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 co-variates are most problematic, or how confounded relationships can be diagnosed to better interpret the Bateman gradient, remains largely unexplored. To address these gaps, we simulate nine plausible biological scenarios where the effect of male mating success on reproductive success is confounded. We find that co-variances between male mating success and female fecundity or egg allocation confound the male Bateman gradient more strongly than co-variances between male mating success and ejaculate traits. These differences in the impact of male-female versus male-male co-variances are especially pronounced in systems with high levels of anisogamy and no sperm competition. We provide guidelines for empiricists to visually identify such co-variances by recording mating order, and suggest that researchers explicitly state causal assumptions when interpreting Bateman gradients. Additionally, when the co-variate 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.