Stochastic theory of population genetics

Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.     

The interface between epidemiology and population genetics

Modern biology increasingly integrates disparate disciplines. Here, Steve Paterson and Mark Viney examine the interface between epidemiology and population genetics. They argue that infection and inheritance can be considered as analogous processes, and that epidemiology and population genetics share many common features. They consider the potential for existing population genetic theory to dissect epidemiological patterns in field studies and they consider other relationships between genetics and epidemiology that provide a research challenge for the future.     

Bacterial population genetics, evolution and epidemiology.

Asexual bacterial populations inevitably consist of an assemblage of distinct clonal lineages. However, bacterial populations are not entirely asexual since recombinational exchanges occur, mobilizing small genome segments among lineages and species. The relative contribution of recombination, as opposed to de novo mutation, in the generation of new bacterial genotypes varies among bacterial populations and, as this contribution increases, the clonality of a given population decreases. In consequence, a spectrum of possible population structures exists, with few bacterial species occupying the extremes of highly clonal and completely non-clonal, most containing both clonal and non-clonal elements. The analysis of collections of bacterial isolates, which accurately represent the natural population, by nucleotide sequence determination of multiple housekeeping loci provides data that can be used both to investigate the population structure of bacterial pathogens and for the molecular characterization of bacterial isolates. Understanding the population structure of a given pathogen is important since it impacts on the questions that can be addressed by, and the methods and samples required for, effective molecular epidemiological studies.     

Determining the source of individuals: multilocus genotyping in nonequilibrium population genetics

Recently founded populations represent an enormous challenge for genetic analysis: new populations are often genetically impoverished, making it hard to find sufficiently variable markers, and what little variation is present tends to be ancestral, rendering phylogenetic methods inappropriate. Recently, novel genetic markers and new statistical analyses have made multilocus genotyping an invaluable tool in the fledgling field of nonequilibrium population genetics. Such advances are not of mere academic interest but address questions of great economic, medical and conservation significance.     

The lattice models of neutral multi-alleles in population genetics theory

The aim of this article is to study lattice models of neutral multi-alleles including Ohta-Kimura's step-wise mutation model. We shall show an outline of the construction of a unique strongly continuous non-negative semi-group associated with the infinite dimensional generator and show a general and straightforward method of obtaining the time dependent and equilibrium solutions of all polynomial moments of the gene frequencies. We shall discuss the spectrum of the diffusion processes and as an application we obtain all higher moments of the homozygosity.     

Molecular population genetics and evolution of Drosophila meiosis genes

While many functional elements of the meiotic process are well characterized in model organisms, the genetic basis of most of the natural phenotypic variation observed in meiotic pathways has not been determined. To begin to address this issue, we characterized patterns of polymorphism and divergence in the protein-coding regions of 33 genes across 31 lines of Drosophila melanogaster and 6 lines of Drosophila simulans. We sequenced genes known to be involved in chromosome segregation, recombination, DNA repair, and related heterochromatin binding. As expected, we found several of the genes to be highly conserved, consistent with purifying selection. However, a subset of genes showed patterns of polymorphism and divergence typical of other types of natural selection. Moreover, several intriguing differences between the two Drosophila lineages were evident: along the D. simulans lineage we consistently found evidence of adaptive protein evolution, whereas along the D. melanogaster lineage several loci exhibited patterns consistent with the maintenance of protein variation.     

Some one-dimensional migration models in population genetics theory

This paper gives a method for calculating the covariance of gene frequencies at any two points of a habitat which is a finite 1-dimensional interval. Selectively neutral genes are considered migrating according to a continuous parameter analogue of the stepping stone model. The method is to solve a partial differential equation for the covariance, together with boundary conditions of zero normal derivative (or reflecting barrier) type.     

Quasispecies theory in the context of population genetics

Background  

A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory.     

PGEToolbox: A Matlab toolbox for population genetics and evolution

Assessing genetic diversity within populations is vital for understanding the nature of evolutionary processes at the molecular level. PGEToolbox is a Matlab-based open-sourced software package for data analysis in population genetics. The main features of this software are as follows: 1) capability for handling both DNA sequence polymorphisms and single nucleotide polymorphisms (SNPs), which include genotype and haplotype data; 2) exhaustive population genetic analyses and neutrality tests based on the coalescent theory; 3) extendibility and scalability for complex and large genome-wide datasets; 4) simple yet effective graphic user interfaces and sophisticated visualization of data and results. For academic uses, PGEToolbox is available free of charge at http://bioinformatics.org/pgetoolbox.     

The evolution of social communication systems in a subdivided population

Evolution of social communication systems is modeled with a quantitative genetic model. The mathematical model describes the coevolutionary process of a social signal (a social character) and responsiveness (a social preference) to the signal. The responsiveness is postulated to influence fitness of senders of the signal. Considerations are extended to subdivided population structure by combining the social selection model with a group selection model. The numerical results derived from the models indicate that the evolutionary rate of social communication systems depends largely on genetic correlation between the signal and the responsiveness. Group selection can reinforce the evolutionary rate and relax its dependence on genetic correlation. The origin of genetic correlation is discussed in relation to group selection.     

The sampling theory of neutral alleles and an urn model in population genetics

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.This research was partially supported by the Sloan Foundation under Grant 85-6-14 and by the National Science Foundation