THE DYNAMICS OF STARVATION AND RECOVERY: A MECHANISTIC MODEL FOR A WITHIN-LINEAGE DRIVER OF COPE'S RULE

The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of its constituent individuals. Of particular importance are the tradeoffs between reproduction and the dynamics of starvation and recovery in resource-limited environments. To elucidate the consequences of this tradeoff, we introduce a minimal nutritional state-structured model that incorporates two classes of consumer: nutritionally replete consumers that reproduce, and undernourished, non-reproducing consumers that are susceptible to mortality. As a function of the transition rates between these replete and undernourished states that are determined by the presence or absence of resources, consumer populations can either undergo cyclic dynamics or reach a steady state. We obtain strong constraints on starvation and recovery rates by deriving allometric scaling relationships and find that population dynamics subject to these constraints can approach the cyclic regime but are typically driven to a steady state. Moreover, we find that these rates fall within a 'refuge' in parameter space, where the probability of extinction of the consumer population is minimized. Thus we identify a potential mechanism that may both drive and constrain the dynamics of animal populations. Our model provides a natural framework that predicts maximum body size for mammals by determining the relative stability of an otherwise homogeneous population to a mutant population with altered percent body fat. For body masses less than ca. 10⁷ g, individuals with increased energetic reserves can invade resident populations, and for body masses greater than ca. 10⁷ g, individuals with lower energetic reserves have the advantage. Our findings thus provide a principled mechanism for a within-lineage driver of Cope's rule.