Effects of ecological differentiation on Lotka-Volterra systems for species with behavioral adaptation and variable growth rates.
We study the properties of a n2-dimensional Lotka-Volterra system describing competing species that include behaviorally adaptive abilities. We indicate as behavioral adaptation a mechanism, based on a kind of learning, which is not viewed in the evolutionary sense but is intended to occur over shorter time scales. We consider a competitive adaptive n species Lotka-Volterra system, n > or = 3, in which one species is made ecologically differentiated with respect to the others by carrying capacity and intrinsic growth rate. The symmetry properties of the system and the existence of a certain class of invariant subspaces allow the introduction of a 7-dimensional reduced model, where n appears as a parameter, which gives full account of existence and stability of equilibria in the complete system. The reduced model is effective also in describing the time-dependent regimes for a large range of parameter values. The case in which one species has a strong ecological advantage (i.e. with a carrying capacity higher than the others), but with a varying growth rate, has been analyzed in detail, and time-dependent behaviors have been investigated in the case of adaptive competition among four species. Relevant questions, as species survival/exclusion, are addressed focusing on the role of adaptation. Interesting forms of species coexistence are found (i.e. competitive stable equilibria, periodic oscillations, strange attractors).
Lacitignola
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Department of Mathematics, University of Lecce, Via Provinciale Lecce-Arnesano, I-73100 Lecce, Italy. deborah.lacitignola@unile.it
Tebaldi
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C
D000220:Adaptation, Biological; D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior; D017753:Ecosystem; D008954:Models, Biological; D011157:Population Dynamics; D012641:Selection, Genetic