Fundamental theorem of natural selection under gene-culture transmission

A generalized fundamental theorem of natural selection is derived for populations incorporating both genetic and cultural transmission. The phenotype is determined by an arbitrary number of multiallelic loci with two-factor epistasis and an arbitrary linkage map, as well as by cultural transmission from the parents. Generations are discrete but partially overlapping, and mating may be nonrandom at either the genotypic or the phenotypic level (or both). I show that cultural transmission has several important implications for the evolution of population fitness, most notably that there is a time lag in the response to selection such that the future evolution depends on the past selection history of the population.