Related papers: Statistical Analysis of Genealogical Trees for Pol…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given…
A probabilistic reconstruction of genealogies in a polyploid population (from 2x to 4x) is investigated, by considering genetic data analyzed as the probability of allele presence in a given genotype. Based on the likelihood of all possible…
We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the…
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,…
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…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
Phylogenetic species trees typically represent the speciation history as a bifurcating tree. Speciation events that simultaneously create more than two descendants, thereby creating polytomies in the phylogeny, are possible. Moreover, the…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
Driven by the popularity of television shows such as Who Do You Think You Are? many millions of users have uploaded their family tree to web projects such as WikiTree. Analysis of this corpus enables us to investigate genealogy…
In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.
With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…