Diagnosing confounded Bateman gradients

The Bateman gradient is a fundamental metric of sexual selection, often interpreted as the fitness advantage individuals gain by increasing their number of mates. However, it is widely recognized that any traits influencing both mating success and reproductive success can confound the Bateman gradient, misrepresenting the strength of pre-copulatory sexual selection. Yet, the magnitude of this misrepresentation across different biological systems (e.g., differing in anisogamy or the strength of sperm competition), which covariates are most problematic, or how confounded relationships can be diagnosed to better interpret the Bateman gradient, remains largely unexplored. To address these gaps, we investigate nine plausible biological scenarios where the effect of male mating success on reproductive success is confounded. We find that covariances between male mating success and female fecundity or egg allocation confound the male Bateman gradient more strongly than covariances between male mating success and ejaculate traits. These differences in the impact of male-female versus male-male covariances are especially pronounced in systems with high levels of anisogamy and no sperm competition. We provide guidelines for empiricists to visually identify such covariations by recording mating order. Additionally, when the covariate is a confounder, not a mediator, we demonstrate that partial Bateman gradients allow better interpretation of the strength of pre-copulatory sexual selection. These insights into the mechanisms driving variation in the Bateman gradient allow us to clarify its meaning, identify scenarios where its interpretation might be problematic, and offer practical solutions to address this.

Bateman梯度（Bateman gradient）是性选择（sexual selection）的核心度量指标，常被解读为个体通过增加交配对象数量所获得的适合度优势（fitness advantage）。然而学界已普遍认识到，任何同时影响交配成功率（mating success）与繁殖成功率（reproductive success）的性状，都会混淆Bateman梯度的解读结果，从而误判交配前性选择（pre-copulatory sexual selection）的强度。不过，目前仍有诸多关键问题尚未得到充分探索：不同生物系统（如配子异型（anisogamy）程度或精子竞争（sperm competition）强度存在差异的系统）中，此类误判的程度如何？哪些协变量（covariates）最易引发此类问题？又该如何诊断被混淆的关联关系，以更准确地解读Bateman梯度？为填补这些研究空白，我们针对九种合理的生物学场景展开研究，这些场景中雄性交配成功率（male mating success）对繁殖成功率的效应存在混淆。研究发现，相较于雄性交配成功率与射精性状（ejaculate traits）间的协方差，雄性交配成功率与雌性繁殖力或卵子分配间的协方差，对雄性Bateman梯度的混淆效应更强。这种雌雄间协方差与雄性间协方差的影响差异，在配子异型程度高且无精子竞争的系统中尤为显著。我们为实验研究者提供了实操指南：通过记录交配顺序（mating order），可直观识别此类协方差。此外，当协变量属于混淆变量（confounder）而非中介变量（mediator）时，我们证明了偏Bateman梯度（partial Bateman gradient）能够更准确地解读交配前性选择的强度。这些关于驱动Bateman梯度变异的机制的研究结果，帮助我们厘清了其内涵，识别出可能导致其解读出现偏差的场景，并为解决这一问题提供了切实可行的方案。