AGE AND GROWTH OF THE CISCO 
291 
Table 69. — Theoretical values of the coefficient of condition ( K ) at different body lengths, calculated 
from equations based on 1981 collections 
Length in millimeters 
130 
140 
150 
100 
170 
180 
190 
200 
210 
220 
230 
250 
270 
290 
310 
330 
350 
370 
390 
1. 332 
1. 266 
1. 207 
1. 154 
1. 107 
1.064 
1. 025 
0. 989 
0. 956 
0. 926 
0. 898 
1.397 
1. 302 
1. 220 
1. 147 
1. 083 
1.026 
.975 
.928 
.886 
.848 
.813 
1. 122 
1. 160 
1. 197 
1. 232 
1. 267 
1.300 
1.332 
1.357 
1.394 
1.424 
1.453 
Clear (females) 
1. 077 
1. 131 
1. 182 
1.233 
1.283 
1.331 
1.379 
1. 426 
1. 471 
1. 517 
1. 5G1 
1. 648 
1.733 
1.815 
1.895 
1.974 
2.051 
2. 126 
2.200 
The remarks, made previously (p. 246), concerning the validity of using length- 
weight equations for the calculation of unknown lengths or weights outside the range 
of the empirical data apply likewise to the calculation of unknown values of K for 
lengths outside the range of empirical data. However, it may be pointed out further, 
on purely mathematical grounds, that the K equations cannot possibly be used for 
the calculation of K values in very small fish, since as length approaches zero the 
values of K increase without limit in the equations with negative exponents and 
approach zero in the equations with positive exponents. 
In the 1931 K equations it may be seen that the order of the four populations 
with respect to the value of the exponent, m, which describes the rate of change of K 
with change of length, is: Muskcllunge Lake, Trout Lake, Silver Lake, Clear Lake. 
The differences in these rates of change are reflected in the forms of the curves of 
figure 10. Here it may be seen that the Muskellunge Lake cisco loses condition 
rapidly with increase in length. The Trout Lake cisco also loses condition with 
increase in length, but at a slower rate than does the Muskellunge Lake cisco. In 
Silver Lake the condition of the cisco improves with increase in length, although this 
improvement is not as rapid as it is in the Clear Lake cisco. The courses of the curves 
indicate further that at a length of between 150 and 160 millimeters the conditions of 
all four populations are closely similar. 
If the above facts are examined in relation to the growth rates of the four popu- 
lations it may be seen that, while the Clear Lake cisco with the most rapid growth 
shows the most rapid progressive improvement in condition, the Trout Lake cisco 
with the least rapid growth does not show the most rapid loss of condition. Although 
the Muskellunge Lake cisco shows better growth than the Trout Lake cisco with 
respect to both length and weight, the loss of condition with increase in length pro- 
ceeds considerably more rapidly in the former population. This fact demonstrates 
at least a partial independence between the factors that determine growth rate and 
the factors that determine condition. Further, the fact that the factors which bring 
about a rapid loss of condition in one population may fail to reduce the growth rate 
of this population below that of a second stock with a less rapid loss of condition 
may be construed as a strong argument for the operation of the “space factor” in 
the determination of growth rate. 
The data of table 68 show that the arrangement of the four lakes with respect 
to average condition and the rate of change of condition follows the reverse order 
of their arrangement with respect to the average abundance of the organic matter 
in the surface samples of plankton. (The greater number of these plankton sam- 
ples were taken during the summer months.) Although the abundance of organic 
matter in surface samples of plankton may not serve as a wholly reliable index of the 
abundance of plankton forms most commonly taken by the ciscoes and in the strata of 
