arXiv subjects

Charline Smadi

Publications and source records attributed to Charline Smadi.

29 records · Page 2Linked to original sources

arXiv2019

A stochastic individual based model for the growth of a stand of Japanese knotweed including mowing as a management technique

Invasive alien species are a growing threat for environment and health. They also have a major economic impact, as they can damage many infrastructures. The Japanese knotweed (Fallopia japonica), present in North America, Northern and Central Europe as well as in Australia and New Zealand, is listed by the World Conservation Union as one of the world's worst invasive species. So far, most models have dealt with how the invasion spreads without management. This paper aims at providing a model able to study and predict the dynamics of a stand of Japanese knotweed taking into account mowing as a management technique. The model we propose is stochastic and individual-based, which allows us taking into account the behaviour of individuals depending on their size and location, as well as individual stochasticity. We set plant dynamics parameters thanks to a calibration with field data, and study the influence of the initial population size, the mean number of mowing events a year and the management project duration on mean area and mean number of crowns of stands. In particular, our results provide the sets of parameters for which it is possible to obtain the stand eradication, and the minimal duration of the management project necessary to achieve this latter.

q-bio.PE↗

arXiv2019

Crossing a fitness valley as a metastable transition in a stochastic population model

We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is random, exponentially distributed.

math.PR↗

arXiv2018

Looking for the right mate in diploid species: how dominance relationships affect population differentiation in sexual trait?

Divergence between populations for a given trait can be driven by natural or sexual selection, interacting with migration behaviour. Mating preference for different phenotypes can lead to the emergence and persistence of differentiated populations. Dominance between alleles encoding for divergent phenotypes can interfere in such processes. Using a diploid model of trait determining both mating success and migration rate, we explored differentiation between two connected populations, assuming either co-dominance or strict dominance between alleles. The model assumes that individuals prefer mating with partners displaying the same phenotype and therefore tend to move to the other population when their own phenotype is rare. We show that the emergence of differentiated populations in this diploid model is limited as compared to results obtained with the same model assuming haploidy. When assuming co-dominance, differentiation arises only when migration is limited as compared to preference. Such differentiation is less dependent on migration when assuming strict dominance between haplotypes. Dominant alleles frequently invade populations because their phenotype is more frequently expressed, resulting in higher mating success and rapid decrease in migration. However, depending on the initial distribution of alleles, this advantage associated with dominance (i.e. Haldane's sieve) may lead to fixation of the dominant allele throughout both populations. Depending on the initial distribution of heterozygotes, persistence of polymorphisms within populations can also occur because heterozygotes displaying the predominant phenotype benefit from mating preferences. Altogether, our results highlight that heterozygotes' behaviour has a strong impact on population differentiation and stress out the need of diploid models of differentiation and speciation driven by natural and sexual selection.

q-bio.PE↗

arXiv2017

A stochastic model for speciation by mating preferences

Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the population size. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.

q-bio.PE↗

arXiv2016

The effect of recurrent mutations on genetic diversity in a large population of varying size

Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in the genetic signature left by a selective sweep induced by recurrent mutations at a given locus from an allele A to an allele a, depending on the mutation frequency. We distinguish three possible scales for the mutation probability per reproductive event, which entail distinct genetic signatures. Besides, we study the hydrodynamic limit of the A- and a-population size dynamics when mutations are frequent, and find non trivial equilibria leading to several possible patterns of polymorphism.

math.PR↗

arXiv2016

Asymptotic behaviour of exponential functionals of Lévy processes with applications to random processes in random environment

Let $ξ=(ξ_t, t\ge 0)$ be a real-valued Lévy process and define its associated exponential functional as follows \[ I_t(ξ):=\int_0^t \exp\{-ξ_s\}{\rm d} s, \qquad t\ge 0. \] Motivated by important applications to stochastic processes in random environment, we study the asymptotic behaviour of \[ \mathbb{E}\Big[F\big(I_t(ξ)\big)\Big] \qquad \textrm{as}\qquad t\to \infty, \] where $F$ is a non-increasing function with polynomial decay at infinity and under some exponential moment conditions on $ξ$. In particular, we find five different regimes that depend on the shape of the Laplace exponent of $ξ$. Our proof relies on a discretisation of the exponential functional $I_t(ξ)$ and is closely related to the behaviour of functionals of semi-direct products of random variables. We apply our main result to three {questions} associated to stochastic processes in random environment. We first consider the asymptotic behaviour of extinction and explosion for {stable} continuous state branching processes in a Lévy random environment. Secondly, we {focus on} the asymptotic behaviour of the mean of a population model with competition in a Lévy random environment and finally, we study the tail behaviour of the maximum of a diffusion process in a Lévy random environment.

math.PR↗

arXiv2016

Genealogies of two linked neutral loci after a selective sweep in a large population of stochastically varying size

We study the impact of a hard selective sweep on the genealogy of partially linked neutral loci in the vicinity of the positively selected allele. We consider a sexual population of stochastically varying size and, focusing on two neighboring loci, derive an approximate formula for the neutral genealogy of a sample of individuals taken at the end of the sweep. Individuals are characterized by ecological parameters depending on their genetic type and governing their growth rate and interactions with other individuals (competition). As a consequence, the "fitness" of an individual depends on the population state and is not an intrinsic characteristic of individuals. We provide a deep insight into the dynamics of the mutant and wild type populations during the different stages of a selective sweep.

math.PR↗

arXiv2015

Reduced two-type decomposable critical branching processes with possibly infinite variance

We consider a Galton-Watson process $\mathbf{Z}% (n)=(Z_{1}(n),Z_{2}(n))$ with two types of particles. Particles of type 2 may produce offspring of both types while particles of type 1 may produce particles of their own type only. Let $Z_{i}(m,n)$ be the number of particles of type $i$ at time $m<n$ having offspring at time $n$. Assuming that the process is critical and that the variance of the offspring distribution may be infinite we describe the asymptotic behavior, as $m,n\rightarrow \infty $ of the law of $\mathbf{Z}(m,n)=(Z_1(m,n),Z_2(m,n))$ given $\mathbf{Z}(n)\neq \mathbf{0}$. We find three different types of coexistence of particles of both types. Besides, we describe, in the three cases, the distributions of the birth time and the type of the most recent common ancestor of individuals alive at time $n\rightarrow \infty .$

math.PR↗

arXiv2015

The interplay of two mutations in a population of varying size: a stochastic eco-evolutionary model for clonal interference

Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a wide variety of competitive interactions which can be found in nature. In particular, we relax the classical assumption of transitivity between the different mutations. It allows us to predict genetic patterns, such as coexistence of several mutants or emergence of Rock-Paper-Scissors cycles, which were not explained by existing models. In addition, we call into questions some classical preconceived ideas about fixation time and fixation probability of competing mutations.

math.PR↗

arXiv2014

An Eco-Evolutionary approach of Adaptation and Recombination in a large population of varying size

We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behaviour for large K, where K scales the population size. We focus on two loci: one under selection and one neutral. We distinguish a soft sweep occurring after an environmental change, from a hard sweep occurring after a mutation, and express the neutral proportion variation as a function of the ecological parameters, recombination probability r\_K, and K. We show that for a hard sweep, two recombination regimes appear according to the order of r\_K log K.

math.PR↗

arXiv2013

On the extinction of Continuous State Branching Processes with catastrophes

We consider continuous state branching processes (CSBP) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a Lévy process with bounded variation paths. We construct a process of this class as the unique solution of a stochastic differential equation. The quenched branching property of the process allows us to derive quenched and annealed results and to observe new asymptotic behaviors. We characterize the Laplace exponent of the process as the solution of a backward ordinary differential equation and establish the probability of extinction. Restricting our attention to the critical and subcritical cases, we show that four regimes arise for the speed of extinction, as in the case of branching processes in random environment in discrete time and space. The proofs are based on the precise asymptotic behavior of exponential functionals of Lévy processes. Finally, we apply these results to a cell infection model and determine the mean speed of propagation of the infection.

math.PR↗