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07 February 2025
 
  » arxiv » 1608.8995

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The dynamics of starvation and recovery
Justin D. Yeakel ; Christopher P. Kempes ; Sidney Redner ;
Date 3 Sep 2016
AbstractThe eco-evolutionary dynamics of species is 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, the 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 $lesssim 10^7$g, individuals with increased energetic reserves can invade resident populations, and vice versa for body mass $gtrsim 10^7$g, thus providing a principled mechanism for a within-lineage driver of Cope’s rule.
Source arXiv, 1608.8995
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