Related papers: General triallelic frequency spectrum under demogr…
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…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
Rate variation among the sites of a molecular sequence is commonly found in applications of phylogenetic inference. Several approaches exist to account for this feature but they do not usually enable the investigator to pinpoint the sites…
The detection of molecular signatures of selection is one of the major concerns of modern population genetics. A widely used strategy in this context is to compare samples from several populations, and to look for genomic regions with…
Genotype networks are a method used in systems biology to study the "innovability" of a set of genotypes having the same phenotype. In the past they have been applied to determine the genetic heterogeneity, and stability to mutations, of…
Private collection of statistics from a large distributed population is an important problem, and has led to large scale deployments from several leading technology companies. The dominant approach requires each user to randomly perturb…
Social networks play an important role in analyzing the impact of individual-level interactions on societal or economic outcomes. We model interactive decision making for a community of individuals with different traits, represented by a…
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…
The reconstruction of a species phylogeny from genomic data faces two significant hurdles: 1) the trees describing the evolution of each individual gene--i.e., the gene trees--may differ from the species phylogeny and 2) the molecular…
A haplotype block, or simply a block, is a chromosomal segment, DNA base sequence or string that occurs in only a few variants or types in the genomes of a population of interest, and that has an encapsulated or 'private' frequency…
Very long and noisy sequence data arise from biological sciences to social science including high throughput data in genomics and stock prices in econometrics. Often such data are collected in order to identify and understand shifts in…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
A procedure is described for estimating evolutionary rate matrices from observed site frequency data. The procedure assumes (1) that the data are obtained from a constant size population evolving according to a stationary Wright-Fisher…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the…
We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the…