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W J Ewens

Publications and source records attributed to W J Ewens.

13 recordsLinked to original sources
PubMed1992

An optimizing principle of natural selection in evolutionary population genetics.

This paper brings together two themes in evolutionary population genetics theory. The first concerns Fisher's Fundamental Theorem of Natural Selection: a recent interpretation of this theorem claims that it is an exact result, relating to the so-called "partial" increase in mean fitness. The second theme concerns the desire to find an optimality principle in genetic evolution. Such a principle is found here: of all gene frequency changes which lead to the same partial increase in mean fitness as the natural selection gene frequency changes, the natural selection values minimize a generalized distance measure between parent and daughter generation gene frequency values.

Alleles↗
PubMed1992

Statistical analysis of in situ hybridization data: derivation and use of the zmax test.

There are many situations in which grain distributions resulting from in situ hybridization of radioactively labeled probes to unique genes should be subjected to a statistical analysis. However, the problems posed by analysis of in situ hybridization data are not straightforward, and no completely satisfying method is currently available. We have developed a procedure in which the major and any number of minor site(s) of hybridization may be specifically located and the significance of each tested. This zmax procedure first tests the overall distribution for departure from randomness and then identifies significantly overlabeled whole chromosomes (or chromosome arms or other large segments), a process that may be repeated to pinpoint significantly overlabeled regions within these chromosomes. We describe in detail the derivation of the zmax statistic, present tables of significant zmax levels, and show with examples how zmax is used in tests of significance of in situ hybridization data.

Animals↗
PubMed1991

Genome mapping with anchored clones: theoretical aspects.

As part of our effort to construct a physical map of the genome of Arabidopsis thaliana we have made a mathematical analysis of our experimental approach of anchoring yeast artificial chromosome clones with genetically mapped RFLPs and RAPDs. The details of this analysis are presented and their implications for mapping the Arabidopsis genome are discussed.

Chromosome Mapping↗
PubMed1989

Remarks on ascertainment.

Genetic Analysis Workshop data come from various sources, with possibly different ascertainment procedures in each. It is plausible that classical ascertainment models do not accurately describe the ascertainment process in each data source. For this reason, we review the biases which can arise from an incorrect specification on the ascertainment process and discuss their relevance for the GAW5 data analysis.

Child↗
PubMed1989

An interpretation and proof of the Fundamental Theorem of Natural Selection.

Fisher's "Fundamental Theorem of Natural Selection" has long caused controversy in population genetics theory. Viewed as a statement about the increase, or rate of increase, of mean fitness over time, it encounters difficulties with cases arising in a multi-locus system for which mean fitness can decrease. An interpretation of the theorem is put forward here which implies that it is correct as a mathematical statement, but of less biological value than was claimed by Fisher.

Gene Frequency↗
PubMed1989

Is knowing the age-order of alleles in a sample useful in testing for selective neutrality?

The most powerful, and most frequently used, test of selective neutrality, based on data consisting of observed allelic frequencies in a sample of genes at some locus, is the procedure of G. A. Watterson. This procedure uses the sample homozygosity F* as the test statistic, and in effect leads to rejection of the hypothesis of selective neutrality if the observed value of F* differs significantly from neutral theory expectations. The homozygosity statistic is invariant under relabeling of the alleles and thus cannot use any further information on the alleles which might be available. We present results which suggest that information concerning the age order of the alleles cannot be used to provide a more powerful testing procedure than that of Watterson.

Alleles↗
PubMed1977

Properties of equilibria in multi-locus genetic systems.

The classical mathematical theory of population genetics considered, for simplicity, almost exclusively one-locus systems. In the last two decades much work has been done on two-locus and, less frequently, multi-locus systems. This research has usually involved investigating properties of systems with given, and usually rather special, fitness parameters. Real genetic fitness systems are undoubtedly multi-locus and seldom will possess simplifying characteristics. One aim of this paper is to study generalized systems where no special assumptions are made about fitness structure, the number of alleles at each locus, the number of loci involved or the recombination structure between loci. A second aim is to consider marginal properties (often one-locus properties) of complex systems: the fact that many observations involve data from only on locus makes this second aim relevant.

Alleles↗
PubMed1976

Remarks on the evolutionary effect of natural selection.

The so-called "Fundamental Theorem of Natural Selectiion", than the mean fitness of a population increases with time under natural selection, is known not to be true, as a mathematical theorem, when fitnesses depend on more than one locus. Although this observation may not have particular biological relevance, (so that mean fitness may well increase in the great majority of interesting situations), it does suggest that it is of interest to find an evolutionary result which is correct as a mathematical theorem, no matter how many loci are involved. The aim of the present note is to prove an evolutionary theorem relating to the variance in fitness, rather that the mean: this theorem is true for an arbitrary number of loci, as well as for arbitrary (fixed) fitness parameters and arbitrary linkage between loci. Connections are briefly discussed between this theorem and the principle of quasi-linkage equilibrium.

Biological Evolution↗
PubMed1975

A note on the variance of the number of loci having a given gene frequency.

In a recent not in this journal (MARUYAMA 1973), one of us has considered, for a certain genetic model, the variance of the distribution of the number of loci having a given gene frequency. The formula given is incorrect. This brief note considers this problem and notes the correct solution in one particular case.

Analysis of Variance↗