BEVERTON AND HOLT LIFE-HISTORY INVARIANTS RESULT FROM OPTIMAL TRADE-OFF OF REPRODUCTION AND SURVIVAL

The Beverton and Holt invariants are three special relations among lif e history parameters: Mx(m) = C-1, M/K = C-2, and L(x(m))/L(inf) = C-3 , where M is the instantaneous natural mortality rate per individual, x(m) is age at maturity, K is the von Bertalanffy growth coefficient, L(x(m)) is length at maturity, L(inf) is asymptotic length, and C-1, C -2, and C-3 are constants. In this study the Beverton and Holt invaria nts were obtained from maximization of the fecundity function that opt imizes the trade-off between survival and fecundity; this approach app lies conventional fishery models and provides estimates of the constan ts C-1, C-2, and C-3. These estimates can be compared with the estimat es obtained by regression of 1/M on x(m), M on K, and L(x(m)) on L(inf ) across species and across populations within species. The values of the constants obtained from regression across species agree closely wi th the theoretical values of the constants. In fishery assessments, na tural mortality is often approximated using growth parameters, and the analyses reported here indicate that the relations are not just stati stical relations, but rather result from fundamental ecological relati ons among the parameters.