Related papers: Time fluctuations in a population model of adaptiv…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…
We examine the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated in the realm of ecology on a problem of population establishment. Here, by assuming a…
During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space, How such multimodal patterns in phenotype space can emerge from a single ancestral…
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…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Dynamics of a social population is analyzed taking into account some physical constraints on individual behavior and decision making abilities. The model, based on Evolutionary Game Theory, predicts that a population has to pass through a…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
When a collection of phenotypically diverse organisms compete with each other for limited resources, with competition being strongest amongst the most similar, the population can evolve into tightly localised clusters. This process can be…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. We introduce theclimate shift due to {\it Global Warming} and discuss the dynamicsof the…
We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
Following previous works about integro-differential equations of parabolic type modelling the Darwinian evolution of a population, we study a two-population system in the cooperative case. First, we provide a theoretical study of the limit…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…