Sigmoid Selection and the Beverton and Holt Yield Equation

Abstract

The analytic or yield-per-recruit model of R.H. Beverton and S.J. Holt has gained wide utility in both temperate and tropical situations since its introduction in the 1950s. The model is currently applied to fish stocks with widely different growth and mortality coefficients and longevities, with the usual assumption of knife-edge selection. We examine the effect of replacing the conventional knife-edge assumption with sigmoid selection. An expression incorporating sigmoid selection is presented with relative yield per recruit expressed as a function of E {= F/Z), C {= Lsof4.,), MIK and se lection range, defined by AC = {L75 - L50)/L_, The relative differences between the yield isopleths using knife-edge selection and those obtained using sigmoid selection are evaluated using various plausible values of M/K, C and selection range. The results indicate considerable bias generated by the knife-edge assumption in yield-per-recruit analysis applied to short-lived, tropical species {i.e., low 4.,) where the selection range usually covers a large fraction of the population size distribution.