Related papers: Statistical Genetics in and out of Quasi-Linkage E…
The phase of Quasi-Linkage Equilibrium (QLE) in evolutionary populations is analogous to the thermal equilibrium state in statistical mechanics, a concept pioneered by Kimura in 1965 for two-locus two-allele models. QLE describes a…
The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution,…
We consider a population evolving due to mutation, selection and recombination, where selection includes single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). We further consider the problem of inferring…
Describing the evolution of a population of genomes evolving in a complex fitness landscape is generally very hard. We here introduce an approximate Gaussian closure scheme to characterize analytically the statistics of a genomic population…
The genetic composition of a naturally developing population is considered as due to mutation, selection, genetic drift and recombination. Selection is modeled as single-locus terms (additive fitness) and two-loci terms (pairwise epistatic…
A central question in evolutionary biology is how to quantitatively understand the dynamics of genetically diverse populations. Modeling the genotype distribution is challenging, as it ultimately requires tracking all correlations (or…
Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of…
The quasi-static evolution of steady states far from equilibrium is investigated from the point of view of quantum statistical mechanics. As a concrete example of a thermodynamic system, a two-level quantum dot coupled to several reservoirs…
We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic…
Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus,…
The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form $X_t=\sigma_tZ_t$, where the unobservable volatility $\sigma_t$ is a parametric function of…
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…
Since the foundations of Population Genetics the notion of genetic equilibrium (in close analogy to Classical Mechanics) has been associated to the Hardy-Weinberg (HW) Principle and the identification of equilibrium is currently assumed by…
We investigate the evolutionary dynamics of a finite population of RNA sequences adapting to a neutral fitness landscape. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive…
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 develop a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by $S$, and the average Hamming distance between them, denoted by $H$. We argue that a…