Aoki K
Department of Anthropology, Faculty of Science, University of Tokyo, Japan.
Theor Popul Biol. 1991 Dec;40(3):354-68. doi: 10.1016/0040-5809(91)90060-s.
The time required for gene frequency change under natural selection in a deterministic model of gene-culture coevolution is investigated. A discrete generations model is formulated, and its continuous time approximation is derived. In passing to the continuous time limit, it is assumed that the frequency of the culturally transmitted trait does not change under oblique (between generations) transmission. The system of ordinary differential equations thus obtained are solved, and the dependence on the parameters of horizontal (within generations) transmission and natural selection is examined. The time required is found to be substantially longer when the determination of a phenotypic difference subject to natural selection is partly cultural rather than completely genetic. The predictions are relevant to the possibility of the coevolution of lactose absorbers and milk drinkers in some human populations. Alternative hypotheses are briefly discussed in the light of the theoretical results.
研究了在基因-文化共同进化的确定性模型中，自然选择下基因频率变化所需的时间。构建了一个离散世代模型，并推导了其连续时间近似。在过渡到连续时间极限时，假设文化传递性状的频率在斜向（代际之间）传递下不变。求解由此得到的常微分方程组，并研究其对水平（代内）传递和自然选择参数的依赖性。结果发现，当受自然选择影响的表型差异的决定部分是文化的而非完全是遗传的时，所需时间要长得多。这些预测与某些人类群体中乳糖吸收者和牛奶饮用者共同进化的可能性相关。根据理论结果简要讨论了替代假说。
