Robustness of spontaneous pattern formation in spatially distributed genetic populations

Abstract

Spatially distributed genetic populations that compete locally for resources and mate only with sufficiently close neighbors, may give rise to spontaneous pattern formation. Depending on the population parameters, like death rate per generation and size of the competition and mating neighborhoods, isolated groups of individuals, or demes, may appear. The existence of such groups in a population has consequences for genetic diversity and for speciation. In this paper we discuss the robustness of demes formation with respect to two important characteristics of the population: the way individuals recognize the demarcation of the local neighborhoods and the way competition for resources affects the birth rate in an overcrowed situation. Our results indicate that demes are expected to form only for sufficiently sharp demarcations and for sufficiently intense competition. I IntroductionAnimals don't live completely free in the wild because their living space is confined by natural boundaries. The size of the area used is determined often by individual and species needs and environmental limitation. Within the geographic distribution of the species, the range, only areas of suitable habitat are occupied.The living area normally inhabited by an animal is its Home Range. It may belong to a single individual, a mated pair, or a social unit. Within the home range there is often a defended area which is identified as a territory. Typical behavior is usually associated with establishing and defending or protecting the animal's territory. This behavior and the reproductive behavior associated with the territory is unique for each species, and allows several different animal species to live in the same space without rivalry, using different niches within the habitat. Territories are marked so that other members of the species can recognize it. Optical, acoustic, or olfactory cues, or a combination of these are often used. Olfactory demarcation is very common among mammals with a well-developed sense of smell. Urine, feces and products of special scent glands are used alone or in conjunction to mark out the territory.Theoretical biologists have become increasingly aware of the importance of space in ecology, evolution and epidemiology. Home ranges and territories have become important parameters in mathematical models of population dynamics [1,2]. It has also become apparent that inhomogeneities in spatially distributed populations can fundamentally change the dynamics of these systems [3][4][5][6][7][8][9][10]. The spatial variations so common to species in the wild, for instance, is usually attributed to variations in selective forces, i.e., differences in the environment. However, it has been shown that spatially distributed systems can develop inhomogeneity through symmetry breaking and spontaneous pattern formation, independently of environmental inhomogeneity [11,12]. Understanding the mechanisms that may lead to spatial inhomogeneities, and the eventual isolation of groups, is of fundamental importance for the study of g...

Evolution in spatial predator–prey models and the “prudent predator”: The inadequacy of steady‐state organism fitness and the concept of individual and group selection

“…However, these inquiries have been guided by the framework that uses averaging, and spatial variation that is self-generating rather than imposed externally has not been included in a consistent manner. Recent studies [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] have emphasized the importance of self-generated patterns of spatial variation that dramatically alter the characteristic properties and behavior of evolutionary processes. These studies also formalize conceptual aspects of Wright's Shifting Balance Theory [10,44], which suggested local groups of organisms (demes) could differ from each other as part of the process of significant shifts in population genetic types.…”

“…The second class includes reaction-diffusion partial differential equations, used to model pigment patterns in animal skins [18, see pp 621-698] and ecological processes [54]. Finally, lattice models [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] treat space as a discrete set of sites, or regions, whose states are determined by local interaction with nearby points. These interactions are generally not limited to weak interactions, and the types of behavior that can be studied are similar to those of partial differential equations.…”

Stable oscillations of a predator–prey probabilistic cellular automaton: a mean-field approach

“…In fact, the role of space in the description of population biology problems has been recognized by several authors in the last years [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. In a very clear manner, Durrett and Levin [11] have pointed out that the modelling of population dynamics systems which are spatially distributed by interacting particle systems [11,27,28,29] is the appropriate theoretical approach that is able to give the more complete description of the problem.…”

Reaction-diffusion stochastic lattice model for a predator-prey system

“…The model, to be called ST model, is able to exhibit local time oscillations of species populations and stable coexistence. Other deeper investigations on this model and similar models followed [10], [27], [28], [34], [38]. The ST model has a phase diagram displaying an active phase, where there is species coexistence with local time oscillations and coexistence with stationary densities; it also exhibits an absorbing phase which correspond to the extinction of one of the species.…”