The coalescent and infinite-site model of a small multigene family

The infinite-site model of a small multigene family with two duplicated genes is studied. The expectations of the amounts of nucleotide variation within and between two genes and linkage disequilibrium are obtained, and a coalescent-based method for simulating patterns of polymorphism in a small multigene family is developed. The pattern of DNA variation is much more complicated than that in a single-copy gene, which can be simulated by the standard coalescent. Using the coalescent simulation of duplicated genes, the applicability of statistical tests of neutrality to multigene families is considered.     

Efficient simulation under a population genetics model of carcinogenesis

MOTIVATION: Cancer is well known to be the end result of somatic mutations that disrupt normal cell division. The number of such mutations that have to be accumulated in a cell before cancer develops depends on the type of cancer. The waiting time T(m) until the appearance of m mutations in a cell is thus an important quantity in population genetics models of carcinogenesis. Such models are often difficult to analyze theoretically because of the complex interactions of mutation, drift and selection. They are also computationally expensive to simulate because of the large number of cells and the low mutation rate. RESULTS: We develop an efficient algorithm for simulating the waiting time T(m) until m mutations under a population genetics model of cancer development. We use an exact algorithm to simulate evolution of small cell populations and coarse-grained τ-leaping approximation to handle large populations. We compared our hybrid simulation algorithm with the exact algorithm in small populations and with available asymptotic results for large populations. The comparison suggested that our algorithm is accurate and computationally efficient. We used the algorithm to study the waiting time for up to 20 mutations under a Moran model with variable population sizes. Our new algorithm may be useful for studying realistic models of carcinogenesis, which incorporates variable mutation rates and fitness effects.     

Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics

We discuss a selection-migration model in population genetics, involving two alleles A ₁ and A ₂ such that A ₁ is at an advantage over A ₂ in certain subregions and at a disadvantage in others. It is shown that if A ₁ is at an overall disadvantage to A ₂ and the rate of gene flow is sufficiently large than A ₁ must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A ₁ and A ₂ can coexist no matter how great the rate of gene flow.     

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     

Bacterial population genetics

Bacterial population genetics is the study of natural bacterial genetic diversity arising from evolutionary processes. The roles of molecular mistakes, restriction–modification, plasmids and gene transfer in bacteria are also important components of population genetics. These aspects are of considerable scientific importance from a fundamental perspective, because of the short generation times of bacteria, their microscopic cell size, the large population sizes bacteria can achieve and their different mechanisms of gene transfer.     

Bacterial population genetics

Bacterial population genetics is the study of natural bacterial genetic diversity arising from evolutionary processes. The roles of molecular mistakes, restriction–modification, plasmids and gene transfer in bacteria are also important components of population genetics. These aspects are of considerable scientific importance from a fundamental perspective, because of the short generation times of bacteria, their microscopic cell size, the large population sizes bacteria can achieve and their different mechanisms of gene transfer.     

Mantel test in population genetics

The comparison of genetic divergence or genetic distances, estimated by pairwise F_ST and related statistics, with geographical distances by Mantel test is one of the most popular approaches to evaluate spatial processes driving population structure. There have been, however, recent criticisms and discussions on the statistical performance of the Mantel test. Simultaneously, alternative frameworks for data analyses are being proposed. Here, we review the Mantel test and its variations, including Mantel correlograms and partial correlations and regressions. For illustrative purposes, we studied spatial genetic divergence among 25 populations of Dipteryx alata (“Baru”), a tree species endemic to the Cerrado, the Brazilian savannas, based on 8 microsatellite loci. We also applied alternative methods to analyze spatial patterns in this dataset, especially a multivariate generalization of Spatial Eigenfunction Analysis based on redundancy analysis. The different approaches resulted in similar estimates of the magnitude of spatial structure in the genetic data. Furthermore, the results were expected based on previous knowledge of the ecological and evolutionary processes underlying genetic variation in this species. Our review shows that a careful application and interpretation of Mantel tests, especially Mantel correlograms, can overcome some potential statistical problems and provide a simple and useful tool for multivariate analysis of spatial patterns of genetic divergence.