A stochastic model of gene-culture coevolution, suggested by the "culture historical hypothesis" of Simoons and McCracken, is presented. According to this hypothesis, adult lactose absorption, believed to be an autosomal dominant trait, attained a high frequency in some human populations due to the positive selection pressure induced by culturally determined milk use in those populations. Twodimensional Kolmogorov backward equations with appropriate boundary conditions are derived for the ultimate fixation probability of milk users, of the gene for adult lactose absorption, and of both jointly, and for the average time until fixation of the gene. These boundary value problems are solved numerically by the Gauss-Seidel method. I define a theoretical measure of the correlation between gene and culture in terms of the three ultimate fixation probabilities. Monte Carlo simulations are conducted to check and extend the numerical results and also to obtain the first arrival time at gene frequency 0.70, which is approximately the highest observed frequency in any population. Two results that pertain to the culture historical hypothesis are obtained. First, the incomplete correlation observed between adult lactose absorption and milk use does not necessarily constitute evidence against the hypothesis. Second, for the postulated genetic change to have occurred within the 6000-year period since the advent of dairying, either the effective population size was of the order of 100, or, if it was of larger order, the selection coefficient probably had to exceed 5%.It has been proposed that the high frequency of adult humans able to digest and absorb the sugar lactose (adult lactose absorption, ALA) in some populations is the evolutionary consequence of a positive selection pressure induced by culturally determined milk use in those populations. Assuming a genetic basis for ALA, the "culture historical hypothesis," independently proposed by Simoons and McCracken (1-3), stands mainly on the observed correlation between the degree to which adults in a population have traditionally consumed and been dependent on milk and the frequency of lactose absorbers in that population. It has also been pointed out, on the basis of deterministic calculations with a purely genetic model in which all lactose absorbers are tacitly assumed to be milk users, that there has been sufficient time for the genetic trait to have evolved since the advent of dairying some 6000 years ago (4, 5).Unfortunately, a precise coevolutionary perspective is lacking in the arguments of Simoons and McCracken, thus eliciting some pertinent criticisms (6). By a coevolutionary perspective, I mean an interactive view of genetic and cultural variation, such that the evolutionary increase of a genetic variant and an associated cultural variant are mutually dependent. In this paper, I present and analyze a gene-culture coevolution model of ALA and milk use. This problem in "cultural genetics" (3) is very suitable for the interplay between theory and observation for...