Abstract
Modern cultural evolution theory adopts a variety of concepts and methods developed in mathematical biology, in particular population genetics theory. In addition to forward-looking approaches such as two-locus models, backward-looking approaches such as coalescent theory, which describe ancestral states of the current population, have played an important role in population genetics. Here, we show how forward and backward approaches can be applied to two examples in cultural evolution. The first example deals with the number of cultural traits, which can be analyzed by a backward approach. Cultural coalescent theory illustrates many unique aspects of cultural processes such as information transfer (i.e., social learning) from many donors ("cultural parents"), including or excluding the biological parents. Theory predicts that many cultural traits of intermediate (or higher) frequency (popularity) can exist that are surprisingly old. Many unsolved issues remain, however, such as how to incorporate social structure as well as natural and/or cultural selection, which we believe to be an urgent agenda. The second example is the punishment of sibling incest, a problem to which cultural coalescent theory cannot currently be usefully applied. By analyzing forward recursions, we show that punishment is ineffective in suppressing incest, unless the incestuous inclination is diminished by the presence of punishers. Based on these examples, we discuss the merits and demerits of forward and backward approaches.