Related papers: On the Eve property for CSBP
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
This paper uses two new ingredients, namely stochastic differential equations satisfied by continuous-state branching processes (CSBPs), and a topology under which the Lamperti transformation is continuous, in order to provide…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
We consider a model of stationary population with random size given by a continuous state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of…
We generalize the notion of the submartingale property and Doob's inequality. Furthermore, we show how the latter leads to new inequalities for several stochastic processes: certain time series, Levy processes, random walks, processes with…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
Interacting systems of events may exhibit cascading behavior where events tend to be temporally clustered. While the cascades themselves may be obvious from the data, it is important to understand which states of the system trigger them.…
Based on the study of cellular aging using the single-cell model organism of budding yeast and corroborated by other studies, we propose the Emergent Aging Model (EAM). EAM hypothesizes that aging is an emergent property of complex…
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…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…
Recently in Barczy, Li and Pap (2015), the notion of a multi-type continuous-state branching process (with immigration) having d-types was introduced as a solution to an d-dimensional vector- valued SDE. Preceding that, work on affine…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…