Champagnat and Pianet’s® growth curve for Atlantic 
bigeye tuna. 
The estimated total number of bigeye tuna caught by 
the American fleet in 1968 and 1970-74 ranges from about 
500 to 41,200 fish. The largest catch was in 1974, the 
smallest in 1968. 
SOURCES OF BIAS IN THE ESTIMATES 
Several possible sources of bias in the sampling, 
weighting, and substitution procedures could have sig- 
nificantly influenced the estimated length-frequency dis- 
tributions of the catches. Some of the sources are dis- 
cussed below. 
Sampling Bias 
Hennemuth (1957) found a slight  size-depth 
stratification of skipjack tuna but none for yellowfin tuna 
in wells he examined. He mentioned that stratification 
could result from settling of large fish to the bottom of 
the well or from different schools of fish of different sizes 
packed in a layer fashion. 
Early in our sampling program, size-depth stratifica- 
tion was recognized as a possible source of error and steps 
were taken to reduce the influence of this error by 
limiting sampling to wells that did not appear to contain 
fish that were stratified by size and depth. How effective 
this measure was is not known. 
A more serious sampling bias was introduced in 1970 
with the discovery that tunas, particularly large speci- 
mens, contain high levels of mercury which the Food 
and Drug Administration of the United States deemed 
unacceptable for U.S. markets. Canneries in the United 
States, therefore, limited their purchases of large fish, 
and American fishermen were forced either to not land 
large tunas or to sell the large tunas to foreign markets 
where the acceptable level of mercury contamination was 
higher. Because large yellowfin and bigeye tunas caught 
off Africa in 1970 and 1971 were selectively sold and 
transshipped from west African ports directly to foreign 
buyers, fish landed in the United States were biased 
towards the smaller fish. This bias probably affected our 
estimates for 1970. Estimates for 1971 were not affected 
because catches transshipped to foreign ports were 
sampled in west African ports prior to transshipment. 
Weighting Bias 
Some of our length-frequency samples were weighted 
by a factor (number of fish) based on the total tonnage 
and average weight of fish in sets that contributed to the 
catch in the sampled well. As indicated earlier, this tech- 
nique was used because the sample size was not propor- 
tional to the numbers of fish present and the amount of 
tonnage in the well was not known. The use of the total 
tonnage, instead of the tonnage in the sampled well only, 
5Champagnat, C., and R. Pianet. Croissance du patudo (Thunnus 
obesus) dans les regions de Dakar et de Pointe. Unpubl. manuscr., 7 
p. Centre de Recherches Oceanographiques, B. P. 2241, Dakar, Senegal. 
to base a weighting factor introduced a bias of over- 
weighting the samples. For example, a sample from a 
well containing 20 tons of fish from a 80-ton set A and 40 
tons from a 40-ton set B would have a weighting factor 
based on 120 tons, causing the sample to be dispropor- 
tionately weighted by the catch of set A. 
We examined this bias with the August 1973 yellowfin 
tuna catch of area 52 (Table 1) in which the actual ton- 
nages of fish in the three sampled wells were available. A 
biased estimate length composition of the catch was 
derived with weighting factors based on tonnages of 127, 
41, and 17 for the three samples. An unbiased estimated 
length composition of the catch was derived with 
weighting factors based on the actual tonnages in the 
sampled wells of 60, 20, and 15, respectively. The un- 
biased and biased estimated length compositions of the 
catch are not very different (Fig. 5). However, the total 
ix 
ESTIMATED NUMBER OF FISH (x10) 
FORK LENGTH (cm) 
Figure 5.—Estimated length composition of yellowfin tuna caught in 
August 1973 in NMFS area 52. (Solid line — biased weighting fac- 
tors; dashed line — unbiased weighting factors.) 
estimated number of yellowfin tuna is 7% higher in the 
unbiased than in the biased estimate, owing to the 
greater numbers of small fish «61 cm) in the unbiased 
estimate. 
Substitution Bias 
Of all the possible sources of bias in our estimates, sub- 
stitution bias perhaps is the most serious. As indicated 
earlier, 11 to 61% of the strata were not sampled and re- 
quired substitution of samples from adjacent strata. Fur- 
thermore, not all of the sampled strata were sampled 
adequately. Between 20 to 43% of the strata sampled for 
yellowfin tuna and 0 to 33% of the strata sampled for 
skipjack tuna were sampled only once. These samples 
were also used in the substitution procedure, at times 
applied to a large catch (Table 7). 
The effects of our substitution procedure and single 
samples on the estimated length composition of the 
catch were examined with the 1970 data. In that year, 
sampling coverage was poorest. In Figures 6 and 7, we 
show the estimated length composition by month using 
substitutions and also the portion of the composition 
derived from strata with two or more samples only. In 
general, the results indicate that substitutions affected 
