Related papers: Ancestral lines under recombination
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…
We consider a Moran model with recombination in a haploid population of size $N$. At each birth event, with probability $1-\rho_N R$ the offspring copies one parent's chromosome, and with probability $\rho_N R$ she inherits a chromosome…
Edge Constrained Vertex Coloring (ECVC) problems are defined on a finite multigraph, their solutions are characterized, and a linear time algorithm is given for solving $N$ ECVCs on the same underlying multigraph. Using ECVC problems we…
This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We…
The genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies…
Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the…
This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible…
The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent…
In the past decade, advances in genome sequencing have allowed researchers to uncover the history of hybridization in diverse groups of species, including our own. Although the field has made impressive progress in documenting the extent of…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R…
Computer simulations of complex population genetic models are an essential tool for making sense of the large-scale datasets of multiple genome sequences from a single species that are becoming increasingly available. A widely used approach…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Genetic association data from national biobanks and large-scale association studies have provided new prospects for understanding the genetic evolution of complex traits and diseases in humans. In turn, genomes from ancient human…
Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this…
Large scale databases are available that contain homologous gene families constructed from hundreds of complete genome sequences from across the three domains of Life. Here we discuss approches of increasing complexity aimed at extracting…