Measuring the Sensitivity of Single-locus ‘‘Neutrality Tests’’Using a Direct Perturbation ApproachDaniel Garrigan,* Richard Lewontin, and John WakeleyDepartment of Organismic and Evolutionary Biology, Harvard University*Corresponding author: E-mail: [email protected].Present address: Department of Biology, University of Rochester.Associate editor: John H. McDonaldAbstractA large number of statistical tests have been proposed to detect natural selection based on a sample of variation at a singlegenetic locus. These tests measure the deviation of the allelic frequency distribution observed within populations from thedistribution expected under a set of assumptions that includes both neutral evolution and equilibrium populationdemography. The present study considers a new way to assess the statistical properties of these tests of selection, by theirbehavior in response to direct perturbations of the steady-state allelic frequency distribution, unconstrained by anyparticular nonequilibrium demographic scenario. Results from Monte Carlo computer simulations indicate that most testsof selection are more sensitive to perturbations of the allele frequency distribution that increase the variance in allelefrequencies than to perturbations that decrease the variance. Simulations also demonstrate that it requires, on average, 4Ngenerations (N is the diploid effective population size) for tests of selection to relax to their theoretical, steady-statedistributions following different perturbations of the allele frequency distribution to its extremes. This relatively longrelaxation time highlights the fact that these tests are not robust to violations of the other assumptions of the null modelbesides neutrality. Lastly, genetic variation arising under an example of a regularly cycling demographic scenario issimulated. Tests of selection performed on this last set of simulated data confirm the confounding nature of these tests forthe inference of natural selection, under a demographic scenario that likely holds for many species. The utility of usingempirical, genomic distributions of test statistics, instead of the theoretical steady-state distribution, is discussed as analternative for improving the statistical inference of natural selection.Key words: DNA sequence, infinite-allele model, infinite-sites model, natural selection, polymorphism.IntroductionA major question pertinent to understanding the geneticvariation within and between species is how important nat-ural selection has been in determining that variation. Thatis, how much of the observed genetic differentiation isa consequence of direct physiological, developmental,and behavioral causal relations between DNA sequencevariation and variation in fertility and probability of survivalof individuals carrying these sequences. The obvious directapproach to this problem would be to measure the com-ponents of reproductive fitness in different genotypes, butthere are a number of serious limitations inherent in thisapproach, especially for animals (Orr 2009). First, it is ex-tremely difficult, if not impossible, to obtain complete fit-ness components, including probabilities of differentmatings, fertility schedules, and life tables for organismswhose life cycle cannot be observed in detail under naturalconditions. Second, even if complete life cycle componentscan be obtained, large enough sample sizes to detect selec-tion are not possible unless fitness effects are drastic (e.g.,see the study by Christiansen and Frydenberg [1973] of anesterase polymorphism in the live-bearing fish Zoarcesviviparus, where all the components of fitness couldbe measured). Third, measures of fitness components inpresent-day environments may not necessarily reflect fit-ness in past environments.One solution offered to circumvent these difficulties hasbeen to attempt to infer the occurrence of natural selectionfrom extant patterns of standing genetic variation in thegenome of one or more populations. This has taken theform of a large number of statistical tests based on the ‘‘nullhypothesis’’ that there has been no natural selection andthat the frequency distribution of variants in a sample canbe predicted under the assumptions that the population isat a stochastic steady state expected in populations ofa fixed breeding size and fixed model of mutation. If a sam-ple shows a statistically significant deviation from the ex-pected theoretical distribution, the null hypothesis thatthere is no selection is rejected.The problem with this indirect approach to detect se-lection is one shared by all statistical procedures that claimto test a null hypothesis. What these statistical proceduresactually test is not a null hypothesis, but rather, a null‘‘structure’’—a set of claims about a universe, one claimbeing isolated as the ‘‘hypothesis’’ and remainder being rel-egated to the category of ‘‘assumptions.’’ The test proce-dures themselves do not distinguish between thehypothesis and the assumptions. For example, until com-puter simulations became possible, it was not known© 2009 The AuthorsThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/2.5), which permits unrestricted non-commercial use, distribution, andreproduction in any medium, provided the original work is properly cited.Open AccessMol. Biol. Evol. 27(1):73–89. 2010 doi:10.1093/molbev/msp209 Advance Access publication September 10, 2009 73Research articlewhether the t-test for the difference between means wasvery sensitive to the assumption of normality or whetherthe equality of variances of the distributions was critical tothe test. As it turned out, the test is robust against bothnon-normality and unequal variances. However, the F testfor the equality of variances from two populations turnsout to be extremely sensitive to the assumption of under-lying normal distributions of the variable. To validate var-ious tests for ‘‘selection,’’ a similar program of examiningtheir sensitivity to the assumptions needs to be carriedout systematically. The question becomes how such a sys-tematic examination is to be carried out.The usual set of assumptions inherent in the null struc-ture of neutral evolution includes:1) a constant mutation rate in which each mutation is toa new allele (infinite-alleles tests) or at a new site in DNAsequence