Related papers: A stochastic model for phylogenetic trees
An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples…
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…
Modern biological techniques enable very dense genetic sampling of unfolding evolutionary histories, and thus frequently sample some genotypes multiple times. This motivates strategies to incorporate genotype abundance information in…
We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is…
We study the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a…
The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a…
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…
Phylogenetic trees represent evolutionary relationships and can be uniquely defined by sets of finite-state biological characteristics. Despite prior work showing that sufficiently large trees can be determined by $r$-state character sets,…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…
Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…
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.…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate. We assume that individuals independently…
The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the…