Related papers: Colonization and collapse on Homogeneous Trees
The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman…
Evolutionary systems must learn to generalize, often extrapolating from a limited set of selective conditions to anticipate future environmental changes. The mechanisms enabling such generalization remain poorly understood, despite their…
Theoretically, communities at or near their equilibrium species number resist entry of new species. Such 'biotic resistance' recently has been questioned because of successful entry of alien species into diverse natural communities. Data on…
Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing…
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…
Assume that individuals alive at time $t$ in some population can be ranked in such a way that the coalescence times between consecutive individuals are i.i.d. The ranked sequence of these branches is called a coalescent point process. We…
The paper written in 1925 by G. Udny Yule that we celebrate in this special issue introduces several novelties and results that we recall in detail. First, we discuss Yule (1925)'s main legacies over the past century, focusing on empirical…
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial,…
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…
In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the ponds are shown to grow exponentially, with law of large…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…
The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at constant rate, to iid copies of themselves. It also established…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
In social tagging systems, the diversity of tag vocabulary and the popularity of such tags continue to increase as they are exposed to selection pressure derived from our cognitive nature and cultural preferences. This is analogous to…
The metaphor of holey adaptive landscapes provides a pictorial representation of the process of speciation as a consequence of genetic divergence. In this metaphor, biological populations diverge along connected clusters of well-fit…
Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…