Data from: Evolution of phenotype-environment associations by genetic responses to selection and phenotypic plasticity in a temporally autocorrelated environment

Covariation between population-mean phenotypes and environmental variables, sometimes termed a ‘phenotype-environment association’ (PEA), can result from phenotypic plasticity, genetic responses to natural selection, or both. PEAs can potentially provide information on the evolutionary dynamics of a particular set of populations, but this requires a full theoretical characterization of PEAs and their evolution. Here, we derive formulas for the expected PEA in a temporally fluctuating environment for a quantitative trait with a linear reaction norm. We compare several biologically relevant scenarios, including constant versus evolving plasticity, and the situation where an environment affects both development and selection but at different time periods. We find that PEAs are determined not only by biological factors (e.g., magnitude of plasticity, genetic variation), but also environmental factors, such as the association between the environments of development and of selection, and in some cases the level of temporal autocorrelation. We also describe how a PEA can be used to estimate the relationship between an optimum phenotype and an environmental variable (i.e., the environmental sensitivity of selection), an important parameter for determining the extinction risk of populations experiencing environmental change. We illustrate this ability using published data on the predator-induced morphological responses of tadpoles to predation risk.种群平均表型与环境变量之间的协变关系有时被称为“表型-环境关联（phenotype-environment association, PEA）”，其成因可归结为表型可塑性、对自然选择的遗传响应，或二者共同作用。表型-环境关联（PEA）有望为特定种群类群的进化动态提供参考，但该应用的前提是完成对PEA及其演化过程的完整理论表征。本研究推导了具有线性反应规范（reaction norm）的数量性状在时变环境下的期望PEA计算公式。我们对比了多种具备生物学意义的情景，包括恒定可塑性与演化可塑性的差异，以及环境在不同时段分别影响发育与选择的情形。研究发现，PEA不仅由生物学因素（如可塑性强度、遗传变异水平）决定，还受环境因素影响——例如发育环境与选择环境之间的关联，在部分情形下还与时序自相关程度相关。此外，本研究还阐明了如何利用PEA估算最优表型与环境变量之间的关联（即选择的环境敏感性），该参数是评估遭遇环境变化的种群灭绝风险的关键指标。我们借助已发表的蝌蚪捕食风险诱导形态响应的相关数据，对该应用方法进行了演示。