Abstract
Population distributions depend upon the aggregate behavioural responses of individuals to a range of environmental factors. We extend a model of ideally motivated populations to describe the local and regional consequences of interactions between three populations distinguished by their levels of cooperation and exploitation. Inspired by the classic prisoner's dilemma game, stereotypical fitness functions describe a baseline non-cooperative population whose per capita fitness decreases with density, obligate co-operators who initially benefit from the presence of conspecifics, and kleptoparasites who require heterospecifics to extract resources from the environment. We examine these populations in multiple combinations, determine where both local and regional coexistence is permitted, and investigate conditions under which one population will invade another. When they invade co-operators in resource-rich areas, kleptoparasites initiate a dynamic instability that leads to the loss of both populations; however, selfish hosts, who can persist at low densities, are immune to this risk. Furthermore, adaptive movement may delay the onset of instability as dispersal relieves dynamic stress. Selfish and cooperative populations default to mutual exclusion, but asymmetric variations in interference strength may relax this condition and permit limited sympatry within the environment. Distinct sub-communities characterize the overall spatial structure.
Highlights
Competition, cooperation and other interactions influence the persistence or exclusion of populations within a community
We employ a modelling framework that bridges game theory and ecological modelling to study the pairwise and collective interactions of three populations characterized by distinct levels of cooperation or parasitism
We examine both the local population dynamics and the spatial arrangements that arise when individuals adaptively disperse across the landscape
Summary
Increased density reduces individual fitness by prolonging the time required to obtain local resources due to interference competition (equation (2.3a)), ∂f1/∂u1 < 0 These populations are excellent pioneer 5 species and disperse across heterogeneous landscapes to every contiguous location where resources sustain a local population, R > μ1h1/r1. The corresponding fitness function features an Allee effect (2.3b), and initially increases with density before declining as resources become exhausted This function generates a strong tendency towards aggregation into clusters, which can result in spatial instabilities and a potential absence of well-posedness in the model similar to chemotaxis. The parasitized host’s fitness (2.3a,b) is commensurately reduced by a factor of (1 − θju3)
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