Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution
Genealogies and ages of cultural traits: An application of the theory of duality to the research on cultural evolution
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DOI：
10.1016/j.tpb.2018.04.007
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发表时间：
2018-09-01
影响因子：
1.4
通讯作者：
Ohtsuki, Hisashi
中科院分区：
文献类型：
--
作者：
Kobayashi, Yutaka;Wakano, Joe Yuichiro;Ohtsuki, Hisashi
描述了一种有限种群、离散生成的文化进化模型，其中多个离散特征是独立传播的。在这个模型中，每个新生儿都可能从不同文化背景的父母那里继承一种特征。与群体遗传学不同，传播失败的概率为正。为该模型导出了一个模拟个体样本文化谱系的祖先过程。这个祖先过程，用M-表示，被证明是对偶的过程M+描述一个特征的频率的变化。年龄-频率谱被定义为一个二维数组，其（i, k）元素是k代前引入的不同文化特征的预期数量，现在由特定尺寸n的样本中的i个个体携带。数值计算表明，年龄-频率谱和相关指标经历了一个关键的转变，从一个具有中等数量的年轻、罕见特征的阶段到一个具有大量非常古老、当每个人期望的文化父母数量超过一个时，共同特征。证明了M+和M-收敛于分支过程或确定性过程，这取决于种群规模趋于无穷的方式，并且这些极限过程具有一定的对偶关系。原始过程M+和M-的临界行为用分支过程的相变来解释。结合极限过程的结果，我们推导出很好地近似年龄-频谱和其他指标的解析公式。(C) 2018爱思唯尔公司版权所有。
A finite-population, discrete-generation model of cultural evolution is described, in which multiple discrete traits are transmitted independently. In this model, each newborn may inherit a trait from multiple cultural parents. Transmission fails with a positive probability unlike in population genetics. An ancestral process simulating the cultural genealogy of a sample of individuals is derived for this model. This ancestral process, denoted by M-, is shown to be dual to a process M+ describing the change in the frequency of a trait. The age-frequency spectrum is defined as a two-dimensional array whose (i, k) element is the expected number of distinct cultural traits introduced k generations ago and now carried by i individuals in a sample of a particular size n. Numerical calculations reveal that the age-frequency spectrum and related metrics undergo a critical transition from a phase with a moderate number of young, rare traits to a phase with numerous very old, common traits when the expected number of cultural parents per individual exceeds one. It is shown that M+ and M- converge to branching or deterministic processes, depending on the way population size tends to infinity, and these limiting processes bear some duality relationships. The critical behavior of the original processes M+ and M- is explained in terms of a phase transition of the branching processes. Using the results of the limiting processes in combination, we derive analytical formulae that well approximate the age-frequency spectrum and also other metrics. (C) 2018 Elsevier Inc. All rights reserved.