Warren J. Ewens

The sampling theory of selectively neutral alleles

Abstract In this paper a beginning is made on the sampling theory of neutral alleles. That is, we consider deductive and subsequently inductive questions relating to a sample of genes from a selectively neutral locus. The inductions concern estimation, confidence intervals and hypothesis testing. In particular the test of the hypothesis that the alleles being sampled are indeed selectively neutral will be considered. In view of the large amount of data currently being obtained by electrophoretic methods on allele frequencies and numbers, and the current interest in the possibility of extensive “non-Darwinian” evolution, such a sampling theory seems necessary. However, a large number of unsolved problems in this area remain, a partial listing being given towards the end of this paper.

Common genetic variants account for differences in gene expression among ethnic groups

Variation in DNA sequence contributes to individual differences in quantitative traits, but in humans the specific sequence variants are known for very few traits. We characterized variation in gene expression in cells from individuals belonging to three major population groups. This quantitative phenotype differs significantly between European-derived and Asian-derived populations for 1,097 of 4,197 genes tested. For the phenotypes with the strongest evidence of cis determinants, most of the variation is due to allele frequency differences at cis-linked regulators. The results show that specific genetic variation among populations contributes appreciably to differences in gene expression phenotypes. Populations differ in prevalence of many complex genetic diseases, such as diabetes and cardiovascular disease. As some of these are probably influenced by the level of gene expression, our results suggest that allele frequency differences at regulatory polymorphisms also account for some population differences in prevalence of complex diseases.

Statistical Methods in Bioinformatics

In a precision printing machine utilizing a cylindrical drum on which are characters for printing on an adjacent tape, the drum is rotatable in either direction and slidable along an axis in either direction by means of pulse motors. The machine is so designed that the final steps in the printing operation prior to the printing itself always consist of motion of the drum in the same predetermined axial direction and rotation of the drum in the same preselected rotational direction. By this means, possible errors due to gear backlash, and imprecision in machine components are minimized.

Population Genetics Theory - The Past and the Future

Classical population genetics theory was largely directed towards processes relating to the future. Present theory, by contrast, focuses on the past, and in particular is motivated by the desire to make inferences about the evolutionary processes which have led to the presently observed patterns and nature of genetic variation. There are many connections between the classical prospective theory and the new retrospective theory. However, the retrospective theory introduces ideas not appearing in the classical theory, particularly those concerning the ancestry of the genes in a sample or in the entire population. It also introduces two important new distributions into the scientific literature, namely the Poisson-Dirichlet and the GEM: these are important not only in population genetics, but also in a very wide range in science and mathematics. Some of these are discussed. Population genetics theory has been greatly enriched by the introduction of many new concepts relating to the past evolution of biological populations.

On the concept of the effective population size

Abstract The concept of the effective population size is discussed. It is shown that the “eigenvalue” and the “inbreeding” effective population sizes are in principle different, even though they have been sometimes identified in the literature. On the other hand the “eigenvalue” and “variance” effective sizes are usually both close when the latter exists. Since, however, there are many models for which a variance effective size cannot in principle exist, it seems useful to introduce the eigenvalue effective size and to examine some of its properties.

A note on the sampling theory for infinite alleles and infinite sites models

Abstract This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology of Kimura ( Theor. Pop. Biol. 2 , 174–208 (1971) ), the “infinite sites” model of Karlin and McGregor ( Proc. Fifth Berkeley Symp. Math. Statist. Prob. 4 , 415–438 (1967) ) rather that the “infinite alleles” model of Kimura and Crow ( Genetics 49 , 174–738 (1964) ). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens ( Theor. Pop. Biol. 3 , 87–112 (1972) ) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper by Watterson (submitted for publication (1974) ) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.

A Review of Family-Based Tests for Linkage Disequilibrium between a Quantitative Trait and a Genetic Marker

Quantitative trait transmission/disequilibrium tests (quantitative TDTs) are commonly used in family-based genetic association studies of quantitative traits. Despite the availability of various quantitative TDTs, some users are not aware of the properties of these tests and the relationships between them. This review aims at outlining the broad features of the various quantitative TDT procedures carried out in the frequently used QTDT and FBAT packages. Specifically, we discuss the “Rabinowitz” and the “Monks-Kaplan” procedures, as well as the various “Abecasis” and “Allison” regression-based procedures. We focus on the models assumed in these tests and the relationships between them. Moreover, we discuss what hypotheses are tested by the various quantitative TDTs, what testing procedures are best suited to various forms of data, and whether the regression-based tests overcome population stratification problems. Finally, we comment on power considerations in the choice of the test to be used. We hope this brief review will shed light on the similarities and differences of the various quantitative TDTs.

Markov-Recapture Population Estimate: A Tool for Improving Interpretation of Trapping Experiments

This paper describes a method of population estimation in which a random, unknown number of individuals is marked using a self—marking bait station (a trap modified for mark and release); animals (both marked and unmarked) may then be captured in an otherwise identical trap, which is available simultaneously. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking and capture are assumed to be equal. The population size estimator is based on the maximum likelihood technique, and is given by the nest integer less than N = (C + R)2/2(R + 1), where R and C are, respectively, the numbers of marked and unmarked individuals found in the trap. The estimator is almost unbiased for a wide range of true population sizes, and over a wide range of times over which the experiment is run, although it becomes negatively biased when the mean number of recaptures is <5. Confidence limits may be obtained using asymptotic maximum likelihood arguments, although relative likelihood methods perform better when the number of recaptures is small.

Some simulation results for the neutral allele model, with interpretations

Our aim in this paper is to describe a number of results arising from a simulation study of a particular “neutral mutations” model. This simulation was carried out because the stochastic process under consideration does not appear to yield theoretical answers to several questions of biological interest; however, wherever possible, we have attempted to supplement our simulation results with partial theoretical support. Our main concern is to consider the behavior of gene frequencies and of tests of the neutral mutations model based on these gene frequencies in various circumstances, in particular where the population is geographically subdivided and also where full identification of alleles is not possible. We conclude that the effect of geographical subdivision, unless extremely strong, is quite minor, while that of non-identification is moderate.

Population Genetics Theory in Relation to the Neutralist-Selectionist Controversy

The fundamental ingredients of the Darwinian theory of evolution are variation and natural selection. This theory, recast in the framework of Mendelian genetics, remains the fundamental principle of all biology and has been reinforced and enriched over the last 75 years by experimental, observational, and theoretical population genetics. No one seriously doubts that the visually observed nature of the biological world is explained, in convincing detail, by this theory. In terms of population genetics, the Darwinian theory states that a succession of gene substitutions, directed by natural selection, has led to the present genetic composition of populations, which manifests itself to us in the diversity and adaptedness of living organisms. Theoretical population genetics, including in particular the seminal works of Fisher, Haldane, and Wright (whose differences of opinion on points of detail do not alter their agreement on this main issue), confirms and in part quantifies this principle. And yet from theoretical population genetics has recently emerged a somewhat different view of evolution which has received increasing attention over the last decade and which has caused sharp differences of opinion among population geneticists as to its plausibility and acceptability.