Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation

Roger Arditi (1, 2) , Claude Lobry (3, 4) , Tewfik Sari (5, 6)

1 EPC - Ecologie des Populations et Communautés
2 UNIFR - Université de Fribourg = University of Fribourg
3 UNS - Université Nice Sophia Antipolis (1965 - 2019)
4 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
5 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
6 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

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 analyzed. Here, we complete this analysis and we delineate the conditions under which fragmentation 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 analyze 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.

Mots clés: Intraspecific competition; fragmentation; SLOSS; slow-fast systems

Domaines: Systèmes dynamiques [math.DS]; Sciences du Vivant [q-bio]

Roger Arditi, Claude Lobry, Tewfik Sari. Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation. 2015. ⟨hal-01153368v2⟩