Related papers: Ancestral reproductive bias in branching processes
A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…
The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
Most massive passive galaxies are compact at high redshifts, but similarly compact massive galaxies are rare in the local universe. The most common interpretation of this phenomenon is that massive galaxies have grown in size by a factor of…
We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions.…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time…
We consider the dynamics imposed by natural selection on the populations of two competing, sexually reproducing, haploid species. In this setting, the fitness of any genome varies over time due to the changing population mix of the…
The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to…
The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet…
In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been…
Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random…
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…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
The composition of cellular metabolism is different across species. Empirical data reveal that bacterial species contain similar numbers of metabolic reactions but that the cross-species popularity of reactions is so heterogenous that some…
The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
Despite increasing data from population-wide sequencing studies, the risk for recessive disorders in consanguineous partnerships is still heavily debated. An important aspect that has not sufficiently been investigated theoretically, is the…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…