The logic of conventional and reversed Bateman gradients

The Bateman gradient is a central concept in sexual selection theory that relates reproductive success to mate number, with important consequences for sex-specific selection. The conventional expectation is that Bateman gradients are steeper in males than females, implying that males benefit more from multiple mating than females do. This claim is supported by much empirical evidence as well as mathematical modelling. However, under some reproductive systems, reversed Bateman gradients are observed, perhaps most notably in syngnathid fishes with male pregnancy. Unlike conventional Bateman gradients, the causal basis of such reversed Bateman gradients has never been modelled mathematically. Here, we present a sex-neutral mathematical model demonstrating how restrictions in capacity for carrying or incubating gametes and embryos (brooding) interact with anisogamy, generating both conventional and reversed Bateman gradients from a single mathematical model. The results clearly demonstrate how anisogamy tends to cause conventional Bateman gradients, but diminishing male brooding capacity under male pregnancy or nesting causes a gradual reversal from conventional to fully 'reversed' Bateman gradients.