title: Coexistence of competing juvenile-adult structured populations.
abstract: The Leslie-Gower model is a discrete time analog of the competition Lotka-Volterra model and is known to possess the same dynamic scenarios of that famous model. The Leslie-Gower model played a historically significant role in the history of competition theory in its application to classic laboratory experiments of two competing species of flour beetles (carried out by Park in the 1940s-1960s). While these experiments generally supported what became the Competitive Exclusion Principle, Park observed an anomalous coexistence case. Recent literature has discussed Park's 'coexistence case' by means of non-Lotka-Volterra, non-equilibrium dynamics that occur in a high dimensional model with life cycle stages. We study this dynamic possibility in the lowest possible dimension, that is to say, by means of a model involving only two species each with two life cycle stages. We do this by extending the Leslie-Gower model so as to describe the competitive interaction of two species with juvenile and adult classes. We give a complete account of the global dynamics of the resulting model and show that it allows for non-equilibrium competitive coexistence as competition coefficients are increased. We also show that this phenomenon occurs in a general class of models for competing populations structured by juvenile and adult life cycle stages.
authors.affiliation: Department of Mathematics, Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA. cushing@math.arizona.edu
authors.forename: J M
authors.initials: JM
authors.lastname: Cushing
authors.forename: Shandelle M
authors.initials: SM
authors.lastname: Henson
authors.forename: Lih-Ing
authors.initials: LI
authors.lastname: Roeger
mesh_terms: D000375:Aging / Q000502:physiology*; D000818:Animals; D001517:Coleoptera / Q000254:growth & development*; D003163:Competitive Behavior / Q000502:physiology*; D008018:Life Cycle Stages / Q000502:physiology*; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics