论文标题
在强烈的异质环境中，性种群中复杂性状的进化动力学：如何正常？
Evolutionary dynamics of complex traits in sexual populations in a strongly heterogeneous environment: how normal?
论文作者
论文摘要
在研究种群在异质环境中的性状分布的动力学时，定量遗传学的经典模型选择查看其时刻系统，特别是前两个。此外，为了关闭所得方程系统，他们经常假设性状分布是高斯（例如，参见Ronce和Kirkpatrick 2001）。本文的目的是引入一个数学框架，该框架遵循整个性状分布（没有事先假设）来研究性行为人群的进化动力学。具体而言，它的重点是复杂的性状，其继承可以通过隔离的无限模型来编码（Fisher 1919）。我们表明，它使我们能够得出一个制度，在该制度中，我们的模型具有与假设高斯性状分布相同的动力学。为了支持这一点，我们将源自我们模型的时刻系统的固定问题与Ronce和Kirkpatrick 2001中的时刻系统的固定问题进行了比较，并表明它们在此制度下是等效的，不需要其他情况。此外，在这种等价方面，我们表明出现了生态和进化时间尺度的分离。对单态的快速放松使我们能够使用缓慢的分析来降低矩系统的复杂性。这种降低使我们能够完成（仍处于这种制度中）对Ronce和Kirkpatrick 2001中的数值不对称平衡的分析描述。在全球范围内，我们提供了明确的建模假设，这些假设允许发生这种局部适应模式。
When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume that the trait distribution is Gaussian (see for instance Ronce and Kirkpatrick 2001). The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher 1919). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming a Gaussian trait distribution. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick 2001 and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick 2001. More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.
