Morphometry of Tuna— SCHAEFER 
117 
some attempt to take this into account in their 
key. 
In order to establish the morphometric char¬ 
acteristics of the stock of yellowfin tuna off 
Costa Rica, for subsequent comparison with 
stocks from other parts of the Pacific, I have 
computed for each dimension measured the 
linear mean-square regression on the total 
length, or on the length of head in the cases 
of length of maxillary and diameter of iris. 
Where the rate of increase of the character 
measured is not proportional to the rate of in¬ 
crease of the total length, that is, where the 
original variables do not yield a linear regres¬ 
sion, a transformation of variables has been 
made so that the new variables yield a linear 
relationship. This was necessary in three cases. 
The rate of increase of length of second dorsal 
and of anal fins is greater than that of total 
length, while the rate of growth of the pectoral 
fin is less than that of total length, over the 
range of sizes examined. 
The statistics describing the regressions are 
tabulated in Table 2. The linear mean-square 
regression is completely specified in each case 
by the means of the two variables, the number 
of specimens, the regression coefficient, and the 
standard deviation from regression. The latter 
is also called the standard error of estimate by 
some authors. Where the regression of the orig¬ 
inal variables is linear we have also tabulated 
the value of the y intercept in order to facili¬ 
tate determination of whether the dependent 
variable may be considered to be in constant 
proportion to the independent variable. 
Over the range of sizes considered, all the 
characters measured, with the exception of the 
lengths of the pectoral, second dorsal, and anal 
fins, bear a linear relationship to the length of 
the fish. That is, the rate of increase of each of 
the dimensions, with these exceptions, is pro¬ 
portional to the rate of increase in total length. 
The proportion of the dimension considered to 
the total length will be constant in a given case, 
however, only if, in addition, the y intercept of 
the regression line is zero. If the intercept dif¬ 
fers from zero, the value of the proportion will 
vary with the size of the fish. Only for the re- 
TABLE 2. STATISTICS DESCRIBING REGRESSIONS OF BODY PROPORTIONS OF YELLOWFIN 
TUNA FROM COSTA RICA 
INDEPENDENT 
VARIABLE X 
DEPENDENT VARIABLE y 
X 
y 
ry.x 
b 
a 
N 
Total length 
Head length. 
931.6 
261.4 
4.39 
0.2350 
37.8 
46 
Total length 
Snout to insertion first dorsal fin.... 
951.6 
282.2 
5.35 
0.2635 
31.5 
46 
Total length 
Snout to insertion second dorsal fin 
951.6 
503.0 
11.45 
0.4768 
49.4 
46 
Total length 
Snout to insertion anal fin. 
951.6 
563.0 
7.58 
0.5351 
53.8 
46 
Total length 
Total length 
Greatest body depth . 
Pectoral insertion to insertion first 
951.6 
243.5 
7.60 
0.2555 
0.4 
46 
dorsal. 
955.1 
144.5 
5.83 
0.1469 
4.2 
44 
Total length 
Length base first dorsal.... 
958.1 
222.4 
10.15 
0.2358 
-3.5 
45 
Total length 
Length longest (first) dorsal ray. 
948.7 
112.8 
5.22 
0.1178 
1.2 
45 
Total length 
Length longest dorsal finlet. 
951.6 
30.9 
2.00 
0.03361 
-1.1 
46 
Log total length 
Log total length 
Length pectoral fin... 
2.9640 
253.5 
7.52 
445.9 
1.694 
45 
Log length second dorsal fin. 
2.9640 
2.1361 
0.0362 
45 
Log total length 
Log length anal fin. 
2.9668 
2.1711 
0.0414 
1.832 
44 
Length second dorsal fin 
Length anal fin . 
151.2 
164.9 
17.62 
1.150 
-9.0 
44 
Length of head 
Diameter of iris. 
266.8 
33.7 
1.303 
0.06038 
17.6 
35 
Length of head 
Length of maxillary. 
261.4 
100.3 
2.17 
0.3781 
1.5 
46 
Log total length 
Log weight (kilos) .. 
2.9538 
1.1222 
0.0266 
2.940 
93 
Logarithms are to the base 10. 
x_— mean of values of x. 
y = mean of values of y. 
ry.x = standard deviation from regression (standard error of estimate), 
b = regression coefficient of y on x. 
a = y intercept of regression line. 
N = number of specimens. 
