Quantifying the effects of migration and mutation on adaptation and demography in spatially heterogeneous environments

How do mutation and gene flow influence population persistence, niche expansion, and local adaptation in spatially heterogeneous environments? In this article, we analyse a demographic and evolutionary model of adaptation to an environment containing two habitats in equal frequencies, and we bridge the gap between different theoretical frameworks. Qualitatively, our model yields four qualitative types of outcomes: (i) global extinction of the population (ii) adaptation to one habitat only, but also adaptation to both habitats with (iii) specialized phenotypes, or (iv) with generalized phenotypes; and we determine the conditions under which each equilibrium is reached. We derive new analytical approximations for the local densities and the distributions of traits in each habitat under a migration--selection--mutation balance, compute the equilibrium values of the means, variances and asymmetries of the local distributions of phenotypes, and contrast the effects of migration and mutation ...突变（mutation）与基因流（gene flow）如何在空间异质环境（spatially heterogeneous environments）中影响种群存续（population persistence）、生态位扩张（niche expansion）与局部适应（local adaptation）？本文针对包含两种等频率分布生境的适应问题，构建了种群统计与进化模型（demographic and evolutionary model），并弥合了不同理论框架（theoretical frameworks）间的理论分歧。定性而言，本模型可产生四类定性结果：(i) 种群全局灭绝（global extinction）；(ii) 仅适应单一生境；此外还可实现(iii) 以特化表型（specialized phenotypes）适应两种生境，或(iv) 以泛化表型（generalized phenotypes）适应两种生境；我们确定了各类平衡态（equilibrium）达成的条件。我们推导了迁移-选择-突变平衡（migration-selection-mutation balance）下各生境的局部密度与性状分布的新型解析近似解，计算了表型局部分布的均值、方差与不对称性的平衡值，并对比了迁移与突变的作用……