Department of Animal Ecology, Netherlands Institute of Ecology (NIOO-KNAW), Wageningen, the Netherlands.
Department of Biometris, Wageningen University & Research, Wageningen, the Netherlands.
J Evol Biol. 2020 Mar;33(3):352-366. doi: 10.1111/jeb.13571. Epub 2019 Dec 9.
Phenotypic plasticity is a central topic in ecology and evolution. Individuals may differ in the degree of plasticity (individual-by-environment interaction (I × E)), which has implications for the capacity of populations to respond to selection. Random regression models (RRMs) are a popular tool to study I × E in behavioural or life-history traits, yet evidence for I × E is mixed, differing between species, populations, and even between studies on the same population. One important source of discrepancies between studies is the treatment of heterogeneity in residual variance (heteroscedasticity). To date, there seems to be no collective awareness among ecologists of its influence on the estimation of I × E or a consensus on how to best model it. We performed RRMs with differing residual variance structures on simulated data with varying degrees of heteroscedasticity and plasticity, sample size and environmental variability to test how RRMs would perform under each scenario. The residual structure in the RRMs affected the precision of estimates of simulated I × E as well as statistical power, with substantial lack of precision and high false-positive rates when sample size, environmental variability and plasticity were small. We show that model comparison using information criteria can be used to choose among residual structures and reinforce this point by analysis of real data of two study populations of great tits (Parus major). We provide guidelines that can be used by biologists studying I × E that, ultimately, should lead to a reduction in bias in the literature concerning the statistical evidence and the reported magnitude of variation in plasticity.
表型可塑性是生态学和进化学的一个核心议题。个体在可塑性程度上可能存在差异（个体-环境互作（I×E）），这对种群响应选择的能力具有重要意义。随机回归模型（RRMs）是研究行为或生活史特征中 I×E 的一种流行工具，但 I×E 的证据存在差异，在物种、种群甚至同一种群的不同研究中都存在差异。研究结果存在差异的一个重要原因是残差方差（异方差）的处理方式不同。迄今为止，生态学家似乎还没有意识到它对 I×E 估计的影响，也没有就如何最好地对其进行建模达成共识。我们使用具有不同残差方差结构的 RRMs 对具有不同异方差和可塑性程度、样本量和环境变异性的模拟数据进行了分析，以测试 RRMs 在每种情况下的表现。RRMs 中的残差结构会影响模拟 I×E 估计的精度和统计功效，当样本量、环境变异性和可塑性较小时，估计精度会大幅下降，假阳性率也会很高。我们表明，使用信息准则进行模型比较可以用于选择残差结构，并通过对两只大山雀（Parus major）研究种群的真实数据进行分析，进一步强调了这一点。我们提供了生物学家研究 I×E 时可以使用的指导方针，最终应减少文献中关于统计证据和可塑性变异性报告幅度的偏差。
