Data from: Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modelling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold’s (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson-Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate samples size. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date – repeatedly described as more evolutionarily stable than expected –, so this skewness should be accounted for when investigating evolutionary dynamics in the wild.野外环境下观测到的表型选择响应（phenotypic responses to selection），往往与基于选择作用与遗传方差测量所得的预测结果存在偏差。用于解释这一进化停滞悖论（paradox of stasis）的一项被忽视的假说认为，偏态表型分布（skewed phenotypic distribution）会对自然选择（natural selection）与进化过程产生影响。我们通过数学建模（mathematical modelling）证实：当针对最优表型（optimum phenotype）开展选择的性状呈现偏态分布时，即便处于进化平衡状态（evolutionary equilibrium，此时表型均值未发生任何改变），依然能够检测到定向选择（directional selection）的存在。若环境效应（environmental effects）呈偏态分布，兰德与阿诺德（Lande and Arnold, 1983）提出的定向选择梯度（directional gradient），其方向与偏态方向恰好相反；与之相对，偏态的育种值（breeding values）可使表型均值偏离最优值，进而引发与偏态方向一致的定向选择。此类效应可通过两类替代选择估计量进行拆分：一类基于个体相对适合度（relative fitness）的平均导数，另一类基于相对适合度与性状间的加性遗传协方差（additive genetic covariances，罗伯逊-普莱斯恒等式（Robertson-Price identity））。我们通过中等样本量下的选择估计模拟实验，评估了上述预测的有效性。正如我们以鸟类产卵日期（avian laying date）为例所展示的那样，生态相关性状（ecologically relevant traits）通常普遍存在偏态分布——这类性状多次被报道其进化稳定性超出预期——因此在探究野外种群的进化动态（evolutionary dynamics）时，应当将偏态效应纳入考量范畴。