Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

预测人口对不断变化的环境的适应对于评估人类活动对生物多样性的影响至关重要。许多理论研究通过对数量性状的进化进行建模来解决这个问题，这些性状受到围绕最佳表型的稳定选择的影响，其值随着时间的推移不断变化。在这种情况下，人口命运是由性状相对于移动最优值的均衡分布产生的。这种分布可能随着选择的形状、繁殖系统、基因座的数量、突变核或它们的相互作用而变化。在这里，我们开发了一种方法，直接从表型分布的整个概况中提供种群适应不良和生存潜力的定量测量，而无需对其形状进行任何先验。我们研究了两种不同的生殖系统（无性遗传和无限小性遗传模型），以及各种形式的选择。特别是，我们恢复了适应度函数，使得选择从最佳状态减弱，导致进化临界点，当环境变化速度太快时，种群会突然崩溃。我们的统一框架可以破译导致这种现象的机制。更一般地说，它允许讨论两个繁殖系统之间的相似性和差异，这最终可以通过表型方差进化的不同约束来解释。我们证明，与无性模型相比，群体的平均适应度很大程度上取决于无穷小有性模型中选择函数的形状。