Displaying similar documents to “Population-size-dependent branching processes.”

Changing the branching mechanism of a continuous state branching process using immigration

Romain Abraham, Jean-François Delmas (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition...

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...

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...

Propagation of Growth Uncertainty in a Physiologically Structured Population

H.T. Banks, S. Hu (2012)

Mathematical Modelling of Natural Phenomena

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In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described ...

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...

Population changes as litmus paper of the socio-economic development level of small towns in Poland

Agnieszka Kwiatek-Sołtys (2015)

Annales Universitatis Paedagogicae Cracoviensis Studia Geographica

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The main aim of the author was to analyse the population changes of small towns in Poland between 2002 and 2012. Small towns’ reaction to the global and regional demographic trends confirms their position between the rural areas and the urban municipalities. The differences between separate towns are significant, however those located within the metropolitan areas in Poland show a positive population dynamics, natural growth and migration balance net indexes. The image of small towns...

Adaptive dynamics in logistic branching populations

Nicolas Champagnat, Amaury Lambert (2008)

Banach Center Publications

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The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we...

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...