相关论文: Asymptotic behaviour of ancestral lineages in subc…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
Let $Z_{n}$ be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming…
The boundary behavior of continuous-state branching processes with quadratic competition is studied in whole generality. We first observe that despite competition, explosion can occur for certain branching mechanisms. We obtain a necessary…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
The goal of this work is to decompose random populations with a genealogy in subfamilies of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We model the genealogical structure of a population by…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
In this paper the asymptotic behavior of a critical multi-type branching process with immigration is described when the offspring mean matrix is irreducible, in other words, when the process is indecomposable. It is proved that sequences of…
We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of…
A general model of catalytic branching process (CBP) with any finite number of catalysis centers in a discrete space is studied. More exactly, it is assumed that particles move in this space according to a specified Markov chain and they…
The problem of conditioning a continuous-state branching process with quadratic competition (logistic CB process) on non-extinction is investigated. We first establish that non-extinction is equivalent to the total progeny of the population…
In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a…
Branching processes in a random environment are natural generalisations of Galton-Watson processes. In this paper we analyse the asymptotic decay of the survival probability for a sequence of slightly supercritical branching processes in an…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…