Abstract
Ecological theory about the dynamics of interacting populations is mainly based on unstructured models that account for species abundances only. In turn, these models constitute the basis for our understanding of the functioning of ecological communities and ecosystems and their responses to environmental change, natural disturbances and human impacts. Structured models that take into account differences between individuals in age, stage or size have been shown to sometimes make predictions that run counter to the predictions of unstructured analogues. It is however unclear which biological mechanisms that are accounted for in the structured models give rise to these contrasting predictions. Focusing on two particular rules-of-thumb that generally hold in unstructured consumer-resource models, one relating to the relationship between mortality and equilibrium density of the consumer and the other relating to the stability of the equilibrium, I investigate the necessary conditions under which accounting for juvenile-adult stage structure can lead to qualitatively different model predictions. In particular, juvenile-adult stage structure is shown to overturn the two rules-of-thumb in case the model also accounts for the energetic requirements for basic metabolic maintenance. Given the fundamental nature of both juvenile-adult stage structure as well as metabolic maintenance requirements, these results call into question the generality of the predictions derived from unstructured models.
Highlights
Basic models of ecological interactions, such as the LotkaVolterra competition or predator-prey model, represent populations essentially as collections of elementary particles, subject to replication and mortality only
Large increases in maturation or reproduction rate compared to the increase in juvenile and adult foraging rate, respectively, occur in particular at resource densities just above the break-even density, where the resource intake of a juvenile or adult is just sufficient to cover its basic maintenance requirements (Fig. 1)
This threshold resource density is referred to as critical resource density or maintenance resource density (Persson et al 1998; Persson and de Roos 2013)
Summary
Basic models of ecological interactions, such as the LotkaVolterra competition or predator-prey model, represent populations essentially as collections of elementary particles, subject to replication and mortality only. These results are derived assuming that resource productivity is constant p(R) = P , juveniles and adults forage with exactly the same rate, fJ(R) = fA(R) := f (R), experience the same mortality, μJ = μA := μ, and similar maintenance costs T , but potentially differ in their efficiency to assimilate the resource. In Appendix C, it is shown that the Jacobian matrix of the specific model (13) can violate the Routh-Hurwitz criterion even though resource production is independent of resource density (p (R) = 0) This implies that the combination of life history structure and somatic maintenance costs can lead to instability of the consumer-resource equilibrium and the occurrence of population cycles, dependent again on the adult-juvenile ratio of resource assimilation and the relative loss rate through mortality compared to maintenance. For larger values of the resource productivity, the equilibrium is always stable; population cycles are primarily expected to occur when productivity is low
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