Asymmetric arms races between predators and prey: a tug of war between the life-dinner principle and the rare-enemy principle

Antagonistic co-evolution can be asymmetric, where one species lags behind another. Asymmetry in a predator-prey context is expressed by the 'life-dinner principle', a classic informal model predicting that prey should be in some sense ahead in this arms race, since prey are running for their lives, while predators lag as they only run for their dinner. The model has undergone surprisingly little theoretical scrutiny. We derive analytical models that show coevolutionary outcomes do not always align with the life-dinner principle. Our results show that other important asymmetries can easily reverse the outcome, especially the rare-enemy principle: predators are usually outnumbered by their prey, sometimes substantially (trophic asymmetry), which can make selection on prey relatively weak. We additionally show that the antagonists typically exhibit different evolutionary responses to a situation where both predator and prey start out as equally fast runners. Although predators sometimes become so efficient that attacks always succeed, attack success often reaches a stable intermediate value. We conclude that the life-dinner principle has some validity as a metaphor, but its effect is of an 'all else being equal' type, which is surprisingly easily overridden by other features of the evolutionary dynamics.