Related papers: Influence of geography on language competition
Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks…
Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a…
Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous…
Computational modelling with multi-agent systems is becoming an important technique of studying language evolution. We present a brief introduction into this rapidly developing field, as well as our own contributions that include an…
Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms…
We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model)…
Indirect competition emerged from the complex organization of human societies, and knowledge of the existing network topology may aid in developing effective strategies for success. Here, we propose an agent-based model of competition with…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
In this paper, we investigate a Lotka-Volterra competition-diffusion system with self-memory effects and spatial heterogeneity under Dirichlet boundary conditions. We focus on how memory strength influences the coexistence and stability of…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third…
Spatial segregation occurs in population dynamics when $k$ species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of $k$ differential equations \[ -\Delta…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Evolutionary game theory has proven to be an elegant framework providing many fruitful insights in population dynamics and human behaviour. Here, we focus on the aspect of behavioural plasticity and its effect on the evolution of…