title: A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism.
abstract: The present work is a contribution to the understanding of the sempiternal problem of the "burden of factor two" implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually born males. This instability implies evolution of the system towards an attractor involving both (sexual and asexual) populations (which does not imply optimality of the population). We also exhibit the analogy with a parasite/host system.
authors.affiliation: Institut Jean Le Rond d'Alembert, UPMC Univ Paris 06 and CNRS, UMR 7190, Sorbonne Universités, 75005, Paris, France.
authors.forename: Evariste
authors.initials: E
authors.lastname: Sanchez-Palencia
authors.affiliation: Château du Fontenil, 61300, Saint Sulpice, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Lherminier
authors.affiliation: Laboratoire Jacques-louis Lions, UPMC Univ Paris 06 and CNRS, UMR 7598, Sorbonne Universités, 75005, Paris, France. Jean-Pierre.Francoise@upmc.fr.
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Françoise
mesh_terms: D000222:Adaptation, Physiological; D000818:Animals; D005075:Biological Evolution; D005260:Female; D006790:Host-Parasite Interactions; D006801:Humans; D008297:Male; D008393:Marriage; D008962:Models, Theoretical; D010312:Parthenogenesis; D011157:Population Dynamics; D012098:Reproduction / Q000502:physiology*; D013559:Symbiosis
keywords: Polygamy; Population dynamics; Sexual and asexual reproduction; Stability