相关论文: Asymptotic behaviour of ancestral lineages in subc…
Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is a…
In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…
Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…
We study the explosion phenomenon of nonlinear continuous-state branching processes (nonlinear CSBPs). First an explicit integral test for explosion is designed when the rate function does not increase too fast. We then exhibit three…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
For a finite measure $\varLambda$ on $[0,1]$, the $\varLambda$-coalescent is a coalescent process such that, whenever there are $b$ clusters, each $k$-tuple of clusters merges into one at rate…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time…
A controlled branching process (CBP) is a modification of the standard Bienaym\'e-Galton-Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites…
The asymptotic behavior of a subcritical Branching Process in Random Environment (BPRE) starting with several particles depends on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS).…
We compute the posterior distributions of the initial population and parameter of binary branching processes, in the limit of a large number of generations. We compare this Bayesian procedure with a more na\"ive one, based on hitting times…
We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…