Related papers: Estimating the growth rate of a birth and death pr…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
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),…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used…
The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
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…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
Our purpose is to estimate the posterior distribution of the parameters of interest for controlled branching processes (CBPs) without prior knowledge of the maximum number of offspring that an individual can give birth to and without…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
Sweepstakes reproduction refers to a highly skewed individual recruitment success without involving natural selection and may apply to individuals in broadcast spawning populations characterised by Type III survivorship. We consider an…
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past…
We consider Gaussian approximation in a variant of the classical Johnson--Mehl birth-growth model with random growth speed. Seeds appear randomly in $\mathbb{R}^d$ at random times and start growing instantaneously in all directions with a…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…