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. T hroughout history, humans have dramatically modified their ecological niche, for example by constructing densely populated settlements, using agriculture, and domesticating animals. This niche construction, which has involved major cultural changes, has influenced our own evolution and that of other species (1-4) by affecting the selective forces that act on human populations. A classic example of this gene-culture coevolution is the spread of dairy farming through Europe and the corresponding increase in the allele frequency of the lactase persistence gene, which enables humans to digest milk into adulthood (5-9). Less widely studied is the evolutionary pressure that one culturally transmitted behavior can exert on another cultural trait, either by altering the rate of transmission or the fitnesses of variants of the latter; this has been called cultural niche construction (4, 10).Assortative mating (homophily), where individuals that share a trait are more likely to mate with one another (11-14), and fitness differences may both affect the evolutionary trajectory of a population. In a previous model of cultural niche construction (15), we considered two dichotomous cultural traits, one that determined a cultural phenotype and one niche-constructing trait that controlled the level of selection and assorting on the other trait. In that model, assorting and selection could induce complex evolutionary dynamics, including stable polymorphisms and multiple simultaneously stable equilibria. Polymorphisms were only possible when the three evolutionary forces in the model interacted: fitness differences between phenotypes, assortative mating, and non-Mendelian transmission of at least one trait. The two elements of cultural niche construction in that model-the levels of selection and as...