Fish Population Dynamic and Stock Assessment

6.5.3. Ricker bell shaped curve

In Ricker’s model it implies that if a stock becomes very large number of recruits, are reduced. The plotting of parent stock and recruits is more bell shaped. Further this model emphasize that a relationship between the parent stock and recruitment stock exists for all size of the spawning stock and that there is an optimum spawners stock size.

The formula used to establish relationship between parent stock and recruit stock.

R=Pr^a(1-P/Pr) ………………………………………… (1)

R = number of recruits

P = number of parents

Pr = Replacement of parent stock i.e. where P=R.

$$e^{a(1-P/Pr)}= R/P$$ …………………………………….. (2)

$$a(1-P/Pr) = \log_{e} (R/P) = \log_{e} R-\log_{e} P$$ ……….. (3)

$$\log_{e} R-\log_{e} P = a-(a/Pr) * P$$ ……………………. (4)

The above equation of linear form with a negative relationship of the type

$$Y = a-bx, Y = \log_{e} R-\log_{e} P, X = P.$$