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The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation…
Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective…
Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving…
It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate…
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and…
Heterozygote disadvantage is potentially a potent driver of population genetic divergence. Also referred to as underdominance, this phenomena describes a situation where a genetic heterozygote has a lower overall fitness than either…
Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
Diverse communities of competing species are generally characterized by substantial niche overlap and strongly stochastic dynamics. Abundance fluctuations are proportional to population size, so the dynamics of rare populations is slower.…
Geographic structure can affect patterns of genetic differentiation and speciation rates. In this article, we investigate the dynamics of genetic distances in a geographically structured metapopulation. We model the metapopulation as a…
We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…
We study a dynamic model of ecosystems where immigration plays an essential role both in assembling the species community and in mantaining its biodiversity. This framework is particularly relevant for insular ecosystems. Population…
The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate…