Data from: Fisher's geometrical model of fitness landscape and variance in fitness within a changing environment

The fitness of an individual can be simply defined as the number of its offspring in the next generation. However, it is not well understood how selection on the phenotype determines fitness. In accordance with Fisher’s fundamental theorem, fitness should have no or very little genetic variance, whereas empirical data suggest that is not the case. To bridge these knowledge gaps, we follow Fisher’s geometrical model and assume that fitness is determined by multivariate stabilizing selection towards an optimum that may vary among generations. We assume random mating, free recombination, additive genes, and uncorrelated stabilizing selection and mutational effects on traits. In a constant environment, we find that genetic variance in fitness under mutation-selection balance is a U-shaped function of the number of traits (i.e. of the so-called “organismal complexity”). Because the variance can be high if the organism is of either low or high complexity, this suggests that complexity has little direct costs. Under a temporally varying optimum, genetic variance increases relative to a constant optimum and increasingly so when the mutation rate is small. Therefore mutation and changing environment together can maintain high genetic variance. These results therefore lend support to Fisher’s geometric model of a fitness landscape.个体的适应度可简单定义为其在下一代中的子代数量。然而，学界对表型选择如何决定适应度的内在机制仍不甚明晰。根据费希尔基本定理（Fisher’s fundamental theorem），适应度的遗传方差应趋近于零或维持在极低水平，但实验观测数据却与之相悖。为弥合这一认知鸿沟，我们采用费希尔几何模型，假设适应度由多变量稳定选择决定，选择所朝向的最优表型可随世代更迭发生变化。本研究假设种群存在随机交配、自由重组、加性基因遗传，且性状所受的稳定选择与突变效应互不相关。在恒定环境下，我们发现突变-选择平衡（mutation-selection balance）下的适应度遗传方差与性状数量（即所谓的“机体复杂性”）呈U型函数关系：当机体复杂性较低或较高时，遗传方差均可维持较高水平，这表明复杂性本身几乎不会带来直接的进化代价。在最优表型随时间动态变化的环境中，适应度遗传方差相较于恒定环境下有所提升，且当突变率较低时，该增幅更为显著。因此，突变与环境变化的共同作用可维持较高水平的适应度遗传方差。上述研究结果为费希尔适应度景观几何模型提供了实证支撑。