A general stock-recruitment curve

The assumptions underlying the Beverton and Holt and the Ricker stock-recruitment models have been combined, leading to a more general stock-recruitment relationship, $N(t+1)=F[μ1+βN(t)]N(t)exp⁡[−μ1+βN(t)][μ1+βN(t)]+μ2FN(t){1−exp⁡[−μ1+βN(t)]}$ where N(t) is the stock size at time t, F the average fecundity, μ₁ a density-independent mortality rate, and μ² and β density-dependent mortality rates. In the appropriate limits this relationship reduces to the Beverton and Holt or the Ricker relationship. An expression is derived for the change in equilibrium stock size, N, for a given change in mortality, μ₁. An increase in μ₁ invariably leads to a decrease in N. It is also shown that the larger μ² and β are, the smaller the effect a given increase in μ₁ has on N.