Offspring resemble their parents for both genetic and environmental reasons. Understanding the relative magnitude of these alternatives has long been a core interest in behavioral genetics research, but traditional designs, which compare phenotypic covariances to make inferences about unmeasured genetic and environmental factors, have struggled to disentangle them. Recently, Kong et al. (2018) showed that by correlating offspring phenotypic values with the measured polygenic score of parents’ nontransmitted alleles, one can estimate the effect of “genetic nurture”—a type of passive gene–environment covariation that arises when heritable parental traits directly influence offspring traits. Here, we instantiate this basic idea in a set of causal models that provide novel insights into the estimation of parental influences on offspring. Most importantly, we show how jointly modeling the parental polygenic scores and the offspring phenotypes can provide an unbiased estimate of the variation attributable to the environmental influence of parents on offspring, even when the polygenic score accounts for a small fraction of trait heritability. This model can be further extended to (a) account for the influence of different types of assortative mating, (b) estimate the total variation due to additive genetic effects and their covariance with the familial environment (i.e., the full genetic nurture effect), and (c) model situations where a parental trait influences a different offspring trait. By utilizing structural equation modeling techniques developed for extended twin family designs, our approach provides a general framework for modeling polygenic scores in family studies and allows for various model extensions that can be used to answer old questions about familial influences in new ways.

由于遗传和环境原因，后代与父母相似。长期以来，了解这些替代方案的相对大小一直是行为遗传学研究的核心兴趣，但传统的设计（比较表型协方差以推断未测量的遗传和环境因素）一直在努力解开它们。最近，Kong 等人。（2018）表明，通过将后代表型值与父母非传播等位基因的测量多基因评分相关联，可以估计“遗传养育”的影响——一种在可遗传的父母性状直接影响后代性状时出现的被动基因-环境协变。 . 在这里，我们在一组因果模型中实例化了这一基本思想，这些模型为估计父母对后代的影响提​​供了新的见解。最重要的是，我们展示了如何联合建模亲本多基因评分和后代表型可以提供对归因于父母对后代的环境影响的变异的无偏估计，即使多基因评分仅占性状遗传力的一小部分。该模型可以进一步扩展到（a）考虑不同类型的配对交配的影响，（b）估计由于加性遗传效应及其与家庭环境的协方差（即完全遗传养育效应）引起的总变异， (c) 模拟父母特征影响不同后代特征的情况。通过利用为扩展双胞胎设计开发的结构方程建模技术，