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The Use of Intraallelic Variability for Testing Neutrality

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Copyright  2001 by the Genetics Society of AmericaThe Use of Intraallelic Variability for Testing Neutrality andEstimating Population Growth RateMontgomery Slatkin* and Giorgio Bertorelle†*Department of Integrative Biology, University of California, Berkeley, California 94720-3140 and†Sezione di Biologia Evolutiva,Dipartimento di Biologia, Universita´di Ferrara, 44100 Ferrara, ItalyManuscript received July 15, 2000Accepted for publication February 28, 2001ABSTRACTTo better understand the forces affecting individual alleles, we introduce a method for finding the jointdistribution of the frequency of a neutral allele and the extent of variability at closely linked marker loci(the intraallelic variability). We model three types of intraallelic variability: (a) the number of nonrecombi-nants at a linked biallelic marker locus, (b) the length of a conserved haplotype, and (c) the number ofmutations at a linked marker locus. If the population growth rate is known, the joint distribution providesthe basis for a test of neutrality by testing whether the observed level of intraallelic variability is consistentwith the observed allele frequency. If the population growth rate is unknown but neutrality can be assumed,the joint distribution provides the likelihood of the growth rate and leads to a maximum-likelihoodestimate. We apply the method to data from published data sets for four loci in humans. We concludethat the ⌬32 allele at CCR5 and a disease-associated allele at MLH1 arose recently and have been subjectto strong selection. Alleles at PAH appear to be neutral and we estimate the recent growth rate of theEuropean population to be ⵑ0.027 per generation with a support interval of (0.017–0.037). Four of therelatively common alleles at CFTR also appear to be neutral but ⌬F508 appears to be significantly advanta-geous to heterozygous carriers.THE age of an allele determines both its frequency Stephens et al. (1998) to conclude that this allele hasbeen subject to strong positive selection.and the extent of variation at closely linked markerloci. Allele age itself cannot be observed, but, given as- In this article, we develop a formal theory of the rela-tionship between allele frequency and the extent ofsumptions about past selection and population growth,it constrains the relationship between frequency and intraallelic variability under general assumptions aboutthe demographic history of a population. Our theoryintraallelic variability. A large discrepancy between al-lele frequency and the extent of intraallelic variability can be used in two ways. If the pattern and rate ofpopulation growth are assumed to be known, our theoryexpected under neutrality provides evidence of past se-lection. For example, at several loci in the major histo- provides a statistical test of neutrality. If the past growthrate is unknown but the allele can be assumed to becompatibility (MHC) region in humans and other spe-cies and at self-incompatibility loci in several plant neutral, our theory provides a way to estimate the pastgrowth rate.species, alleles are found in low frequencies yet exhibitsubstantial variation among different copies of each al- Our results are obtained by combining two models.The first provides the genealogical history of an allele.lele (Richman et al. 1996; Hughes and Yeager 1998).That pattern suggests that balancing selection has re- The second predicts the extent of intraallelic variabilitygiven the intraallelic genealogy. We consider three waystained alleles for much longer times than would beexpected if they were neutral. A quite different pattern of measuring intraallelic variability: (a) the number ofchromosomes carrying the ancestral allele at a linkedis found at the CCR5 locus in humans. A 32-bp deletion(⌬32) retards the onset of AIDS in heterozygous carriers marker locus; (b) the length of a haplotype shared byall copies of an allele; and (c) the number of mutationsand provides resistance to infection by human immuno-deficiency virus in homozygous individuals. This dele- at one or more closely linked marker loci.tion is at a frequency of ⬎10% in Europeans (Stephenset al. 1998). Yet very strong linkage disequilibrium withCOALESCENT MODEL OF THEtwo closely linked microsatellite loci indicates the dele-INTRAALLELIC GENEALOGYtion is young, on the order of 1000 years or less, leadingWe assume that we have a sample of n chromosomesfrom a randomly mating population of diploid individu-als. The history of population size is described by aCorresponding author: Montgomery Slatkin, Department of Inte-function N(t), where t ⫽ 0 is the present and t indicatesgrative Biology, University of California, Berkeley, CA 94720-3140.E-mail: [email protected] number of generations in the past. The currentGenetics 158: 865–874 ( June 2001)866 M. Slatkin and G. Bertorelleber of replicate sets of intraallelic coalescence timesand taking appropriate averages over replicates, we canapproximate the distribution of intraallelic variability,given i, n, and N(t).The intraallelic coalescence times are generated asfollows. A neutral gene genealogy is simulated using amethod similar to that described by Hudson (1990),but allowing for changes in population size. The pro-cedure is to change the time from t to ␶(t) ⫽ 兰t01/(2N(t⬘))dt⬘ and simulate the neutral coalescent modelfor a constant population size using ␶ as the indepen-dent variable (Griffiths and Tavare´1994). On eachFigure 1.—Illustration of a gene genealogy with n ⫽ 9 tipssimulated gene genealogy, each node is tested to deter-and an intraallelic genealogy for the mutant allele A foundmine whether it has i descendants. If it does, then thein i ⫽ 4 copies in the sample. The allele arose at time t1inthe past. The times t2, t3, and t4are the intraallelic coalescenceset of intraallelic coalescence times is recorded andtimes. The time w is the length of the branch joining the intraal-the length, w, of the branch connecting that subtree tolelic genealogy to the rest of the gene genealogy and is thethe rest of the gene genealogy is also recorded (seeweight used to average over replicates, as described in the textFigure 1). Every node in the gene genealogy has to be(redrawn from Slatkin and Rannala 2000). MRCA denotestested and, for small values of i, several subtrees withthe most recent common ancestor of the gene genealogy.i terminal branches are typically found in each genegenealogy.For each subtree


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