Fish Population Dynamic and Stock Assessment

7.3.2. Mean age and size in the yield

When Z is constant from time of recruitment ($$T_r$$) and age at first capture ($$T_c$$) , mean age and mean length in the annual yield could be estimated with the following equation.

$$\overline{T_y}$$ =$$1\over Z+T_c$$

Mean length in annual yield, where $$\overline{T_y}$$ is the mean age in yield

Similarly mean length in the annual yield is $$\overline{L_y}$$ =$$L\infty[1-{z*s}\over{z+k}]$$

S = exp [-K * ($$(T_c - T_o)$$] = 1 -$${L_c}/{L_\infty}$$

$$T_c$$or$$L_c$$ can be replaced by any age from which the fish have a constant mortality, so as to give mean length in that part of population.

Mean weight in annual yield

$$\overline{W_y}$$= Z *$$W_\infty [{1\over Z} – {{3*S}\over{Z+K}}+{{3*S^2}\over{Z+2*K}} -{ {S^3}\over{Z+3*K}}]$$

The three parameters $$\overline{T_y}$$,$$\overline{L_y}$$,$$\overline{W_y}$$ and exploited biomass along with CPUE will decrease by increasing Z i.e. with effort.

In the unexploited fishery, the decrease may be faster for low values of F. In all the three parameters ($$\overline{T_y}$$,$$\overline{L_y}$$,$$\overline{W_y}$$), $$T_c$$forms a common input as $$T_c$$ is determined by mesh size. When the mesh size is large, the mean age and size will be higher.