title: Stability patterns for a size-structured population model and its stage-structured counterpart.
abstract: In this paper we compare a general size-structured population model, where a size-structured consumer feeds upon an unstructured resource, to its simplified stage-structured counterpart in terms of equilibrium stability. Stability of the size-structured model is understood in terms of an equivalent delayed system consisting of a renewal equation for the consumer population birth rate and a delayed differential equation for the resource. Results show that the size- and stage-structured models differ considerably with respect to equilibrium stability, although the two models have completely identical equilibrium solutions. First, when adult consumers are superior foragers to juveniles, the size-structured model is more stable than the stage-structured model while the opposite occurs when juveniles are the superior foragers. Second, relatively large juvenile (adult) mortality tends to stabilise (destabilise) the size-structured model but destabilise (stabilise) the stage-structured model. Third, the stability pattern is sensitive to the adult-offspring size ratio in the size-structured model but much less sensitive in the stage-structured model. Finally, unless the adult-offspring size ratio is sufficiently small, the stage-structured model cannot satisfactorily capture the dynamics of the size-structured model. We conclude that caution must be taken when the stage-structured population model is applied, although it can consistently translate individual life history and stage-specific differences to the population level.
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden. Electronic address: lai.zhang@math.umu.se.
authors.forename: Lai
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800, Denmark.
authors.forename: Michael
authors.initials: M
authors.lastname: Pedersen
authors.affiliation: School of Mathematical Science, Yangzhou University, Yangzhou 225002, China.
authors.forename: Zhigui
authors.initials: Z
authors.lastname: Lin
mesh_terms: D000818:Animals; D049628:Body Size; D008018:Life Cycle Stages; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics
keywords: Characteristic equation; Life history; Size-structured population; Stability; Stage-structured population