To understand the relative importance of natural selection and random genetic drift in finite but growing populations, the asymptotic behavior of a class of generalized Polya urns is studied using the method of ordinary differential equation (ODE). Of particular interest is the replicator process: two balls (individuals) are chosen from an urn (the population) at random with replacement and bal...

The question of language evolution is of interest to linguistics, biology and recently, engineering communicating networks. Previous work on these problems has focused mostly on a fully-connected population. We are extending this study to structured populations, which are generally more realistic and offer rich opportunities for linguistic diversification. Our work focuses on the convergence pr...

where ri,Ki,αi ∈ C(R,R+), αi > Ki, i = 1,2, τi,σi ∈ C(R,R+), i = 1,2, ri, Ki, αi, τi, σi(i = 1,2) are functions of period ω > 0. Since the study on periodic solutions of a population model is of great interest in mathematical biology [5] and many authors [1, 7] have argued that the discrete-time models governed by difference equations are more appropriate than the continuous ones when the popul...

We present a stochastic two-population model that describes the migration and growth of semisedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea of this paper is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop production and associated degradation of la...

It is frequently conveyed, especially in the media, an idea of “increasing impact of natural hazards” typically attributed to their rising frequency and/or growing vulnerability of populations. However, for certain hazard types, this may be mostly a result of increasing population exposure due to phenomenal global population growth, especially in the most hazardous areas. We investigate tempora...

Abstract. We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their lo...

We present and discuss particle based algorithms to numerically study the dynamics of population subjected to an advecting flow condition. We discuss few possible variants of the algorithms and compare them in a model compressible flow. A comparison against appropriate versions of the continuum stochastic Fisher equation (sFKPP) is also presented and discussed. The algorithms can be used to stu...

We present and analyse in this article a mathematical question with a biological origin, the theoretical treatment of which may have far-reaching implications in the practical treatment of cancers. Starting from biological and clinical observations on cancer cells, tumourbearing laboratory rodents, and patients with cancer, we ask from a theoretical biology viewpoint questions that may be trans...

Steven A. Frank Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697–2525 USA The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the population. Deductive theory predicts how pop...

BACKGROUND Extensive studies in different fields have been performed to reconstruct the prehistory of populations in the Japanese archipelago. Estimates the ancestral population dynamics based on Japanese molecular sequences can extend our understanding about the colonization of Japan and the ethnogenesis of modern Japanese. METHODOLOGY/PRINCIPAL FINDINGS We applied Bayesian skyline plot (BSP...