 124.74
+ 395.66 + 9.00
= 529.40 FEU
2
and for Time Block B:
VE daily total= 4,433.33
+ 160.44 + 4.00
= 4,597.77 FEU
2
.
The square root of VE daily total for each time block is the standard
error of Edaily total (SEE daily total). Thus, for Time Block A,
SEE daily total = 529.40 = 23.01 FEU
and for Time Block B,
SEE daily total =\ 4,597.77 = 67.81 FEU.
TABLE 3. CALCULATION OF MEAN DAILY FISHING EFFORT PER STRATUM
(Edaily) WITHIN EACH TIME BLOCK BY AVERAGING VALUES OF Edaily
FROM TABLE 2 (VALUES OF VE AND INTERMEDIATE
CALCULATIONS ARE ALSO GIVEN)
TIME BLOCK A: HIGI
Stratum 1
Edaily = 230 FEU
179
188
221
176
Edaily = 198.80 FEU
I Edaily = 994
(Y Edaily)
2
= 988,036
1 E
2
daily = 200,102
VE = 124.74
FEU
2
H WATER
Stratum 2
39 FEU
115
24
5
80
Edaily = 52.60 FEU
I Edail = 263
(X Edaily) = 69,169
Z E
2
daily = 21,747
V-= 395.66
FEU 2
TIME BLOCK B: LOW WATER
Stratum 1 Stratum 2
Edaiy = 421 FEU 41 FEU
321 73
191 83
Edaily = 311.00 FEU Edaily = 65.67 FEU
I Edaily = 933 1 Edail
x
= 197
(Y Edaily)
2
870,489 (1 Edaily) = 38,809
E
2
daily -= 316,763 Z E
2
daily = 13,899
V = 4,433.33 FEU
2
V- = 160.44 FEU
2
Stratum 3
17 FEU
11
Edaily = 14.00 FEU
I Edaily = 28
(Y Edaily)
2
= 784
Y E
2
daily = 410
V = 9.00
FEU
2
Stratum 3
10 FEU
6
Edaily = 8.00 FEU
I Edaily =16
(Y Edaily)
2
= 256
1 E
2
daily = 136
V = 4.00
FEU
2
(6) Calculate total fishing effort within each time block
(Eblock) by multiplying each Edaily total by the number of days
within the time block. Time Block A contained 214 days and
Time Block B contained 151 days. Thus, for Time Block A:
Eblock = 265.40 FEU X 214 days = 56,796 FEU-days
and for Time Block B:
Eblock = 384.67 FEU X 151 days = 58,085 FEU-days.
(7) The standard error of Eblock for each time block (SEblock)
equals SEE daily total multiplied by the number of days contained
within each time block. Thus, for Time Block A:
SEblock = 23.01 FEU X 214 days = 4,924 FEU-days
and for Time Block B:
SEblock = 67.81 FEU X.151 days = 10,239 FEU-days.
The relative standard error of Eblock (RSEblock) is defined as
(SEblock/Eblock) X 100 and simply expresses the standard error of
total effort as a percentage of total effort. Thus, for Time Block
A:
RSEblock = (4,924 FEU-days/56,796 FEU-days) X 100 = 8.7 percent
and for Time Block B:
RSEblock = (10,239 FEU-days/58,085 FEU-days) X 100 = 17.6 percent.
(8) The daily total effort for the entire year (Eannual daily)
is calculated by taking the weighted sum of Edaily total for each
time block. A time block weight (W) is defined for each time
block as the number of days contained within the time block
divided by the total number of days within the year. Thus, the
weight for Time Block A (WA) = 214/365 = 0.59 and the weight
for Time Block B (WB) = 151/365 = 0.41. Each Edaily total is
multiplied by its respective time block weight and the resulting
values are added together. Thus,
Eannual daily = I WEdaily total.
In the present case,
Eannual daily = 0.59 (265.40) + 0.41 (384.67) = 314.30 FEU.
Total annual effort (E) is then calculated by multiplying
Eannual daily by the number of days
in the year. Thus,
E = 314.30 FEU X 365 days = 114,720 FEU-days.
It may be noted that E can also be estimated by simply adding
the two time block totals (Eblock). This gives E= 56,796 + 58,085
= 114,881 FEU-days. The procedure given above using time
block weights allows the calculation of Eannual daily which can be a
useful summary statistic.
(9) The variance of Eannual daily (VE annual daily) is calculated as
the weighted variance of the values of VE daily total So that
VE annual daily = 1 W2VE daily total.
Thus, in the present case,
The square root of VE annual daily equals the standard error of E
annual daily (SEE annual daily) so that, in the present case,
SEE annual daily = / 957.17 = 30.94 FEU.
The standard error of E (SEE) is equal to SEE annual daily multiplied
by the number of days within the year. Thus,
SEE -= 30.94 FEU X 365 days - 11,292 FEU-days.
The relative standard error of E (RSE) equals (SE/E) X 100 or
(11,292 FEU-days/114,720 FEU-days) X 100 = 9.8 percent.
Calculation of Average Daily Catch
per Unit Effort
For any given SU, an estimate of catch per unit effort per day
or kilograms of fish caught per FEU per day is obtained from
interviews. This value is calculated by dividing the total weight
of fish harvested by the total number of FEU's interviewed and
is taken to represent the catch per FEU for the entire stratum
during the day of interview (Udaily). Thus, unlike estimating
Edaily, the catch per unit effort measured within any given SU is
not expanded by the probability associated with that particular
SU to give a total for the entire stratum; the concern here is to
obtain a representative estimate of daily harvest per FEU.
(1) Calculate a mean catch per FEU per day (Udaily) by
averaging the values of Udaily for each geographical stratum
within each time block. Thus,Udaily for any given stratum within
each time block is calculated as
Udaily = "T X Udaily.
Values of Udaily are given in Table 4.
(2) Calculate the variance of each Udaily as
Vu = T [ EU
2
daily - (XUdaily)
2
/n]
This is a variance of the mean and is exactly analagous to the
formula for VE previously given. Values of Vu are also given in
table 4.
(3) To calculate a mean U over strata within each time
block, each Udaily is weighted by the relative amount of fishing
TABLE 4. CALCULATION OF Udaily BY AVERAGING VALUES OF UdailyFOR EACH
GEOGRAPHICAL STRATUM WITHIN EACH TIME BLOCK: VALUES OF Udaily ARE
ESTIMATES BASED ON CATCH AND EFFORT MEASURED THROUGH
INTERVIEWS (VALUES OF Vu ARE ALSO GIVEN)
TIME BLOCK A: HIGH WATER
Stratum 1 Stratum 2 Stratum 3
Udaily-11.39 7.39 3.75
6.25 13.56 3.75*
3.28 7.50
12.72 3.56
8.36 4.56
Udaily= 8.40 kg/FEU Udaily= 7.31 kg/FEU Udaily= 3.75 kg/FEU
Vy= 2.92 (kg/FEU)
2
Vn
=
3.04 (kg/FEU)
2
Vi=0.00 (kg/FEU)
2
TIME BLOCK B: LOW WATER
Stratum 1 Stratum 2 Stratum 3
Udaily 3.64 3.31 2.12
16.04 1.50 2.12*
4.75 26.35
Udaily= 8.14 kg/FEU Udaily=10.39 kg/FEU Udaily=2.12 kg/FEU
Vu=15.69 (kg/FEU)
2
Vt=63.98 (kg/FEU)
2
Vn=0.00 (kg/FEU)
2
VE annual daily = (0.59)2 (529.40) + (0.41)2(4,597.77) = 957.17 FEU
2
. *Asuedvaue bse o frs smpe
effort (relative number of FEU's) per stratum. On the average,
71 percent, 24 percent, and 5 percent of the fishing ef fort
occurred in stratum 1, 2, and 3, respectively, giving stratum
weights of 0.71 (Wi), 0.24 (W2), and 0.05 (W3). The weighted
mean daily catch per unit effort (Udaily weighted) is calculated as
Udaily weighted = I W~daiiy.
Thus, for Time Block A:
Udaily weightedJ= 0.71 (8.40) ? 0.24 (7.31) + 0.05 (3.75)= 7.91 kg/FEU,
and for Time Block B:
Udaily weighted = 0.71 (8.14) + 0.24 (10.39) + 0.05 (2.12)= 8.38 kg/FEU.
(4) The variance of Udaily weighted is a weighted variance of
the mean (Vw) and is calculated as
VW = I W
2
VU.
Thus, for Time Block A:
Vw = (0.71)2 (2.92) + (0.24)2 (3.04)
+ (0.05)2 (0.00) = 1.65(kg/FEU)
2
,
TABLE 5. ESTIMATION OF Cdaily AS THE PRODUCT OF Edaily AND Udaily
FOR EACH GEOGRAPHICAL STRATUM
TIME BLOCK A: HIGH WATER
Stratum 1 Stratum 2 Stratum 3
Edaily X Udaily -Cdaily Edaily X Udaily = Cdaily Edaily X< Udaily - Cdaily
230 X 11.39 = 2,619 39 >X 7.39 = 288 17 >X 3.75 = 65
179 X 6.25 =1)119 115 X13.56 = 1554 11 X3.75 = 43
188 X 3.28 = 616 24 X 7.50 = 180
221 X 12.72= 2,810 5 X 3.56 = 17
176 X 8.36 = 1,471 80 X 4.56= 364
TIME BLOCK B: LOW WATER
Stratum 1 Stratum 2 Stratum 3
Edaily X Udaily = Cdaily Edaily X Udaily = Cdaily Edaily X Udaily = Cdaily
421 X 3.64 = 1,533 41 X 3.31 = 137 10 X 2.12 = 21
321 X 16.04 = 5,152 73 X 1.50 = 110 6 X 2.12 = 13
191 X 4.75 = 907 83 X 26.35 =2,192
were caleuIasted; calculation Of Cdaily and values of V are given
in table 6.
The total daily catch over all strata within each time block
(Cdaily total) is the sum of all Cdaily. For Time Block A:
Cdaily total = 11,727.00 + 480.00 + 54.00 = 2,261.60 kg,
and for Time Block B:
aaily total= 2,530.67 + 813.00 + 17.00 3,360.67 kg.
Thavrinc ofoarytoal(Ciaiyeotl
iBteoumocal
BThs
Vw = (0.71) 2 (15.69) + (0.24) 2 (63.98) + (0.05)2 (0.00)=
11.59 (kg/FEU)
2
.
The square root of Vw is the standard error of Udaily weighted (SEw).
Thus, for Time Block A,
SEw =-\/ -1.65 1.28 kg/FEU/day,
and for Time Block B,
SEw =v/1=.5 3.40 kg/FEU/day.
Relative standard errors for Udaily weighted (RSEu) are (1.28/7.91)
X 100 = 16.2 percent and (3.40/8.38) >X 100 = 40.6 percent for.
Time Block A and Time Block B, respectively.
(5) An annual estimate ofUdaily over time blocks (U) is
calculated by weighting each Udaily weighted by the time block'
weights previously defined as 0.59 and 0.41 for Time Blocks A
and B, respectively. Thus, in the present case,
U = 0.59 (7.91) + 0.41 (8.38) = 8.10 kg/FEU/day.
The variance of U (Vu) is the weighted sum of Vw and is
calculated as
VU = (0.59)2 (1.65) + (0.41 )2(11 .59) = 2.52 (kg/FEU/day)
2
.
The standard error of U (SEU) = \
t
-Vu= -v/-2.5 = 1.59
kg/FEU/day. The RSE of U= (1.59/8. 10) >X 100= 19.6 percent.
Calculation of Total Annual Catch
The calculation of total annual catch follows the procedure
given for calculating total annual ef fort. Estimates of total daily
catch for each sampled stratum (Cdaily) are calculated as the
product of Edaily X Udaily. These calculations are shown in table
5. Mean daily catch for each geographical stratum (Cdaily) and
the variance Of Cdaily (W) are calculated just as Edaily and VE
f or Time Block A:
VC daily total = 181,903.70
+ 75,408.16 + 121.00 = 257,433
kg
2
,
and f or Time Block B:
VC daily total = 1,750,503.45 + 475,471.00 + 16.00 = 2,225,990 kg.
Standard errors Of Cdaily total are \ -5,3 = 507.38 kg and
\2,225,990 = 1,492 kg,
for Time Block A and B, respectively.
Using analagous subscripts and calculations, given for
calculating total fishing effort (page 7), Cblock = 483,982 kg for
Time Block A and 507,461 kg for Time Block B. Respective
values of SEblock are 108,579 kg and 225,292 kg, giving 22.4
percent and 44.4 percent for values of RSEblock.
An annual estimateof Cdaily (Cannual daily) is calculated as the
weighted sum of the Cdaily total values where the previous
weighting f actors Of WA = 0.59 and WB = 0.41 are again used.
TABLE 6. CALCULATION OF Cdaily BY AVERAGING VALUES OF Cdaiiy FOR EACH
GEOGRAPHICAL STRATUM WITHIN EACH TIME BLOCK
(VALUES OF Vu ARE ALSO GIVEN)
TIME BLOCK A: HIGH WATER
Stratum 1 Stratum 2
Cdaily = 2,619 288
1,119 1,554
616 180
2,810 17
1,471 364
Cdaily = 1,727 kg 2CTdaily
= 480.60 kg2
VE= 181,903.70 kg
2
VE = 75,408.16 kg
2
TIME BLOCK B: LOW WATER
Stratum 1 Stratum 2
Cdaily = 1,533 137
5,152 110
907 2,192
Cdaily = 2,530.67 kg 2Cdaily
= 813.00 kg2
VE= 1,750,503.45 kg
2
Vu = 475,471.00 kg
2
Stratum 3
65
43
Cdaily =
54.0 kg2
VE= 121.00 kg
2
Stratum 3
21
13
Cdaily =
17.00 kg2
VE= 16.00 kg
2
_ _ _ I .
Thus, for the present data, Cannual daily = (0.59) (2,261.60) +
(0.41) (3,360.67) = 2,712.22 kg.
Total annual catch (C) = Cannual daily X 365 days = 989,960 kg.
The variance of Cannual daily (Vc annual daily) is calculated as the
weighted sum of the values
of V so that Vc annual daily
= (0.59)2
(257,433) + (0.41)2 (2,225,990) = 463,801 kg
2
. The standard error
of Cannual daily =/VC annual daily =/463,801= 681.03 kg/day. The
standard error of C = 681.03 kg/day X 365 days = 248,576 kg.
The RSE for C is (248,576 kg/989,960 kg) X 100 = 25.1 percent.
Final Calculations of E and C for 1978
Because the two lower northern tributaries (Rio Cusiana and
Rio Cravo Sur) were not sampled during the 1978 CAS, the
estimates of E and C calculated above must be expanded to
account for the missing rivers. The 1977 frame survey indicated
that for Time Block A, these two tributaries contributed 13
percent of total effort and 10 percent of total catch; for Time
Block B, these tributaries contributed 6 percent of total effort
and 5 percent of total catch. When the time block estimates of
catch and effort for 1978 are expanded upward by these
percentages, estimates of total effort and total catch by time
blocks are:
Time Block A: total effort = 64,541 FEU-days
total catch = 537,758 kg
Time Block B: total effort = 61,793 FEU-days
total catch = 533,608 kg
Summing the above estimates of catch and effort over time
blocks gives the following adjusted values of total annual catch
(C) and total annual effort (E):
C = 1,071,366 kg
E = 126,334 FEU-days
The standard errors associated with the 1978 estimates can be
expanded upward by the same percentages so that the RSE's
previously given remain the same. The annual estimate of U as
previously calculated will be accepted as a representative value
for the entire system. Table 7 gives the final estimated values of
E, C, and U by time blocks and for the entire year.
Verification of Estimate of Annual Harvest (C)
Welcomme (9) found that when annual harvest (C) in metric
tons from various African rivers was plotted against basin area
(A) in square kilometers, the following exponential relationship
was obtained by regression techniques:
C = 0.1326A
0
.
8533
(r2 = 90%),
indicating that basin area is a good predictor of annual harvest.
Welcomme assumed that the harvest estimates available to him
were from river areas where fishing was "sufficiently intense to
attract the attention of fisheries administrators and biologists,"
probably meaning main river channels.
The estimate of total annual harvest from the 1978 CAS on the
Upper Meta River was approximately 1,071 metric tons;
however, only about 751 metric tons were attributable to the
main river channel (Stratum 1). Given that the watershed of the
Upper Meta River is roughly 20,000 square kilometers, Wel-
comme's equation predicts an annual harvest of
C = 0.1326 (20,000)08533 = 620 metric tons,
which is within 20 percent of the CAS estimate of 751 metric tons
from the main river channel. Although the closeness of these two
values does not necessarily verify the accuracy of our estimate in
a true sense, it is reassuring to know that the survey design was
providing reasonable estimates of harvest relative to other
tropical river systems of similar size.
Precision Associated with Estimates of E, C, and U
It is apparent from table 7 that the precision of estimates of E,
C, and U is significantly lower (RSE's are higher) during the low
water period than during the high water period. RSE's less than 20
percent can be considered acceptable for catch assessment
surveys on large aquatic systems (5), although the smaller the
RSE the better. A RSE of 20 percent implies that the 95 percent
confidence interval will be approximately 40 percent of the
mean, which is somewhat large; a RSE of 10 percent gives a 95
percent confidence interval of about 20 percent of the mean,
which is more desirable. The RSE associated with the annual
estimate of E is thus quite acceptable; RSE's for total annual
values of C and U can hopefully be improved. The basic
approach to improving the variability of estimates of C and U
will be to further stratify the hydrological year into more
homogeneous time blocks. Time blocks A and B, although called
the high water and low water periods, respectively, also
included periods of rising and falling water which tended to
make these two time blocks more heterogeneous than desirable.
The following section presents an improved CAS design for the
Upper Meta River, which should improve the precision of
estimates of C and U as well as of E.
TABLE 7. ESTIMATES OF TOTAL EFFORT (E), TOTAL CATCH (C), AND
CATCH PER UNIT OF EFFORT (U) BY TIME BLOCKS AND FOR THE
ENTIRE SURVEY YEAR (1978) ON THE UPPER META RIVER
(RELATIVE STANDARD ERRORS (RSE) ARE ALSO GIVEN)
Item Time Block A Time Block B Annual
C (kg)= 537,758 533,608 1,071,366
(RSE) (22.4%) (44.4%) (25.1%)
E (FEU-days) = 64,541 61,793 126,334
(RSE) (8.7%) (17.6%) (9.8%)
U (kg/FEU/day) = 7.91 8.38 8.10
(RSE) (16.2%) (40.6%) (19.6%)
CAS DESIGN FOR CONTINUED MONITORING
OF THE UPPER META RIVER FISHERY
Sampling designs can vary from relatively simple to highly
complex. The complexity of the design depends on the purpose
to which the survey is directed. Catch assessment surveys (CAS)
on natural aquatic systems are directed toward obtaining
unbiased or accurate estimates of total catch (C), total effort (E),
and catch per unit of effort (U) on an annual basis. The system
may be composed of distinct components, i.e., habitat types,
population groups, and different approaches to fishing, for
which independent estimates of C, E, and U are desired.
Fishery managers are not only concerned with the accuracy of
their estimates, but also with the precision or variability of their
estimates. Highly variable estimates, i.e., estimates with
relatively large standard errors, are of little value for
management or research purposes. To provide relatively precise
and thus useful estimates, the CAS design must take into account
the natural variability within the system. Aquatic systems can be
highly variable because of environmental fluctuations (seasonal
changes for example) and the dynamics (growth, recruitment,
and mortality) of the fish populations. Furthermore, the
fishermen will respond to changes in the biological system as
well as to social, economic, and cultural contingencies, thus
adding another component of variability to the entire system
7
I
Fishermen on the Meta River employ a variety of fishing gear: top
-elderly man displays 'hook-lines' from a small dugout canoe;
bottom -fisherman hurls a 30-foot diameter cast net.
under study, i. e., the fishery. Thus, the CAS design mnay of
necessity be relatively complex to account for, or statistically
control, variability so that accurate and precise estimates of C,
E, and Ui are forthcoming.
'Ihe gains, in terms of accuracy and precision, pr-ovided by an
appropriately complex design mnay, in a real sense, be totally
non-existent if the design necessitates resources (time, money,
and manpower) that cannot reasonably be generated. In this
sense, although gains may be sacrificed, the design should he
practical in terms of government su~pport capabilities; a
workable survey which endeavonrs to mionitor a fishery wxhich is,
or is expected to be, a valuable resource is certainly better than
no assessment at all.
The primary consideration in this prop)osal, in terms of
designing a CAS for continued monitoring of the Upper Meta
River fishery, is that the design be appropriate relative to the
support capabilities of INDERENA. Fortunately, this
consideration does not appear to preclude the opportunity for
obtaining estimates that are precise enough for management
purposes as indicated by the relative standard errors associated
with estimates of C, E, and U from the 1978 CAS (see section on
"Precision Associated with Estimates of E, C, and U,"
page 9). The design presented here drawxs on the results of
the 1978 CAS to stratify the sy'stem in a more efficient manner
relative to the natural heterogeneity of the fishery in time and
space. Although statistical terminology is highly developed, we
hav e endeavored to present the design as simply as possible to
facilitate its understandability and future application.
Division of the System into Time Blocks
and Geographical Strata
Seasonal hydrological fluctuations in the riv er systems of
Colombia have be"en wxell documented, espe~cially on the
Magdalena River (1, 2, 3). These fluctuations are based on
seasonal rainfall patterns which in turn determine biological
patterns associated with the migratory behavior of the fish
populations. Ultimately, the fishermen respond to these cyclical
patterns so that estimates of C, E, and Ul tend to be highly
variable during the hydrological year (defined here to be from
April 1 to March 31). The survey design accounts for this
seasonal variability by dividing the year into relatively
homogeneous seasonal periods corresponding to the
hydrological periods exhibited by the physical/biological
system. Thus, on the Upper Meta River, the following seasonal
strata or time blocks can be defined:
A: rising water (April 1 May 31 =61 days)
B3: high wsater (June 1 November 15 =168 days)
C: falling water (November 16 -December 31 =46
days)
D: low wsater (January 1 -March 31 =90 days)
An indication of the changes which occur between these time
blocks is given in figure 2, which shows seasonal fluctuations in
river depth together with season fluctuations in daily weight
(kilograms) of fish landed at Puerto Lopez (December 1977
March 1979). It is apparent that in terms of weight of fish landed
per day, the shorter periods of rising and falling water represent
tbe most intensiv e periodls of fishing success; the loxv and high
water periods are of lesser importance, with the low water
period producing slightly higher daily yields on the average than
the high wsater period.
V'ariability within the fishery is not only apparent seasonally,
but is also expected geographically as influenced by differing
river habitats, especially wxith reference to the main riser
channel v ersus the tributaries. Unlike the Magdalena System,
backwater lakes (cienegas) are not weldl developed on the Upper
Meta River Sy stem and no fishing effort wxas observed in these
y00
00
900
80o
700
600
500,
400
300
200
00o
A 0 0 D J F MN D0 F M A M
FIG. 2. Relation of Meta River water depth at Puerto Lopez to
quantity of marketed fish, November 1 977-April 1979. Proposed
time blocks (A-D) for fishery surveys are defined.
\ 4
0 ly cath-
Wate, depth -
I I
/
I,
I-
Ir
'lagoons' during the 1977 frame survey. The current design thus
calls for division of the Upper Meta System into only two
geographical strata as follows:
I: Main Meta River
II: Tributaries
The advantages of stratification are two-fold. First,
independent estimates of C, E, and U obtained from each
stratum (time blocks and geographical) may help to
characterize the system in more detail, thus providing a better
understanding of how different components of the system
develop and function relative to one another. Second, because
the strata represent relatively homogeneous segments of the
system, estimates independently obtained within the segments
are expected to be more precise (less variable) than if the entire
system were to be sampled as a whole (4, Chapter 5).
Sampling Within Time Blocks
The practicalities associated with sampling the Upper Meta
River during 1977 and 1978 suggest that it is not reasonable to
expect that more than six samples can be taken within any given
time block. Additionally, the time, manpower, and cost
associated with getting out on the river dictate that it is not
feasible to take only one sample during any given trip, but rather
that two or three samples be taken; that is, two or three sampling
trips should be planned so that a total of six samples is taken
within each time block. It is reasonable to suggest that during the
smaller time blocks (A and C), two trips of three samples each be
planned and during the larger time blocks
(B and D), three trips
of two samples each be planned.
Although the design calls for an equal number of samples
within each time block, because the blocks are of different
duration, sampling intensity actually differs from block to
block. Specifically, sampling intensity on a daily basis is
inversely proportional to the number of days within the time
block. As an example, if the six samples were evenly spaced
throughout each time block, samples would be taken as follows:
Block A: one sample every 10 days
Block B: one sample every 28 days
Block C: one sample every 9 days
Block D: one sample every 15 days
Thus, blocks A and C are being sampled most intensively, which
is justified and desirable because daily fishing intensity is the
greatest during these two periods (rising and falling water).
Block D will be sampled at an intermediate level and Block B at
the lowest level, which correspond to intermediate and low
levels of fishing success as indicated by daily catch rates from
the Puerto Lopez landing, figure 2. This scheme allows more
sampling effort to be expended during the most important
periods of the year relative to daily catch landed. This is logical
in terms of one of the primary goals of the survey, which is to
estimate catch as accurately and precisely as possible.
Theoretically, it is desirable that the sampling periods (the
times during which sampling trips are made) should be
randomly chosen within time blocks. However, past experience
dictates that this is an unrealistic expectation since allocation of
funds for field work will require an average of 3 to 4
weeks between survey trips. In lieu of randomization, then, it is
suggested that sampling trips be as evenly spaced as possible
within each time block. Because the exact dates of the annual
hydrological periods will vary from year to year, it is further
suggested that sampling trips within time blocks be scheduled
according to observed changes in water level on the river rather
than following preconceived fixed dates which may not be
applicable in any given year.
Sampling Within Geographical Strata
There are two geographical strata, Main River (I) and
Tributaries (II), within each time block. Thus, the six samples
within any given time block must be allocated to Stratum I and
Stratum II. Cochran (4, p. 98) gives three basic criteria for
allocation of sampling effort: Within a given stratum take a
larger sample if (1) the stratum is larger, (2) the stratum is more
variable internally, and (3) sampling is cheaper in the stratum.
These three criteria can be combined into a simple formula
which basically says that relative sample size for a given stratum
relative stratum size X relative variation
- relative cost
Table 8 gives values of relative stratum size, relative variation,
and relative cost associated with the main river and tributary
strata as estimated from the 1978 CAS. The appropriate measure
of relative stratum size is taken to be the fraction of the total
annual catch provided by each stratum; relative variation is
measured as the coefficient of variation (CV) of total estimated
catch; and relative cost is the fraction of total cost attributable to
sampling each stratum (on a per sample basis). It is evident from
the table that internal variation (CV) and relative cost per
sample (CS) are roughly the same for the two strata so that
relative sample size (RS) becomes primarily a function of
relative catch (CA). The values for relative sample size show
that roughly twice as many samples should be taken in the main
river stratum as in the tributary stratum (0.23 2 X 0.13). Given
that six samples are to be taken within each time block, the
above information dictates that four samples should be taken
from the main river stratum and two samples from the tributary
stratum. This allocation of sampling effort is optimum in terms
of relative size, variation, and cost per sample within the two
respective strata.
TABLE 8. VALUES OF RELATIVE CATCH (CA), RELATIVE VARIATION (CV),
AND RELATIVE COST PER SAMPLE (CS) FOR THE MAIN
RIVER AND TRIBUTARY STRATA (RELATIVE SAMPLE
SIZE (RS) = CA X CV/'S)
Stratum CA CV CS RS*
I: main river ............ 0.65 0.66 0.47 0.25
II: tributaries ............. .35 .70 .53 .13
*RS values can only be interpreted relative to one another, i.e., roughly twice as
many samples should be taken in Stratum I relative to Stratum II.
Choosing River Sections and Tributaries
for Sampling Purposes
Thus far, the sampling design calls for taking six samples
within each time block, two of which will be tributary samples
and four of which will be main river samples. Thus, within each
time block, two tributaries and four river sections must be
chosen. Statistical validity dictates that tributaries and river
sections should be chosen at random. It is logical that the more
important tributaries, and likewise the more important river
sections, should have a greater chance or probability of being
chosen than areas of lesser importance. It is also logical that these
probabilities should be proportional to the intensity of fishing
exhibited in these areas. The easiest measure of fishing intensity
is fishing effort expressed as number of canoes (or number of
fishing economic units). However, where the relative number
and kinds of fishing gear per canoe differ within the system, the
FEU as a unit of effort can be misleading. In this case, relative
catch would be a better measure of relative fishing intensity
11
Alb
I
4tw
'-a-,.j
-~
MIII
wxhere catch is a function of both number of canoes and] the
fishing powxer per canoe (as wxell as all other env ironinental
factors wxhich might cause differences in abundance
or
catchability of fishes betwveen sampling units).
Catch data are available for the Upper MIeta River and its
tributaries from the 1977 and 1978 survecys.
Sampling
probabilities can thus be based on the relativ e catch,
or
percentage of total catch, contributed by each tributary
within
the tribuitary' stratumn and each section wvithin the mai n risver
stratum. These probabilities are given in table 9. The Upper
Meta River xvas divided into six sections svhich we re each given
an equal probability of being chosen for any gixven sample
because the previous surv ey indicated that catch wxas fairly
esvenly distributed along the entire uipper 111am river
channel.
TLE 9. PHO011-1 iIFS ANM) HA \noxi V ABEH R.A\;F s Fol H'ANi)OMii
(iiooSiN. \F I A HixiEli SFC l IONS (S-1 AR xI \
ANM) 1\1)1\ IM) AL 'M 111IAHIFS (Sl-i' t xiii1),
BAvsri oN\ i\ IA GvFCi-c ii
His er section or tribmitarv
Probabiit) Rnmr
Stratum I
1: Boca (;max mriba - Pto. Lopezi.......
2: Pto. Lopez Boca bipia .............
3: Boca I. ia Pto. Cuadal tpe...........
4: Pto. Guadaluipe -Boca \lanacacias ...
5: Boca \!anacacias - San Pedro ........
6: San Pedro -Orocue ................
Stratum 11
1: 1Ithnnea...............................
2. Tua.............................
3: Pajmire ...........................
4: \Ietica ..........................
5: Cmiasuriba .......................
6: l'pia ............................
7: Socao ...............................
8: \anacacias ......................
9: ('msiana .........................
10: (raxo Stir .......................
1-17
18-34
35-51
.52-68
69-85
86-00
19
10-56
57
58-68
69-73
74-81
82-84
85-89
90-95
96 (0O
Riverside homes of fishermen are left high and dry during the low
water season. During the high water season, these homes will
frequently be inundated to depths of 12 meter or more.
Probahilities associated wxith indiv idual tributaries vary
considerably depending on their independent contributions
to total catch. Table 9 also gives the randlom numbnler ranges
app~ropriate for the giv en probabilities. That is, wxhen a tributary
or mnain riv er section is being randomnly chosen for sample, the
randomn number chosen from a randomn number table (betwxeen
1 and] 100) wxill necessarily fall into one of the ranges given in
table 9: that particular range can then be associated with a
particular tributary or riv er section using the table. Thus, for
each timie block, four randomn numbers wxill be chosen to give
four river sections wvithin Stratum I and two random numbers
w~ill be choseni to giv e t Io tributaries wvithin Stratumi 11. This
T.srn~i 10. TiIE 1980 SAMm iN(. S OF XLI O\ ITHF UPIT Mto Mi I Ri\ H
(Ioms 11)1 ki, Ri ER SE I I IONS ANDI) 'T ARIES COiosl NA'] R.A~ioxi
t'IM IN1 HEO PIM01 Atl BIi~is OVxEN I\TA I lo F)
imeo block Stratm 1: M eta RiveCr* Stratum II: tributaries
A I Upba
5 'Ilnt
Craxo Stir
IIuiiiea
lua
liia
kan acacias
I Iilitl
0 Riser section numbers correspond to those given iii table 9.
* -*0
random sampling procedure (nonuniform probability sam-
pling) was conducted to give the sampling schedule on the
Upper Meta River for 1980, which is shown in table 10.
PROPOSED METHOD OF CONDUCTING INITIAL
SURVEYS OF OTHER MAJOR RIVERS IN
LLANOS REGION
Initial Surveys
Nonuniform probability stratified random sampling can be
applied to initial surveys of river systems other than the Upper
Meta by the use of seasonal time blocks and geographical strata
proposed in the previous section. Probabilities can be based on
canoe (FEU) counts made during overflights of the proposed
study areas prior to initiation of actual surveys. Time blocks can
be defined based on Meta River information, assuming that
similar hydrological cycles exist in all areas of the Llanos
Orientales and that communities of fish and fishermen also
respond in a similar manner. In new areas of study (the main
Orinoco River or the Inirida River, for example) the initial year
of sampling would entail allocating two-thirds of sampling effort
to a main river stratum and one-third to a tributary stratum as
proposed for the Upper Meta River.
A practical sampling unit (SU) within a main river stratum
might be a 50-kilometer section of main river, and sampling units
within the tributary stratum can be defined on an individual
tributary basis. The probability of sampling any given SU within
a stratum will be proportional to the number of canoes counted
in the pre-survey overflight in relation to the total number of
canoes in the entire stratum. Tentatively, four samples could be
taken in a main river stratum and two samples in a tributary
stratum as suggested for the proposed Upper Meta River survey
(page 11). Resulting data can be analyzed using the detailed
methods presented in the section beginning on page 6.
Follow-up Surveys
The decision to: (1) use a sampling fraction of two-thirds in a
main river stratum and one-third in a tributary stratum, (2) use
only the two strata described above, (3) use aerial canoe counts
to determine sampling probabilities, and (4) use four seasonal
time blocks as previously defined, are based on results of the
Upper Meta River survey and on the feasibility of obtaining
canoe counts from overflights. After the initial year of a CAS in a
given study area, the creation of new sampling probabilities will
probably be warranted for future surveys. These new prob-
abilities and possibly new time and space strata will serve to
increase the precision of the resulting estimates of catch, effort,
and catch per unit effort. Thus, as more reliable information
becomes available, this information should be used to improve
the sample survey designs.
It is proposed that all major rivers of Colombia's Orinoco
System other than the intensely sampled Upper Meta System
be surveyed once in the next 10 years. We propose that catch
assessment surveys be carried out in the following order:
1978 Upper Meta River (completed)
1979 Upper Guaviare River (in progress)
1980 Upper Meta River
1981 Lower Meta River
1982 Upper Meta River
1983 Lower Guaviare River
FIG. 3. The Colombian Orinoco River System showing proposed
cycle of catch assessment surveys over the 10-year period, 1979-
89.
1984 Upper Meta River
1985 Orinoco River and the tributaries Vichada and Tomo
rivers
1986 Upper Meta River
1987 Inirida River
1988 Upper Meta River
1989 Arauca River
These river systems and proposed cycling of survey work are
shown in figure 3. As can be seen by the above 10-year survey
plan, the Upper Meta River will be sampled in alternate, even-
numbered years and other systems during odd-numbered
years.
This schedule will provide continuing information on the Upper
Meta River so that short-term changes in the development
of the
fishery can be monitored. The other river systems, which
we
assume to presently have less important fisheries than the Upper
Meta, will be sampled much less frequently, but adequately,
considering their assumed lower level of exploitation and slower
rate of development.
It is hoped that after 1989, if sampling and administrative
logistics improve, areas such as the Upper and Lower Meta,
or
the entire Guaviare and Inirida, can be incorporated into a single
survey region so that the second round of surveys necessary for
completion of surplus yield models (described in the following
section) can be carried out more rapidly.
USE OF THE GRAHAM-SCHAEFER SURPLUS
PRODUCTION MODEL FOR MANAGEMENT OF THE
UPPER META RIVER FISHERY
Surplus yield models are particularly valuable in the early
stages of a fishery investigation to make preliminary appraisals
before more biological data are available. They are
also
important when biological data are scanty or nonexistent, but
catch and effort data can be obtained. Their greatest advantage
is that they require only catch and effort data for their
13
Substantial catch of large catfishes arriving at the Puerto Lopez
municipal landing. The large fish being weighed is a valenton.
application. The other primiary approaches to optimizing
exploitation are the dynamic pool models, which attempt to
describe an exploited population in terms of the basic
parameters of recruitment, growth, and mortality. These
paramneters are typically difficult and expensive to measure and
in certain situations may not be measurable at all, such as with
age and growth relationships in tropical ecosystems.
The Graham-Schaefer surplus yield model postulates that
recruitment, growth, and mortality are dependent on the fish
population biomass (density dependent) such that these
parameters can all be combined into a single common function.
This function predicts the rate of population change based solely
on the mean population size during a period of time when the
population is stable or in equilibrium with the fishery, i.e., rates
of growth and recruitment are exactly balanced by rates of
natural and fishing mortality. M\lean population size is, in turn,
assumed to be a function of fishing pressure; thus, a given
population size or biomass has associated with it a certain level
of fishing effort. The population size and its associated level of
fishing effort determine the amount of yield available to the
fishery. In a biological sense, this yield is the biomass over and
above that needed to exactly replace the population and is thus
termied surplus yield or surplus production.
In theory, yield is taken to be a parabolic function of stock
biomass as indicated in figure 4. The maximum stock biomass
(B...ax) is the carrying capacity of the environment, or the
population size which can be supported prior to the advent of
fishing. Fishing acts to reduce B,a to some lower biomass (B)
and the population then responds by producing surplus biomass
in an effort to return to Bmax. This surplus biomass is available to
the fishery as yield and if this surplus is harvested, the
population biomass will remain stable at B. It is evident from the
hypothetical curve in figure 4 that maximum surplus yield is
attainable when the population biomass equals Bm,/2 or 50
percent of the carrying capacity of the unfished system. When B
is reduced below Bm.ax/2 by fishing, the yield falls below the
maximum sustainable yield (MNISY), and if fishing pressure is
not great enough so that B is greater than Bmax/2, then yield again
falls below MISY.
In terms of regulating a given fishery', it is obviously
desirable to know B,,ax/2. More importantly, it is desirable to
know the level of fishing effort associated with Bma/2. This level
of fishing effort is the optimum level for the fishery (EoePT) and,
if maintained, will theoretically provide MSY. Fortunately, it has
been shown mathematically (6, section 13.3) that Eoepr can easily
be determined by simply obtaining values of catch per unit
effort (kilograms of fish caught per fishing unit U) and effort
(E) during at least two periods when the fishery has stabilized,
i.e., during at least two periods in which effort is constant, or
changing only gradually. These periods should reasonably be at
least 3 years in duration to ensure that the fish community utinder
exploitation has come into biological equilibrium with the fish-
ery. When the equilibrium values of U are regressed against the
equilibrium values of E for the two (or more) equilibrium
periods using the linear equation U = a - bE, then EOPT = a/2b.
That is, the optimum level of fishing effort simply equals the y-
FIG. 4. Diagram depicting yield as a parabolic function of stock
biomass. Maximum sustained yield (MSY) and optimum fishing
effort (E) are attained at Bax/2. See text for explanation.
MSY
BMAX/2 BMAX
(EOPT)
Stock Biomoss
Improvement of the road from Puerto Lopez to Villavicencio will
increase accessibility of fish harvested from the Upper Meta River
to population centers in Villavicencio and Bogota. As a result,
fishing pressure will likely increase dramatically in the near future.
intercept (a) divided by 2 times the slope (b) where a and b are
determined from the linear regression equation. Additionally,
the maximum sustainable yield can be calculated as MSY
a
2
/4b.
The general difficulty with using the above approach is that
the development or expansion of the fishery may be so rapid that
equilibrium periods, or periods when effort is relatively constant
for a minimum of 3 years, may not be forthcoming. I lowever, it
appears that the commercial fishery on the Upper Meta River
has remained stable over the past few years so that the estimates
of E and U from the 1978 CAS can be used as the first set of
equilibrium values. These values (rounded off), from table 7,
are:
E = 126,300 ? 12,400 FEU-days
U = 8.10 ? 1.60 kg/FEU/day
It is likely that a second set of equilibrium values of E and U
will be forthcoming in the near future with the paving of the
road from Villavicencio to Puerto Lopez. Improvement of
transportation systems stimulate increased supply and demnand
and eventually lead to increased exploitation of the fishery
resource. When the road from Villavicencio to Puerto Lopez is
paved, the ease with which fish can be transported to
Villavicencio and Bogota will be greatly increased. The demand
for fish is high in these areas and because fish prices increase as
distance from the resource increases, fishermen will be
encouraged to increase fish supply, i.e., to increase exploitation.
Th ultimate predicted result is that fishing effort will take a
quantumn leap on the Upper Meta River when the road is paved;
the situation will then be ideal for obtaining another set of
equilibrium values of E and 1' (assuming that the fishery again
stabilizes). It thus appears that the current situation, in terms of
future development plans in the Llanos Orientales, is ideal for
use of the surplus yield model as a management tool.
It should be stressed that, given the present state of
knowledge concerning the dynamics of the fish community in
the Meta River, the surplus yield approach is the only method
available for estimating an optimal level of fishing effort and its
associated MSY. The method may be overly simplistic, but it has
been applied to multi-species stocks in African lakes with
promising results (8).
REFERENCES
(1) BAzi(;()s, (. P., J. M. KAPETSK A\ Ni) J. iA\A ()Dos. 1975.
Integrated Sampling Designs for the Complex Inland
Fishery of the Magdalena River Basin, Colombia.
FI:)DP/COL/72/552 Working Paper No.4. 58 pp.
(2) , Ax)nJ. Es(m)BAI 1977.
The Present State of the Fishery of the Magdalena River
Basin, Colombia. FI:DP/COL/72 552 Working Paper
No. 2. 30 pp).
(3) Cii\I'si\, 1). V . 1977. Total lHarvest and Economic
Value of the Fisher of the Rio Magdalena and Flood
Plain System. Final Report to FA()O/C(OL 552.
(4) ConIt \,, w. G. 1977. Sampling Techniques. John
WViley and Sons, New York. 428 pp.
(5) MAIAES'I' To S. P., %V. D. DAVIES. AN)\W. L. SIIELTON.
1978. An Evaluation of the Roving Creel Survey with
Nonuniformn Probability Sampling. Trans. Am. Fish.
Soc. 108:257-262.
(6) RItCKElt, W. E. 1975. Computation and Interpretation of
Biological Statistics of Fish Populations. Fish. Res. Bd.
Can. Bull. 191. 382 pp.
(7) Sc i,,. H. J., J. F. G(;HAZ ,, M. A. Tolmu,:s \ ) M. C.
B1_\(:() 1980. Management of the t'pper Meta Hiver
Food-Fish Fishery. 'pper Meta River Investigations
(Part 1) Report to INDERENA, Bogota, Colombia,
USAID, AID/LA-C-1176. 110 pp.
(8) T \iI J. L. 1978. Status of Various Multispecies Fish-
eries of Lake Victoria, Tanganyika and Malawi Based on
Catch and Effort Data. Pages 4-15 in R. L. X\ elcominme,
ed. Syn i)posium on River and Flood Plain Fisheries in
Africa. CIFA Technical Paper No. 5. Food and Agricul-
tural (O)rganization of the United Nations, Rome, Italy.
(9) RVElcotitE, 1. L. 1976. Some General and Theoretical
Considerations on the Fish Yield of African Rivers. J.
Fish. Biol. 8:351-364.