CONDITIONS FOR POSITIVE AND NEGATIVE CORRELATIONS BETWEEN FITNESS ANDHETEROZYGOSITY IN EQUILIBRIUM POPULATIONS

The past decades have witnessed extensive efforts to correlate fitness traits with genomic heterozygosity. While positive correlations are r evealed in most of the organisms studied, results of no/negative corre lations are not uncommon. There has been little effort to reveal the g enetic causes of these negative correlations. The positive correlation s are regarded either as evidence for functional overdominance in larg e, randomly mating populations at equilibrium, or the results of popul ations at disequilibrium under dominance. More often, the positive cor relations are viewed as a phenomenon of heterosis, so that it cannot p ossibly occur under within-locus additive allelic effects. Here we giv e exact genetic conditions that give rise to positive and negative cor relations in populations at Hardy-Weinberg and linkage equilibria, thu s offering a genetic explanation for the observed negative correlation s. Our results demonstrate that the above interpretations concerning t he positive correlations are not complete or even necessary. Such a po sitive correlation can result under dominance and potentially under ad ditivity, even in populations where associated overdominance due to li nked alleles at different loci is not significant. Additionally, negat ive correlations and heterosis can co-occur in a single population. Al though our emphasis is on equilibrium populations and for biallelic ge netic systems, the basic conclusions are generalized to non-equilibriu m populations and for multi-allelic situations.