An investigation of the statistical power of neutrality tests based on comparative and population genetic data

In this report, we investigate the statistical power of several tests of selective neutrality based on patterns of genetic diversity within and between species. The goal is to compare tests based solely on population genetic data with tests using comparative data or a combination of comparative and population genetic data. We show that in the presence of repeated selective sweeps on relatively neutral background, tests based on the d(N)/d(S) ratios in comparative data almost always have more power to detect selection than tests based on population genetic data, even if the overall level of divergence is low. Tests based solely on the distribution of allele frequencies or the site frequency spectrum, such as the Ewens-Watterson test or Tajima's D, have less power in detecting both positive and negative selection because of the transient nature of positive selection and the weak signal left by negative selection. The Hudson-Kreitman-Aguadé test is the most powerful test for detecting positive selection among the population genetic tests investigated, whereas McDonald-Kreitman test typically has more power to detect negative selection. We discuss our findings in the light of the discordant results obtained in several recently published genomic scans.     

Contrasting signatures of population growth for mitochondrial DNA and Y chromosomes among human populations in Africa

A history of Pleistocene population expansion has been inferred from the frequency spectrum of polymorphism in the mitochondrial DNA (mtDNA) of many human populations. Similar patterns are not typically observed for autosomal and X-linked loci. One explanation for this discrepancy is a recent population bottleneck, with different rates of recovery for haploid and autosomal loci as a result of their different effective population sizes. This hypothesis predicts that mitochondrial and Y chromosomal DNA will show a similar skew in the frequency spectrum in populations that have experienced a recent increase in effective population size. We test this hypothesis by resequencing 6.6 kb of noncoding Y chromosomal DNA and 780 basepairs of the mtDNA cytochrome c oxidase subunit III (COIII) gene in 172 males from 5 African populations. Four tests of population expansion are employed for each locus in each population: Fu's Fs statistic, the R(2) statistic, coalescent simulations, and the mismatch distribution. Consistent with previous results, patterns of mtDNA polymorphism better fit a model of constant population size for food-gathering populations and a model of population expansion for food-producing populations. In contrast, none of the tests reveal evidence of Y chromosome growth for either food-gatherers or food-producers. The distinct mtDNA and Y chromosome polymorphism patterns most likely reflect sex-biased demographic processes in the recent history of African populations. We hypothesize that males experienced smaller effective population sizes and/or lower rates of migration during the Bantu expansion, which occurred over the last 5,000 years.     

Chloroplast microsatellites reveal colonization and metapopulation dynamics in the Canary Island pine

Chloroplast microsatellites are becoming increasingly popular markers for population genetic studies in plants, but there has been little focus on their potential for demographic inference. In this work the utility of chloroplast microsatellites for the study of population expansions was explored. First, we investigated the power of mismatch distribution analysis and the F(S) test with coalescent simulations of different demographic scenarios. We then applied these methods to empirical data obtained for the Canary Island pine (Pinus canariensis). The results of the simulations showed that chloroplast microsatellites are sensitive to sudden population growth. The power of the F(S) test and accuracy of demographic parameter estimates, such as the time of expansion, were reduced proportionally to the level of homoplasy within the data. The analysis of Canary Island pine chloroplast microsatellite data indicated population expansions for almost all sample localities. Demographic expansions at the island level can be explained by the colonization of the archipelago by the pine, while population expansions of different ages in different localities within an island could be the result of local extinctions and recolonization dynamics. Comparable mitochondrial DNA sequence data from a parasite of P. canariensis, the weevil Brachyderes rugatus, supports this scenario, suggesting a key role for volcanism in the evolution of pine forest communities in the Canary Islands.     

Bayesian tests for random mating in polyploids

Hardy–Weinberg proportions (HWP) are often explored to evaluate the assumption of random mating. However, in autopolyploids, organisms with more than two sets of homologous chromosomes, HWP and random mating are different hypotheses that require different statistical testing approaches. Currently, the only available methods to test for random mating in autopolyploids (i) heavily rely on asymptotic approximations and (ii) assume genotypes are known, ignoring genotype uncertainty. Furthermore, these approaches are all frequentist, and so do not carry the benefits of Bayesian analysis, including ease of interpretability, incorporation of prior information, and consistency under the null. Here, we present Bayesian approaches to test for random mating, bringing the benefits of Bayesian analysis to this problem. Our Bayesian methods also (i) do not rely on asymptotic approximations, being appropriate for small sample sizes, and (ii) optionally account for genotype uncertainty via genotype likelihoods. We validate our methods in simulations and demonstrate on two real datasets how testing for random mating is more useful for detecting genotyping errors than testing for HWP (in a natural population) and testing for Mendelian segregation (in an experimental S1 population). Our methods are implemented in Version 2.0.2 of the hwep R package on the Comprehensive R Archive Network https://cran.r-project.org/package=hwep .     

Power for detecting genetic divergence: differences between statistical methods and marker loci

Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.     

Genetic diversity and population history of the red panda (Ailurus fulgens) as inferred from mitochondrial DNA sequence variations

The red panda (Ailurus fulgens) is one of the flagship species in worldwide conservation and is of special interest in evolutionary studies due to its taxonomic uniqueness. We sequenced a 236-bp fragment of the mitochondrial D-loop region in a sample of 53 red pandas from two populations in southwestern China. Seventeen polymorphic sites were found, together with a total of 25 haplotypes, indicating a high level of genetic diversity in the red panda. However, no obvious genetic divergence was detected between the Sichuan and Yunnan populations. The consensus phylogenetic tree of the 25 haplotypes was starlike. The pairwise mismatch distribution fitted into a pattern of populations undergoing expansion. Furthermore, Fu's F(S) test of neutrality was significant for the total population (F(S) = -7.573), which also suggests a recent population expansion. Interestingly, the effective population size in the Sichuan population was both larger and more stable than that in the Yunnan population, implying a southward expansion from Sichuan to Yunnan.     

Test statistics for detecting aneuploidy and hyperdiploidy

Possible approaches to the analytical evaluation of ploidy patterns are discussed and two specific problems are considered: detection of early onset of aneuploidy and detection of moderate hyperdiploidy. A statistical model for a euploid DNA pattern is formulated in terms of a mixture distribution. A test statistic for detecting deviations from this pattern is defined, and its performance is evaluated for simulated data representing differing degrees of severity of aneuploidy. An analysis based on a discriminant function using order statistics of the sample cumulative distribution functions is proposed for detecting hyperdiploidy. This procedure has the advantage of being relatively distribution-free; its performance is evaluated for simulated data and is compared with that of its classical counterparts. Although the results reported are only preliminary, they indicate that tailor-made statistical analyses can provide early detection of aneuploidy and hyperdiploidy with known and acceptable error rates using clinically reasonable sample sizes.     

Microsatellite allele sizes: a simple test to assess their significance on genetic differentiation

The mutation process at microsatellite loci typically occurs at high rates and with stepwise changes in allele sizes, features that may introduce bias when using classical measures of population differentiation based on allele identity (e.g., F(ST), Nei's Ds genetic distance). Allele size-based measures of differentiation, assuming a stepwise mutation process [e.g., Slatkin's R(ST), Goldstein et al.'s (deltamu)(2)], may better reflect differentiation at microsatellite loci, but they suffer high sampling variance. The relative efficiency of allele size- vs. allele identity-based statistics depends on the relative contributions of mutations vs. drift to population differentiation. We present a simple test based on a randomization procedure of allele sizes to determine whether stepwise-like mutations contributed to genetic differentiation. This test can be applied to any microsatellite data set designed to assess population differentiation and can be interpreted as testing whether F(ST) = R(ST). Computer simulations show that the test efficiently identifies which of F(ST) or R(ST) estimates has the lowest mean square error. A significant test, implying that R(ST) performs better than F(ST), is obtained when the mutation rate, mu, for a stepwise mutation process is (a) >/= m in an island model (m being the migration rate among populations) or (b) >/= 1/t in the case of isolated populations (t being the number of generations since population divergence). The test also informs on the efficiency of other statistics used in phylogenetical reconstruction [e.g., Ds and (deltamu)(2)], a nonsignificant test meaning that allele identity-based statistics perform better than allele size-based ones. This test can also provide insights into the evolutionary history of populations, revealing, for example, phylogeographic patterns, as illustrated by applying it on three published data sets.     

Statistical properties of Teng and Risch's sibship type tests for detecting an association between disease and a candidate allele

Risch and Teng [Genome Res 1998;8:1273-1288] and Teng and Risch [Genome Res 1999;9:234-241] proposed a class of transmission/disequilibrium test-like statistical tests based on the difference between the estimated allele frequencies in the affected and control populations. They evaluated the power of a variety of family-based and nonfamily-based designs for detecting an association between a candidate allele and disease. Because they were concerned with diseases with low penetrances, their power calculations assumed that unaffected individuals can be treated as a random sample from the population. They predicted that this assumption rendered their sample size calculations slightly conservative. We generalize their partial ascertainment conditioning by including the status of the unaffected sibs in the calculations of the distribution and power of the statistic used to compare the allele frequency in affected offspring to the estimated frequency in the parents, based on sibships with genotyped affected and unaffected sibs. Sample size formulas for our full ascertainment methods are presented. The sample sizes for our procedure are compared to those of Teng and Risch. The numerical results and simulations indicate that the simplifying assumption used in Teng and Risch can produce both conservative and anticonservative results. The magnitude of the difference between the sample sizes needed by their partial ascertainment approximation and the full ascertainment is small in the circumstances they focused on but can be appreciable in others, especially when the baseline penetrances are moderate. Two other statistics, using different estimators for the variance of the basic statistic comparing the allele frequencies in the affected and unaffected sibs are introduced. One of them incorporates an estimate of the null variance obtained from an auxiliary sample and appears to noticeably decrease the sample sizes required to achieve a prespecified power.     

Genetic spatial autocorrelation can readily detect sex-biased dispersal

Sex-biased dispersal is expected to generate differences in the fine-scale genetic structure of males and females. Therefore, spatial analyses of multilocus genotypes may offer a powerful approach for detecting sex-biased dispersal in natural populations. However, the effects of sex-biased dispersal on fine-scale genetic structure have not been explored. We used simulations and multilocus spatial autocorrelation analysis to investigate how sex-biased dispersal influences fine-scale genetic structure. We evaluated three statistical tests for detecting sex-biased dispersal: bootstrap confidence intervals about autocorrelation r values and recently developed heterogeneity tests at the distance class and whole correlogram levels. Even modest sex bias in dispersal resulted in significantly different fine-scale spatial autocorrelation patterns between the sexes. This was particularly evident when dispersal was strongly restricted in the less-dispersing sex (mean distance <200 m), when differences between the sexes were readily detected over short distances. All tests had high power to detect sex-biased dispersal with large sample sizes (n ≥ 250). However, there was variation in type I error rates among the tests, for which we offer specific recommendations. We found congruence between simulation predictions and empirical data from the agile antechinus, a species that exhibits male-biased dispersal, confirming the power of individual-based genetic analysis to provide insights into asymmetries in male and female dispersal. Our key recommendations for using multilocus spatial autocorrelation analyses to test for sex-biased dispersal are: (i) maximize sample size, not locus number; (ii) concentrate sampling within the scale of positive structure; (iii) evaluate several distance class sizes; (iv) use appropriate methods when combining data from multiple populations; (v) compare the appropriate groups of individuals.     

Testing Hardy–Weinberg Equilibrium and Homogeneity of Hardy–Weinberg Disequilibrium using Complex Survey Data

Summary For studies on population genetics, the use of representative random samples of the target population can avoid ascertainment bias. Genetic variation data from over a hundred genes were collected in a U.S. nationally representative sample in the Third National Health and Nutrition Examination Survey (NHANES III). Surveys such as the NHANES have complex stratified multistage cluster sample designs with sample weighting that can inflate variances and alter the expectations of test statistics. Thus, classical statistical tests of Hardy–Weinberg equilibrium (HWE) and homogeneity of HW disequilibrium (HHWD) for simple random samples are not suitable for data from complex samples. We propose using Wald tests for HWE and generalized score tests for HHWD that have been modified for complex samples. Monte Carlo simulation studies are used to investigate the finite sample properties of the proposed tests. Rao–Scott corrections applied to the tests were found to improve their type I error properties. Our methods are applied to the NHANES III genetic data for three loci involved in metabolizing lead in the body.     

Pop‐Inference: An educational application to evaluate statistical differences among populations

Pop‐Inference is an educational tool designed to help teaching of hypothesis testing using populations. The application allows for the statistical comparison of demographic parameters among populations. Input demographic data are projection matrices or raw demographic data. Randomization tests are used to compare populations. The tests evaluate the hypothesis that demographic parameters differ among groups of individuals more that should be expected from random allocation of individuals to populations. Confidence intervals for demographic parameters are obtained using the bootstrap. Tests may be global or pairwise. In addition to tests on differences, one‐way life table response experiments (LTRE) are available for random and fixed factors. Planned (a priori) comparisons are possible. Power of comparison tests is evaluated by constructing the distribution of the test statistic when the null hypothesis is true and when it is false. The relationship between power and sample size is explored by evaluating differences among populations at increasing population sizes, while keeping vital rates constant.     

Tests for deletion

It has been suggested in the ecological literature that species may be excluded (or "deleted") from an environment because they do not differ sufficiently from other species in the environment. We develop tests of various deletion hypotheses based on the assumption of a random distribution of species sizes. The results provide information on the behavior of quantities of interest to ecologists studying this phenomenon, namely contiguous ratios, and allow us to gauge the extent of deletion required before we can be confident of detecting it. The results indicate that this random-effects approach leads to tests which have low power for ecological applications but may be more useful in fields which permit larger sample sizes.     

Genetic diversity and population structure of Panonychus citri (Acari: Tetranychidae), in China based on mitochondrial COI gene sequences

The citrus red mite, Panonychus citri (McGregor) (Acari: Tetranychidae), is regarded as one of the most important citrus pests in many countries, such as Japan, Spain, and China. In this study, the mitochondrial cytochrome oxidase subunit I gene was used to analyze genetic diversity and population structure of 15 P. citri populations collected from three citrus (Citrus spp.) planting regions of China. Our analysis found that these populations had relatively low genetic diversities. Bayesian tree and haplotype network showed that the 22 haplotypes of P. citri formed two lineages with low Bayesian posterior probabilities (0.55 and 0.63), and haplotypes in a sample were scattered throughout the Bayesian tree, indicating that there may be no significant genealogical structure among populations. However, when Yuxi and Danjiangkou populations (both without H7 haplotype) were excluded from the analysis, analysis of molecular variance found a weak, but significant, geographic structuring. Mantel test indicated a significant and positive correlation between genetic and geographical distances, reflecting certain degree of isolation by distance. The genetic differentiation based on pairwise F(ST) was not significant between most populations, and some F(ST) were even negative, indicating remarkable gene flow among these populations. The weak population structure of P. citri in this study was probably influenced by high gene flow between some populations due to long-distance dispersal of this species, which may be largely relied on the movement of plants between populations. The mismatch distribution analysis showed that no signal of population growth, but the Fu's F(S) value was significantly negative for total populations and the star-like shape of haplotype network, suggesting a history of population expansion of P. citri in China.     

Y-chromosome mismatch distributions in Europe.

Ancient demographic events can be inferred from the distribution of pairwise sequence differences (or mismatches) among individuals. We analyzed a database of 3,677 Y chromosomes typed for 11 biallelic markers in 48 human populations from Europe and the Mediterranean area. Contrary to what is observed in the analysis of mitochondrial polymorphisms, Tajima's test was insignificant for most Y-chromosome samples, and in 47 populations the mismatch distributions had multiple peaks. Taken at face value, these results would suggest either (1) that the size of the male population stayed essentially constant over time, while the female population size increased, or (2) that different selective regimes have shaped mitochondrial and Y-chromosome diversity, leading to an excess of rare alleles only in the mitochondrial genome. An alternative explanation would be that the 11 variable sites of the Y chromosome do not provide sufficient statistical power, so a comparison with mitochondrial data (where more than 200 variable sites are studied in Europe) is impossible at present. To discriminate between these possibilities, we repeatedly analyzed a European mitochondrial database, each time considering only 11 variable sites, and we estimated mismatch distributions in stable and growing populations, generated by simulating coalescent processes. Along with theoretical considerations, these tests suggest that the difference between the mismatch distributions inferred from mitochondrial and Y-chromosome data are not a statistical artifact. Therefore, the observed mismatch distributions appear to reflect different underlying demographic histories and/or selective pressures for maternally and paternally transmitted loci.     

Statistical Tests of Neutrality of Mutations against Population Growth, Hitchhiking and Background Selection

The main purpose of this article is to present several new statistical tests of neutrality of mutations against a class of alternative models, under which DNA polymorphisms tend to exhibit excesses of rare alleles or young mutations. Another purpose is to study the powers of existing and newly developed tests and to examine the detailed pattern of polymorphisms under population growth, genetic hitchhiking and background selection. It is found that the polymorphic patterns in a DNA sample under logistic population growth and genetic hitchhiking are very similar and that one of the newly developed tests, F(s), is considerably more powerful than existing tests for rejecting the hypothesis of neutrality of mutations. Background selection gives rise to quite different polymorphic patterns than does logistic population growth or genetic hitchhiking, although all of them show excesses of rare alleles or young mutations. We show that Fu and Li''s tests are among the most powerful tests against background selection. Implications of these results are discussed.     

Recovery of mutations of different sizes from a population sample of DNA sequences under variable mutation rates across sites.

Mutations may be classified according to their positions of occurrence in the genealogy of the sampled DNA sequences from a population. A mutation is said to be of size i if it has i descendants in the sample. Such classifications for mutations may yield detailed insights into the evolutionary history and properties of the population. Statistical methods based on such classification have been developed and shown to be efficient and powerful. However, the utility of these statistical methods critically depends on reliable and robust recovery of mutations of different sizes. We investigated the distributional changes of mutations of different sizes due to genealogy reconstruction using the unweighted pair-group method with arithmetic mean (UPGMA) and the performance of maximum-parsimony method in inferring mutations of different sizes on a given topology. Genealogy reconstruction by UPGMA was found to change the distribution of mutations of different sizes on constructed topologies. Multiple hits at some nucleotide sites made it difficult to infer mutations of different sizes with the maximum-parsimony method, even when the true topology was designated. These results suggest that while the newly developed statistical methods employing information on mutations of different sites are powerful, they also impose significant new challenges for developing methods to accurately recover mutations of different sizes from population DNA sequence data.     

Testing Linear Contrasts of Means in Experimental Design Without Assuming Normality and Homogeneity of Variances

We investigate the efficiencies of TIKU'S (1967, 1980) modified maximum likelihood (MML) estimators of location and scale parameters of symmetric distributions and show that they are remarkably efficient (jointly). We develop test statistics (based on MML estimators), analogous to the classical tests based on sample means and variances, for testing the equality of two means (the population variances not necessarily equal). We show that these tests are remarkably robust to distributional assumptions and generally more powerful than the well-known nonparametric tests (WILCOXON , normal-score, KOLMOGOROV -SMIRNOV ). We generalize the results to testing linear contrasts of means in experimental design (the error variances not necessarily equal). We show that the analogous tests based on ‘adaptive’ robust estimators (wave, bisquare, HAMPEL ,) etc., GROSS (1976, and other ‘adaptive’ robust estimators) give misleading Type I errors.