Fish Population Dynamic and Stock Assessment

7.2.2. Equation

The relative yield per recruit is defined by

(Y/R)' =$$ E * U^{M/K}*[1-{3U\over{1+M}}+{{3U^2}\over{1+2M}}+{{3U^3}\over{1+3M}}]$$

 

Where

M =$${1-E}\over{M/K}$$ =$$K/Z$$

U = 1 -$${Lc}/{L\infty}$$

E = $$F/Z$$

The (Y/R)’ is mainly attributed to U and E. The needed parameters are M/K. The values (Y/R)’ could be plotted with values of E ranging from 0 to 1, with corresponding F values from 0 to $$\infty$$ . A curve thus obtained gives a maximum value of EMSY for a given value of Lc. Thus knowing Lc, L$$\infty$$ and M/K for a certain fishery, the E exploitation rate can be compared with EMSY level. Accordingly, better management strategies could be proposed.

Yield per recruit from length data when L$$\infty$$ and Lr are known instead of , and , the Y/R from length data could be obtained

Y/R = F * A * W$$\infty [1- {1\over Z} - {{3U}\over{Z+K}} - {{3U^2}\over{Z+2K}} - { {3U^3}\over{Z+3K}}]$$

Where U = 1 – $${Lc}/{L\infty}$$

A = $$[L\infty - {Lc}/{L\infty} - Lr]^{M/K}$$