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Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…
We investigate the Volterra ecosystem driven by correlated noises. The competition of the predators induces an increasing in population density of the predators. The competition of the preys, however, leads the predators to decay. The…
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the…
Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
We have analyzed the interplay between noise and periodic modulations in a classical Lotka-Volterra model of two-species competition. We have found that the consideration of noise changes drastically the behavior of the system and leads to…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
Environmental fluctuations have important consequences in the organization of ecological communities, and understanding how such a variability influences the biodiversity of an ecosystem is a major question in ecology. In this paper, we…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model,…