Abstract
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.
Highlights
The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of their constituent individuals
Our model makes several basic predictions: (i) the dynamics are typically driven to a refuge far from cyclic behavior and extinction risk, (ii) the steady-state conditions of the nutritional state-structured model (NSM) accurately predict the measured biomass densities for mammals described by Damuth’s law[25,26,27,28], (iii) there is an allometrically constrained upper bound for mammalian body size, and (iv) the NSM provides a selective mechanism for the evolution of larger body size, known as Cope’s rule[29,30,31,32]
The rate equations (1) are general and can in principle be used to explore the starvation-recovery dynamics for most organisms, here, we focus on allometric relationships for terrestrial-bound lower-trophic-level endotherms (Table 1), herbivorous mammals, which range from a minimum of M ≈ 1 g to a maximum of M ≈ 107 g
Summary
The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of their constituent individuals. 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. Our model makes several basic predictions: (i) the dynamics are typically driven to a refuge far from cyclic behavior and extinction risk, (ii) the steady-state conditions of the NSM accurately predict the measured biomass densities for mammals described by Damuth’s law[25,26,27,28], (iii) there is an allometrically constrained upper bound for mammalian body size, and (iv) the NSM provides a selective mechanism for the evolution of larger body size, known as Cope’s rule[29,30,31,32]
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