title: Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation.
abstract: The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been completely analysed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated to dispersal is either beneficial or detrimental to total population abundance. Therefore, this is a contribution to the SLOSS question. Importantly, we also show that, depending on the underlying mechanism, there is no unique way to generalize the logistic model to a patchy situation. In many cases, the standard model is not the correct generalization. We analyse several alternative models and compare their predictions. Finally, we emphasize the shortcomings of the logistic model when written in the r-K parameterization and we explain why Verhulst's original polynomial expression is to be preferred.
authors.affiliation: University of Fribourg, Department of Biology, Chemin du Musée 10, 1700 Fribourg, Switzerland; Sorbonne Universités, UPMC Univ Paris 06, Institute of Ecology and Environmental Sciences (iEES-Paris), 75252 Paris Cedex 5, France. Electronic address: roger.arditi@unifr.ch.
authors.forename: Roger
authors.initials: R
authors.lastname: Arditi
authors.affiliation: INRA, INRIA, Projet Modemic, UMR Mistea, 2 place Pierre Viala, 34060 Montpellier Cedex 2, France; Université de Nice-Sophia-Antipolis, France. Electronic address: claude.lobry@inria.fr.
authors.forename: Claude
authors.initials: C
authors.lastname: Lobry
authors.affiliation: IRSTEA, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier Cedex 5, France; Université de Haute Alsace, LMIA, 4 rue des Frères Lumière, 68093 Mulhouse Cedex, France. Electronic address: tewfik.sari@irstea.fr.
authors.forename: Tewfik
authors.initials: T
authors.lastname: Sari
mesh_terms: D000465:Algorithms; D003247:Conservation of Natural Resources / Q000379:methods; D006801:Humans; D016015:Logistic Models; D008954:Models, Biological; D008962:Models, Theoretical; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth
keywords: Fragmentation; Intraspecific competition; SLOSS; Slow–fast systems