Complexity in models of cultural niche construction with selection and homophily.

Niche construction is the process by which organisms can alter the ecological environment for themselves, their descendants, and other species. As a result of niche construction, differences in selection pressures may be inherited across generations. Homophily, the tendency of like phenotypes to mate or preferentially associate, influences the evolutionary dynamics of these systems. Here we develop a model that includes selection and homophily as independent culturally transmitted traits that influence the fitness and mate choice determined by another focal cultural trait. We study the joint dynamics of a focal set of beliefs, a behavior that can differentially influence the fitness of those with certain beliefs, and a preference for partnering based on similar beliefs. Cultural transmission, selection, and homophily interact to produce complex evolutionary dynamics, including oscillations, stable polymorphisms of all cultural phenotypes, and simultaneous stability of oscillation and fixation, which have not previously been observed in models of cultural evolution or gene-culture interactions. We discuss applications of this model to the interaction of beliefs and behaviors regarding education, contraception, and animal domestication.