Simulations provide a mechanistic interpretation of Bateman gradients

The Bateman gradient (BG or ) is a fundamental metric of sexual selection, and is often interpreted as the fitness advantage individuals can gain by increasing their number of mates. However, researchers commonly misconceive the relationship between mating success (MS) and reproductive success (RS) as always being causal, leading to a misinterpretation of the BG. The BG is phenomenological and therefore uninformative about the mechanisms leading to correlations between MS and RS. Here, we simulate sequential matings in males from biological systems with varying levels of anisogamy and sperm competition, to better understand the underlying processes that modulate male BGs. We show that the BG does not solely reflect the causal influence of MS on RS as is typically interpreted, but is also a consequence of covariances between male MS and male ejaculate traits, female fecundity, or female post-mating decisions. For example, we show that the BG is substantially shallower when the ejaculate size of males negatively co-varies with their MS, such as in species with alternative male reproductive tactics. Such covariances can lead to a misinterpretation of the measured BG, because here, it does not merely represent the strength of selection on intra-sexual competition for mates. We suggest how such covariances can be visually assessed, and accounted for using partial Bateman gradients, to better interpret the influence of MS on RS, thus the strength of pre-copulatory sexual selection. Among other simplifications, our simulations have a male-only focus, but they provide insights into the mechanisms driving inter- and intra-specific variation in the BG, clarify its meaning, and improve our understand of sexual selection.