Cultural and biological evolutionary processes: gene-culture disequilibrium

The dynamics of the interaction between genetic and cultural transmission are studied by using a simple two-phenotype diallelic haploid genetic system. The value of an individual's phenotype is determined by cultural transmission from its parent or by a randomly chosen member of the parental population. In the absence of phenotypic selection, polymorphic equilibria of the gene and trait frequencies are obtained. The correlation between genotype and phenotype within or between populations depends on a quantity formally similar to linkage disequilibrium and is determined by a relationship among transmission coefficients analogous to a coefficient of epistasis. With natural selection on the phenotype and no mutation, only degenerate transmission rules allow polymorphic equilibria to be attained, and, in general, the genotype allowing the strongest transmission of the favored phenotype is successful.