Fish Population Dynamic and Stock Assessment

4.2.3.2. Correlation of ‘M’ with longevity of fishes (Pauly’s method)

The growth co-efficient in fishes is closely linked with their longevity. In nature, the oldest fishes of a given stock grow to about 95 percent of their asymptotic size length. Thus,

Lt = L$$\infty$$(1-e^-k(t-t_o⁾)

t-t₀ = $${log_e({1-{L_t\over L_\infty}})\over -k$$

If 95 percent of L$$\infty$$ is inserted for the oldest fish

t – t_o =$$2.9977 \over -k$$

$$t max \approx {3 \over K}$$

‘t max’ is the longevity of the fishes in question.

Thus, natural mortality is correlated with size, since large fishes should have, as a rule, fewer predators than small fishes.