The evolution of variance in sequential defences

Abstract

The defences used by organisms against predators display a great degree of variability. Defence phenotypes can differ substantially among individuals of the same species, and a single individual can itself deploy a variety of defences. Here, we use a mathematical model that includes mutation and selection to understand the evolutionary origin of this variability in a population of a species that deploys defences sequentially (“first” and “second” defences). Typically, the first defence evolves to have lower variance, i.e. appears more closely accumulated around the ideal phenotype, than the second defence (even when the breaching the first defence incurs more fitness loss than breaching the second defence with the other parameters the same for both defences). However, if the first defence is much less effective in repelling predators, or is much less tolerant of deviation from the ideal phenotype, then the first defence can evolve to have higher variance than the second. Other factors like mutation strength and the losses in the fitness when each defence fails also influence the defence variance. Larger mutation rate incurs larger equilibrium variances, and when the comparative importance in fitness of one defence increases, then the ratio between the variances of this defence and the other defence decreases. Sequentially acting defences are found in many organisms, so we encourage empirical research to test our theoretical predictions.