Related papers: Randomly evolving trees I
Sexual selection theory models evolution of sexual signals and preferences using simple life histories. However, life-history models predict that males benefit from increasing sexual investment approaching old age, producing age-dependent…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
Standard evolutionary theories of aging and mortality, implicitly based on assumptions of spatial averaging, hold that natural selection cannot favor shorter lifespan without direct compensating benefit to individual reproductive success.…
Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
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…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have $n$ extant species today, we look at the tree distribution of the reconstructed trees-- i.e. the trees…
Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can…
Many life-history traits, like the age at maturity or adult longevity, are important determinants of the generation time. For instance, semelparous species whose adults reproduce once and die have shorter generation times than iteroparous…
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…