Displaying similar documents to “Ancestral processes with selection: Branching and Moran models”

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...

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...

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.

Mathematical Modeling and Quantitative Analysis of the Demographic and Ecological Aspects of Russian Supermortality

A. K. Cherkashin, Ya. A. Leshchenko (2011)

Mathematical Modelling of Natural Phenomena

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We have carried out a polysystem analysis of the population dynamics by using a variety of hypotheses and their respective models based on different system interpretations of the phenomenon under investigation. Each of the models supplements standard dynamic equations for explaining the effects observed. A qualitative model-based analysis is made of the age-specific male mortality for a Siberian industrial city. The study revealed the ...

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...

The impatience mechanism as a diversity maintaining and saddle crossing strategy

Iwona Karcz-Duleba (2016)

International Journal of Applied Mathematics and Computer Science

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The impatience mechanism diversifies the population and facilitates escaping from a local optima trap by modifying fitness values of poorly adapted individuals. In this paper, two versions of the impatience mechanism coupled with a phenotypic model of evolution are studied. A population subordinated to a basic version of the impatience mechanism polarizes itself and evolves as a dipole centered around an averaged individual. In the modified version, the impatience mechanism is supplied...

Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations

A.S. Novozhilov (2012)

Mathematical Modelling of Natural Phenomena

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We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed...