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.     

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.     

Sam Karlin and the stochastic theory of evolutionary population genetics

Sam Karlin’s role in the development of the stochastic theory of evolutionary population genetics is outlined, together with his work in developing BLAST theory.     

The relation between multilocus population genetics and social evolution theory

Evolution at multiple gene positions is complicated. Direct selection on one gene disturbs the evolutionary dynamics of associated genes. Recent years have seen the development of a multilocus methodology for modeling evolution at arbitrary numbers of gene positions with arbitrary dominance and epistatic relations, mode of inheritance, genetic linkage, and recombination. We show that the approach is conceptually analogous to social evolutionary methodology, which focuses on selection acting on associated individuals. In doing so, we (1) make explicit the links between the multilocus methodology and the foundations of social evolution theory, namely, Price's theorem and Hamilton's rule; (2) relate the multilocus approach to levels-of-selection and neighbor-modulated-fitness approaches in social evolution; (3) highlight the equivalence between genetical hitchhiking and kin selection; (4) demonstrate that the multilocus methodology allows for social evolutionary analyses involving coevolution of multiple traits and genetical associations between nonrelatives, including individuals of different species; (5) show that this methodology helps solve problems of dynamic sufficiency in social evolution theory; (6) form links between invasion criteria in multilocus systems and Hamilton's rule of kin selection; (7) illustrate the generality and exactness of Hamilton's rule, which has previously been described as an approximate, heuristic result.     

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.     

Strategic analysis in evolutionary genetics and the theory of games

This paper is written in memory of John Maynard Smith. In a brief survey it discusses essential aspects of how game theory in biology relates to its counterpart in economics, the major transition in game theory initiated by Maynard Smith, the discrepancies between genetic and phenotypic models in evolutionary biology, and a balanced way of reconciling these models. In addition, the paper discusses modern problems in understanding games at the genetic level using the examples of conflict between endosymbionts and their hosts, and the molecular interactions between parasites and the mammalian immune system.     

James F. Crow and the stochastic theory of population genetics

Research in population genetics theory has two main strands. The first is deterministic theory, where random changes in allelic frequencies are ignored and attention focuses on the evolutionary effects of selection and mutation. The second strand, stochastic theory, takes account of these random changes and thus is more complete than deterministic theory. This essay is one in the series of Perspectives and Reviews honoring James F. Crow on the occasion of his 95th birthday. It concerns his contributions to, and involvement with, the stochastic theory of evolutionary population genetics.     

Human genetics of infectious diseases: a unified theory

Since the early 1950s, the dominant paradigm in the human genetics of infectious diseases postulates that rare monogenic immunodeficiencies confer vulnerability to multiple infectious diseases (one gene, multiple infections), whereas common infections are associated with the polygenic inheritance of multiple susceptibility genes (one infection, multiple genes). Recent studies, since 1996 in particular, have challenged this view. A newly recognised group of primary immunodeficiencies predisposing the individual to a principal or single type of infection is emerging. In parallel, several common infections have been shown to reflect the inheritance of one major susceptibility gene, at least in some populations. This novel causal relationship (one gene, one infection) blurs the distinction between patient-based Mendelian genetics and population-based complex genetics, and provides a unified conceptual frame for exploring the molecular genetic basis of infectious diseases in humans.     

DNA tests of neutral theory: applications in marine genetics

The principal methods of using DNA sequence information to test the neutral theory of evolution and polymorphism are described. These include the use of synonymous and nonsynonymous substitutions for detecting purifying and positive selection, the analysis of nucleotide diversity, mismatch analysis and the HKA, McDonald-Kreitman, Tajima and Ewens-Watterson tests. Analysis of the covariation of different kinds of molecular markers and the relationship between genetic variation and fitness is also considered. Examples of the use of these approaches in a wide variety of marine organisms are described. It is emphasised that tests of neutral theory, in addition to providing important fundamental knowledge about the action of evolutionary forces, provide valuable information about the influence of environmental and demographic factors.