Progressive diseases: Interpretation of genetic data.
Baum, Larry, Baum, Eric (1999)
Journal of Theoretical Medicine
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Baum, Larry, Baum, Eric (1999)
Journal of Theoretical Medicine
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I. Koźniewska (1957)
Colloquium Mathematicae
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Sophie Ancelet, Gilles Guillot, Olivier François (2007)
Journal de la société française de statistique
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Spatial bayesian clustering algorithms can provide correct inference of population genetic structure when applied to populations for which continuous variation of allele frequencies is disrupted by small discontinuities. Here we review works which used bayesian clustering algorithms for studying the Scandinavian brown bears, with particular attention to a recent method based on hidden Markov random field. We provide a summary of current knowledge about the genetic structure of this endangered...
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.
Tzen-Ping Liu, M.E. Thompson (1985)
Aequationes mathematicae
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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...
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...
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...
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...
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...
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 ...
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...
Andrzej Polański, Marek Kimmel (2003)
International Journal of Applied Mathematics and Computer Science
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The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.