Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA.
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA.
J Theor Biol. 2021 Jul 21;521:110669. doi: 10.1016/j.jtbi.2021.110669. Epub 2021 Mar 18.
The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via "mean-field coupling," whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.
绝大多数多细胞生物都是异型配子的，这意味着雄性和雌性配子在大小上存在差异。这种不对称状态是如何进化而来的，仍然是一个悬而未决的问题，其可能是由所有配子大小大致相同的对称同型配子状态（来自同一分布）演变而来的。在这里，我们使用非线性动力系统研究中的工具来为这一现象建立一个简单的数学模型。与一些之前的工作不同，我们不假设存在交配类型。我们还通过“平均场耦合”来模拟频率相关的选择，即配子存活的可能性与其大小相对于群体平均配子大小的关系是一个递增函数。通过理论分析和数值模拟，我们证明这种基于均值的竞争几乎必然会导致稳定的异型配子平衡，因此同型配子可能会自然地导致异型配子。
