Mathematical models of conformity and anti-conformity have commonly included a set of simplifying assumptions. For example, (1) there are cultural variants in the population, (2) naive individuals observe the cultural variants of adult “role models,” and (3) individuals’ levels of conformity or anti-conformity do not change over time. Three recent theoretical papers have shown that departures from each of these assumptions can produce new population dynamics. Here, we explore cases in which multiple, or all, of these assumptions are violated simultaneously: namely, in a population with variants of a trait where conformity (or anti-conformity) occurs with respect to role models, we study a model in which the conformity rates at each generation are random variables that are independent of the variant frequencies at that generation. For this model a class of symmetric constant equilibria exist, and it is possible that all of these equilibria are simultaneously stochastically locally stable. In such cases, the effect of initial conditions on subsequent evolutionary trajectories becomes very complicated.

中文翻译：

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论多歧性特征文化传播中的随机从众偏差

整合和反整合的数学模型通常包括一组简化的假设。例如，(1) 人群中存在文化差异，(2) 天真的个体观察成人“榜样”的文化差异，以及 (3) 个体的从众或反从众水平不会随时间而改变。最近的三篇理论论文表明，偏离这些假设都可能产生新的人口动态。在这里，我们探讨了多个或全部这些假设同时被违反的情况：即，在具有某种特征变体的人群中，在角色模型方面发生顺从（或反顺从），我们研究了一个模型，其中每一代的符合率都是随机变量，与该代的变异频率无关。对于该模型，存在一类对称常数平衡，并且所有这些平衡有可能同时随机局部稳定。在这种情况下，初始条件对后续进化轨迹的影响变得非常复杂。