Dynamics of starvation and recovery predict extinction risk and both Damuth's law and Cope's rule

The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of their constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To elucidate this interplay, here we introduce a nutritional state-structured model that incorporates two classes of consumers: nutritionally replete, reproducing consumers, and undernourished, nonreproducing consumers. We obtain strong constraints on starvation and recovery rates by deriving allometric scaling relationships and find that population dynamics are typically driven to a steady state. Moreover, these rates fall within a "refuge" in parameter space, where the probability of population extinction is minimized. We also show that our model provides a natural framework to predict steady state population abundances known as Damuth's law, and maximum mammalian body size. By determining the relative stability of an otherwise homogeneous population to a competing population with altered percent body fat, this framework provides a principled mechanism for a selective driver of Cope's rule.