Stability of fixed life histories to perturbation by rare diapause

TL;DR

This paper analyzes how rare developmental delays, like diapause, influence the long-term growth rate of populations with fixed life histories, showing that even small delays can be evolutionarily advantageous.

Contribution

It extends previous models to include rare diapause in fixed life histories, revealing its effect on stochastic growth rates and evolutionary stability.

Findings

Rare diapause increases stochastic growth rate as (log ε^{-1})^{-1} when delay rate ε approaches zero.

Small delays in life history are favored by natural selection due to their positive impact on growth rate.

The model generalizes to multiple sites with equal growth rates, showing consistent effects of diapause.

Abstract

We follow up on a companion work that considered growth rates of populations growing at different sites, with different randomly varying growth rates at each site, in the limit as migration between sites goes to 0. We extend this work here to the special case where the maximum average log growth rate is achieved at two different sites. The primary motivation is to cover the case where `sites' are understood as age classes for the same individuals. The theory then calculates the effect on growth rate of introducing a rare delay in development, a diapause, into an otherwise fixed-length semelparous life history. Whereas the increase in stochastic growth rate due to rare migrations was found to grow as a power of the migration rate, we show that under quite general conditions that in the diapause model --- or in the migration model with two or more sites having equal individual stochastic growth rates --- the increase in stochastic growth rate due to diapause at rate $\epsilon$ behaves like $(\log \epsilon^{-1})^{-1}$ as $\epsilon\downarrow 0$. In particular, this implies that a small random disruption to the deterministic life history will always be favored by natural selection, in the sense that it will increase the stochastic growth rate relative to the zero-delay deterministic life history.