Related papers: The evolving beta coalescent
Trees corresponding to $\Lambda$- and $\Xi$-$n$-coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$-coalescent. This has consequences for inference of a well-fitting…
We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process $(A_i; i\ge 1)$, where $A_i$ is the…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider 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…
We consider a model of a population in which individuals are sampled from different species. The Yule-Kingman nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a…
Existing theories for the evolution of aging and death treat senescence as a side-effect of strong selection for fertility. These theories are well-developed mathematically, but fit poorly with emerging experimental data. The data suggest…
Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…
The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of $n$ genes as the population size $N$ tends to infinity. Unlike traditional approach in…
We present an elementary model of random size varying population given by a stationary continuous state branching process. For this model we compute the joint distribution of: the time to the most recent common ancestor, the size of the…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
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…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
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…
Kingman's coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it…
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…
Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…