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.