2014/11/01 by Fabio Dercole, Dercole, Fabio
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #math.DS #nlin.AO #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1411.0075
Submitted to Journal of Mathematical Biology on Feb. 3, 2014
arxiv created 2014/11/01 · openalex publication_date 2014/11/01 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A general procedure to formulate asexual (unstructured, deterministic) population dynamical models resulting from individual pairwise interactions is proposed. Individuals are characterized by a continuous strategy that represents all their behavioral, morphological, and functional traits. Populations group conspecific individuals with identical strategy and are measured by densities in space. Species can be monomorphic, if only one strategy is present, or polymorphic otherwise. The procedure highlights the structural properties fulfilled by the population per-capita growth rates. In particular, the effect of perturbing a set of similar strategies is proportional to the product of the corresponding densities, with a proportionality coefficient that is density-dependent only through the total density. This generalizes the law of mass action, which traditionally refers to the case in which the per-capita growth rates are linearly density-dependent and insensitive to joint strategy perturbations. Being underpinned with individual strategies, the proposed procedure is most useful for evolutionary considerations, in the case strategies are inheritable. The developed body of theory is exemplified on a Holling-type-II many-prey-one-predator system and on a model of a cannibalistic community.