Related papers: Spatial patterns of competing random walkers
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
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…
Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations.…
Spatial structure is one of the simplest and most studied ecological factors that affect the evolution of cooperation. It has been shown that spatial reciprocity promotes cooperation due to the formation of cooperative clusters, which…
Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory.…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two species whose fitness is determined by the species composition of the local environment, as…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
A great number of biological organisms live in aqueous environments. Major evolutionary transitions, including the emergence of life itself, likely occurred in such environments. While the chemical aspects of the role of water in biology…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
Competitive interactions represent one of the driving forces behind evolution and natural selection in biological and sociological systems. For example, animals in an ecosystem may vie for food or mates; in a market economy, firms may…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate $p$ on the…