arXiv subjects

Warren J. Ewens

Publications and source records attributed to Warren J. Ewens.

3 recordsLinked to original sources

arXiv2010

There's plenty of time for evolution

Objections to Darwinian evolution are often based on the time required to carry out the necessary mutations. Seemingly, exponential numbers of mutations are needed. We show that such estimates ignore the effects of natural selection, and that the numbers of necessary mutations are thereby reduced to about $K\log{L}$, rather than $K^L$, where $L$ is the length of the genomic "word", and $K$ is the number of possible "letters" that can occupy any position in the word. The required theory makes contact with the theory of radix-exchange sorting in theoretical computer science, and the asymptotic analysis of certain sums that occur there.

math.PR↗

arXiv2010

Kingman and mathematical population genetics

Mathematical population genetics is only one of Kingman's many research interests. Nevertheless, his contribution to this field has been crucial, and moved it in several important new directions. Here we outline some aspects of his work which have had a major influence on population genetics theory.

math.PR↗

arXiv2006

Computing the distribution of the maximum in balls-and-boxes problems, with application to clusters of disease cases

We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time $O(mn)$, where $m$ is the desired maximum and $n$ is the number of variables. We apply the method to the analysis of two situations where an apparent clustering of cases of a disease in some locality has raised the possibility that the disease might be communicable, and this possibility has been discussed in the recent literature. We conclude that one of these clusters may be explained on purely random grounds, whereas the other may not.

math.ST↗