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.个体的适合度可简单定义为其下一代的子代数量。然而，表型选择如何决定适合度，目前尚未得到充分阐明。根据费希尔基本定理，适合度的遗传方差应趋近于零或维持在极低水平，但经验数据却与此相悖。为弥合这一认知鸿沟，我们沿用费希尔几何模型，假设适合度由多变量稳定选择决定，其选择最优值可随世代更迭发生变化。我们假设随机交配、自由重组、加性基因，且对性状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-选择平衡下的适合度遗传方差，随性状数量（即所谓的“机体复杂度”）呈U型函数关系：当生物体复杂度极低或极高时，遗传方差均可维持较高水平，这表明复杂度本身几乎不存在直接成本。在最优值随时间变化的环境中，适合度遗传方差相较于恒定环境下有所提升，且突变率越低，这种提升效应越显著。因此，突变与环境变化共同作用，可维持较高的适合度遗传方差。上述结果为费希尔适合度景观几何模型提供了理论支撑。