Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

Abstract

A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects.

Discovering the effect of nonlocal payoff calculation on the stabilty of ESS: Spatial patterns of Hawk–Dove game in metapopulations

“…In Section 2, we did not specify the neighborhoods or the spatial dimension of the habitat. Here we first describe the simple nearest neighbor dispersal and interaction in 1D and 2D spatial habitats used in both ecological studies by [12,47,26,30,8], and game theoretical studies initiated by [34,35]. Then we give a general form of the mean field equation and find the conditions under which the ESS can be destabilized.…”

“…The emergence of spatial inhomogeneity is related to the nonlocal (or quasi-local) interactions that are shown to be a mechanism for spatial pattern formation for a number of ecolgical processes [7,14,3,4,25,12,30,26,47]. In these earlier works it was shown that the spatial inhomegeniety is due to the fluctuating density of a species.…”

A note on semi-discrete modelling in the life sciences

“…Kisdi & Utz (2005) put the model by Geritz & Kisdi (2004) in the spatially explicit context of a patchy environment and studied the formation of patterns along a chain of patches. Utz et al (2007) prolonged this work, adding a more detailed structure of the consumer population to the model and proposed an explanation to the emergence of an Allee effect.…”

Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

“…These riches include cyclic and chaotic behaviour with complicated bifurcation patterns, multiple attractors with fractal basins of attraction, and spatial pattern formation of various kinds (e.g. Kaneko 1990Kaneko , 1998Hastings 1993;Gyllenberg et al 1993;Doebeli 1995;Lloyd 1995;Doebeli and Ruxton 1998;Utz et al 2007). Because of this inherently complex dynamics, much work on discrete-time metapopulations falls back on numerical analysis and simulations, and hence is forced to commit to particular choices such as using the logistic map, or assuming nearest-neighbour dispersal or a Gaussian dispersal kernel.…”