Maintenance of genetic polymorphism under conditions of genotype-dependent growth and size-selective mortality

Abstract

Associations between heterozygosity at one or more electrophoretically detected enzyme loci and growth rate have been reported for several species of plants and animals, including several commercially important species of finfish and shellfish. The general pattern is for heterozygotes to grow faster than homozygotes, although there is some variation in growth response even within a species. Regardless of the physiological or biochemical basis of genotype-dependent growth, polymorphism at a locus affecting growth rate in an overdominant manner may be lost if larger individuals have a greater mortality rate than smaller ones. In an exploited population, mortality of this sort is likely to result from size-selective fishing pressure. Using a continuous-time single-locus model of natural selection, we have related the maintenance of polymorphism at a locus to two measures of fishing effort: β, the legal minimum size below which there is no mortality, and f, an instantaneous mortality rate owing to fishing (above the legal minimum size). We considered two different models of fishing mortality. In model 1, fishing mortality above the legal minimum size is constant; in model 2, fishing mortality is a linear function of size (above β). Numerical analysis of model 1 indicates that maintenance of polymorphism requires either a low rate of fishing mortality or a value of β that is close to zero or close to the maximum attainable size. Analysis of model 2 gives similar results, suggesting that the conclusions are not dependent on the exact form of the mortality function.Key words: heterozygosity, growth, size, mortality.