Related papers: Wright's adaptive landscape versus Fisher's fundam…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
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…
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Evolution is a fundamental process that shapes the biological world we inhabit, and reinforcement learning is a powerful tool used in artificial intelligence to develop intelligent agents that learn from their environment. In recent years,…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…
We consider the dynamics imposed by natural selection on the populations of two competing, sexually reproducing, haploid species. In this setting, the fitness of any genome varies over time due to the changing population mix of the…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
We investigate evolutionary dynamics related to periodicity fossil biodiversity. Coherent periodic fluctuation in origination/extinction of marine genera that survive <45 million years is the source of an observed ~62 million year…
In the article I study the evolutionary adaptivity of two simple population models, based on either altruistic or egoistic law of energy exchange. The computational experiments show the convincing advantage of the altruists, which brings us…
Adaptation is a central topic in theoretical biology, of practical importance for analyzing drug resistance mutations. Several authors have used arguments based on extreme value theory in their work on adaptation. There are complications…
Population genetics lies at the heart of evolutionary theory. This topic forms part of many biological science curricula but is rarely taught to physics students. Since physicists are becoming increasingly interested in biological…
Niche and neutral theory are two prevailing, yet much debated, ideas in ecology proposed to explain the patterns of biodiversity. Whereas niche theory emphasizes selective differences between species and interspecific interactions in…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
In this article, we study the growth and spread of a new species in a river network with two or three branches via the Fisher-KPP advection-diffusion equation over some simple graphs with every edge a half infinite line. We obtain a rather…