Towards robust evolutionary inference with integral projection models

Integral projection models (IPMs) are extremely flexible tools for ecological and evolutionary inference. IPMs track the distribution of phenotype in populations through time, using functions describing phenotype-dependent development, inheritance, survival and fecundity. For evolutionary inference, two important features of any model are the ability to (i) characterize relationships among traits (including values of the same traits across ages) within individuals, and (ii) characterize similarity between individuals and their descendants. In IPM analyses, the former depends on regressions of observed trait values at each age on values at the previous age (development functions), and the latter on regressions of offspring values at birth on parent values as adults (inheritance functions). We show analytically that development functions, characterized this way, will typically underestimate covariances of trait values across ages, due to compounding of regression to the mean across projec...积分投影模型（Integral projection models，IPMs）是用于生态学与进化推断的极具灵活性的研究工具。该模型借助一系列刻画表型依赖的发育、遗传、存活与繁殖力的函数，追踪种群内表型分布随时间的动态变化。针对进化推断任务，任一模型需具备两项核心能力：（i）刻画个体内部各性状间的关联（包括同一性状在不同年龄的取值）；（ii）刻画个体与其后代间的相似性。在IPM分析框架中，前者基于各年龄观测性状值对前一年龄性状值的回归分析（即发育函数），后者则基于子代出生时的性状值对亲本成年个体性状值的回归分析（即遗传函数）。我们通过解析推导证明，以此方式构建的发育函数，通常会低估不同年龄间性状值的协方差，其成因在于均值回归效应在跨projec...过程中发生了复合。