Crop species experienced strong selective pressure directed at genes controlling traits of agronomic importance during their domestication and subsequent episodes of selective breeding. Consequently, these genes are expected to exhibit the signature of selection. We screened 501 maize genes for the signature of selection using microsatellites or simple sequence repeats (SSRs). We applied the Ew...

An exact sampling formula for a Wright-Fisher population of fixed size N under the infinitely many neutral alleles model is deduced. This extends the Ewens formula for the configuration of a random sample to the case where the sample is drawn from a population of small size, that is, without the usual large-N and small-mutation-rate assumption. The formula is used to prove a conjecture ascertai...

W. J. Ewens, following G. R. Price, has stressed that Fisher's fundamental theorem of natural selection about the increase in mean fitness is of general validity without any restrictive assumptions on the mating system, the fitness parameters, or the numbers of loci and alleles involved, but that it concerns only a partial change in mean fitness. This partial change is obtained by replacing the...

In linkage analysis for mapping genetic diseases, the transmission/disequilibrium test TDT uses the linkage disequilibrium LD between some marker and trait loci for precise genetic mapping while avoiding confounding due to population stratification. The sib-TDT S-TDT and combinedTDT C-TDT proposed by Spielman and Ewens can combine data from families with and without parental marker genotypes PM...

A diffusion process model of the frequency of a mutation • Reversibility of a 1-dimensional diffusion process • Frequency spectrum and age of a mutation General binary coalescent trees • Combinatorial derivation of the age of a mutation • Ewens' sampling formula, a combinatorial derivation • Coalescent lineage distributions Gene trees and Coalescent trees • DNA sequences and the infinitely-many...

There has been much interest in detecting genomic identity by descent (IBD) segments from modern dense genetic marker data and in using them to identify human disease susceptibility loci. Here we present a novel Bayesian framework using Markov chain Monte Carlo (MCMC) realizations to jointly infer IBD states among multiple individuals not known to be related, together with the allelic typing er...

The neutral theory of S. P. Hubbell postulates a two-scale hierarchical framework consisting of a metacommunity following the speciation-drift equilibrium characterized by the "biodiversity number" theta, and local communities following the migration-drift equilibrium characterized by the "migration rate" m (or the "fundamental dispersal number" I). While Etienne's sampling formula allows simul...

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinitealleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various bi...

David Alonso* and Alan J. McKane Ecology and Evolutionary Biology, University of Michigan 830 North University Avenue, Ann Arbor MI 48109-1048, USA ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr Aiguader 80, 08003 Barcelona, Spain Department of Theoretical Physics, University of Manchester, Manchester M13 9PL, UK *Correspondence: E-mail: [email protected] Abstract In the context of neu...

Abstract: This paper derives distributional properties of a class of exchangeable bridges closely related to the Poisson-Dirichlet (α, θ) family of bridges. As demonstrated in previous works, stochastic equations based on Poisson-Dirichlet (α, θ) processes, play an important role in a variety of applications. Here we focus on their role in obtaining/identifying otherwise difficult distributiona...