Displaying similar documents to “A Brownian population model.”

Linking population genetics to phylogenetics

Paul G. Higgs (2008)

Banach Center Publications

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Population geneticists study the variability of gene sequences within a species, whereas phylogeneticists compare gene sequences between species and usually have only one representative sequence per species. Stochastic models in population genetics are used to determine probability distributions for gene frequencies and to predict the probability that a new mutation will become fixed in a population. Stochastic models in phylogenetics describe the substitution process in the single sequence...

Mathematical Modeling Describing the Effect of Fishing and Dispersion on Hermaphrodite Population Dynamics

S. Ben Miled, A. Kebir, M. L. Hbid (2010)

Mathematical Modelling of Natural Phenomena

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In order to study the impact of fishing on a grouper population, we propose in this paper to model the dynamics of a grouper population in a fishing territory by using structured models. For that purpose, we have integrated the natural population growth, the fishing, the competition for shelter and the dispersion. The dispersion was considered as a consequence of the competition. First we prove, that the grouper stocks may be less sensitive...

Some mathematical problems arising in heterogeneous insular ecological models.

Sébastien Gaucel, Michel Langlais (2002)

RACSAM

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En esta nota se analizan dos modelos matemáticos deterministas planteados en problemas ecológicos causados por la introducción de nuevas especies en ambientes insulares heterogéneos. En el primero desarrollamos un modelo epidemológico con transmisión indirecta del virus por medio del ambiente. En el segundo se introduce un modelo específico de depredador-presa que exhibe la extinción en tiempo finito de las especies. Ambos modelos involucran sistemas de ecuaciones en derivadas parciales...

Do Demographic and Disease Structures Affect the Recurrence of Epidemics ?

A. Castellazzo, A. Mauro, C. Volpe, E. Venturino (2012)

Mathematical Modelling of Natural Phenomena

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In this paper we present an epidemic model affecting an age-structured population. We show by numerical simulations that this demographic structure can induce persistent oscillations in the epidemic. The model is then extended to encompass a stage-structured disease within an age-dependent population. In this case as well, persistent oscillations are observed in the infected as well as in the whole population.

Large time behavior in a density-dependent population dynamics problem with age structure and child care

Vladas Skakauskas (2003)

Banach Center Publications

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Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the...

Drift, draft and structure: some mathematical models of evolution

Alison M. Etheridge (2008)

Banach Center Publications

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Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to...

Ancestral processes with selection: Branching and Moran models

Ellen Baake, Robert Bialowons (2008)

Banach Center Publications

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We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population...