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To establish lists of words with unexpected frequencies in long sequences,
for instance in a molecular biology context, one needs to
quantify the exceptionality of families of word frequencies in random
sequences. To this aim, we
study large deviation probabilities of multidimensional word counts
for Markov and hidden Markov models.
More specifically, we compute local Edgeworth expansions
of arbitrary degrees for multivariate partial sums of lattice valued
functionals of finite Markov...
We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...
We consider the spatial -Fleming–Viot process model (Electron. J. Probab.15(2010) 162–216) for frequencies of genetic types in a population living in , in the special case in which there are just two types of individuals, labelled and . At time zero, everyone in a given half-space has type 1, whereas everyone in the complementary half-space has type . We are concerned with patterns of frequencies of the two types at large space and time scales. We consider two cases, one in which the dynamics...
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 environmental...
It is well established that resource variability generated by spatial patchiness and turbulence is an important
influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations
indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can
be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...
Whether the size of an animal population is environmentally limited or regulated
by density dependent negative feedback mechanisms is of ecological interest. Proponents of
limitation theory have issued a set of specific challenges which are addressed in this paper
using field data for the insect Tipula paludosa. This species is known to be subject to population crashes caused by adverse environmental conditions and assumed to be limited.
We re-examine published data in support of this hypothesis...
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 that...
Relaxation oscillations are limit cycles with two clearly different
time scales. In this article the spatio-temporal dynamics of a
standard prey-predator system in the parameter region of relaxation
oscillation is investigated. Both prey and predator population are
distributed irregularly at a relatively high average level between a
maximal and a minimal value. However, the slowly developing complex
pattern exhibits a feature of “inverse excitability”: Both
populations show collapses which occur...
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