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.     

POWSIM: a computer program for assessing statistical power when testing for genetic differentiation

Knowledge of statistical power is essential for sampling design and data evaluation when testing for genetic differentiation. Yet, such information is typically missing in studies of conservation and evolutionary genetics, most likely because of complex interactions between the many factors that affect power. powsim is a 32‐bit Windows/DOS simulation‐based computer program that estimates power (and α error) for chi‐square and Fisher's exact tests when evaluating the hypothesis of genetic homogeneity. Optional combinations include the number of samples, sample sizes, number of loci and alleles, allele frequencies, and degree of differentiation (quantified as F_ST). powsim is available at http://www.zoologi.su.se/~ryman .     

塔里木河中下游地区荒漠河岸林群落种间关系分析

采用 2× 2列联表, 应用Fisher精确检验法研究了新疆塔里木河中下游荒漠河岸林群落种间关系, 测定了16种植物、共 12 0个种对的种间联结性。研究结果表明 :1) 12 0个种对中有 17个种对分别在不同的样方尺度中表现出显著或极显著的种间联结, 约占总数的 14.2 % ;其中 13个种对为正关联, 4个种对为负关联 ;2 ) 不同取样面积对种间联结性分析的有效性有影响, 不同种对表现出种间联结的最小样方尺度不同 ;3) 随着样方面积的增大, 各种对自有不同的种间联结变化规律, 可归纳为 4种类型 ;4 ) 17个具种间联结的种对以灌木草本和草本草本的种对居多, 占总数的 76.5 % ;主要乔木树种胡杨 (Populuseuphratica) 与灌木之间、灌木和灌木之间趋向独立分布。     

山西翅果油树群落种间关系的数量分析

应用 2× 2列联表的 Fisher精确检验、Pearson相关系数和 Spearm an秩相关系数检验研究了山西翅果油树群落的种间关系 ,分别测定了 42种植物 ,共 86 1个种对的种间关联 (或相关 )。结果表明 :1) 2× 2列联表的精确检验共有 2 8个种对为正关联 ,14个种对为负关联 (p <0 .0 5或 p<0 .0 1,下同 ) ;Peaorson相关系数有 5 6个种对为正相关 ,14个种对为负相关 ;Spearman秩相关系数有 96个种对呈正相关 ,46个种对呈负相关。 2 ) 2× 2列联表的Fisher精确检验不能反映两个种对间的数量变化关系 ,应用 Pearson相关系数和 Spearman秩相关检验来刻划种对间的数量变化关系 ;与 Pearson相关系数检验相比 ,Spearman秩相关系数检验具有较高的灵敏度。 3)种对间的正关联和正相关 ,主要是由于它们具有相近的生物学特性 ,对生境具有相似的生态适应性和相互分离的生态位所致 ;而种对间的负关联和负相关 ,则主要是由于它们具有不同的生物学特性 ,对生境具有不同的生态适应性和相互重叠的生态位所致。     

chifish: a computer program testing for genetic heterogeneity at multiple loci using chi‐square and Fisher's exact test

chifish is a 32‐bit Windows/DOS program evaluating divergence at multiple gene loci. It tests the hypothesis of no difference at any locus both by means of Pearson's traditional chi‐square and by using Fisher's method of combining P values obtained by Fisher's exact test. Input data are read from a file formatted for genepop . Commonly used population genetics software do not perform chi‐square tests, and the simultaneous application of both techniques aids in situations where poor power of the ‘exact approach’ may prevent detection of true differentiation (e.g. few populations and few alleles per locus).     

A cautionary note on exact unconditional inference for a difference between two independent binomial proportions

Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.     

Drawbacks to noninteger scoring for ordered categorical data

A proposal to improve trend tests by using noninteger scores is examined. It is concluded that despite improved power such tests are usually inferior to the simpler integer scored approach.     

基于统计差表与加权投票的高精度剪接位点预测

基于机器学习的高精度剪接位点识别是真核生物基因组注释的关键.本文采用卡方测验确定序列窗口长度,构建卡方统计差表提取位置特征,并结合碱基二联体频次表征序列;针对剪接位点正负样本高度不均衡这一情形,构建10个正负样本均衡的支持向量机分类器,进行加权投票决策,有效解决了不平衡模式分类问题. HS~3D数据集上的独立测试结果显示,供体、受体位点预测准确率分别达到93.39%、90.46%,明显高于参比方法.基于卡方统计差表的位置特征能有效表征DNA序列,在分子序列信号位点识别中具有应用前景.     

Adjusting O'Brien's test to control type I error for the generalized nonparametric Behrens-Fisher problem

O'Brien (1984, Biometrics 40, 1079-1087) introduced a simple nonparametric test procedure for testing whether multiple outcomes in one treatment group have consistently larger values than outcomes in the other treatment group. We first explore the theoretical properties of O'Brien's test. We then extend it to the general nonparametric Behrens-Fisher hypothesis problem when no assumption is made regarding the shape of the distributions. We provide conditions when O'Brien's test controls its error probability asymptotically and when it fails. We also provide adjusted tests when the conditions do not hold. Throughout this article, we do not assume that all outcomes are continuous. Simulations are performed to compare the adjusted tests to O'Brien's test. The difference is also illustrated using data from a Parkinson's disease clinical trial.     

Conditioning in 2 x 2 tables

Summary .  Two-by-two tables arise in a number of diverse settings in biomedical research, including analysis of data from a clinical trial with a binary outcome and gating methods in flow cytometry to separate antigen-specific immune responses from general immune responses. These applications offer interesting challenges concerning what we should really be conditioning on—the total number of events, the number of events in the control condition, etc. We give several biostatistics examples to illustrate the complexities of analyzing what appear to be simple data.     

Hierarchical analyses of genetic differentiation in a hybrid zone of Sorex araneus (Insectivora: Soricidae)

Microsatellites are used to unravel the fine-scale genetic structure of a hybrid zone between chromosome races Valais and Cordon of the common shrew ( Sorex araneus ) located in the French Alps. A total of 269 individuals collected between 1992 and 1995 was typed for seven microsatellite loci. A modified version of the classical multiple correspondence analysis is carried out. This analysis clearly shows the dichotomy between the two races. Several approaches are used to study genetic structuring. Gene flow is clearly reduced between these chromosome races and is estimated at one migrant every two generations using R -statistics and one migrant per generation using F -statistics. Hierarchical F - and R -statistics are compared and their efficiency to detect inter- and intraracial patterns of divergence is discussed. Within-race genetic structuring is significant, but remains weak. F _ST displays similar values on both sides of the hybrid zone, although no environmental barriers are found on the Cordon side, whereas the Valais side is divided by several mountain rivers. We introduce the exact G -test to microsatellite data which proved to be a powerful test to detect genetic differentiation within as well as among races. The genetic background of karyotypic hybrids was compared with the genetic background of pure parental forms using a CRT–MCA. Our results indicate that, without knowledge of the karyotypes, we would not have been able to distinguish these hybrids from karyotypically pure samples.     

A generalizing,analytic model for 2-way cross-classifications. extensions and ramifications. part 1

A generalizing, analytic model is developed for 2-way cross-classifications with fixed class sizes The model is expressed in closed form as a simple operator formula, and is readily extended to n-way cross-classifications, and to such cases where one or more cells are vacuous or fixed. The model permits easy derivation, by means of simple differential operators, of the exact power moments, product moments, and factorial moments of the cell frequencies. From this, the moments of the exact sampling distribution of the conventional x₂-statistic can be computed, which, in turn, leads to a reappraisal of the Chi-square approximation for sparse and isotropic contingency tables. Here, the Gamma distribution is considered, and numerical results are presented that would suggest preference of the Gamma approximation over the Chi-square in such cases.     

遗传多样性的取样策略

合理取样是生物多样性有效保护、利用和研究所面临的最基本问题 ,它在很大程度上受到植物自身的生物学特性、环境条件和取样目的的影响。遗传多样性的取样策略是指对一定地理分布范围内的生物个体取样时 ,使样本具有代表性和包含尽可能多的遗传变异的最佳取样方法 ,包括了取样数目 (一个给定区域的居群数和一个居群的个体数 )以及取样方式。包括“哈迪 温伯格平衡 (Hardy WeinbergEquilibrium)”定律在内的居群遗传学基本原理是研究取样策略的理论基础 ,在此基础上可以对居群内的取样个体数及应获取的居群数进行理论计算 ,同时还可以根据物种居群的遗传结构特点和环境条件的异质性来决定取样的方式。因此 ,应该依据研究对象本身的特点和取样的目的来确定某一特定区域的居群取样数 ,以及某一居群内的样本数及取样方式。     

Likelihood ratio testing for admixture models with application to genetic linkage analysis

Summary We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a two‐component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. This model is widely used in genetic linkage analysis under heterogeneity in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard, and the LRT statistic does not converge to a conventional χ² distribution. In this article, we investigate the asymptotic behavior of the LRT for general admixture models and show that its limiting distribution is equivalent to the supremum of a squared Gaussian process. We also discuss the connection and comparison between LRT and alternative approaches such as modifications of LRT and score tests, including the modified LRT ( Fu, Chen, and Kalbfleisch, 2006 , Statistica Sinica 16 , 805–823). The LRT is an omnibus test that is powerful to detect general alternative hypotheses. In contrast, alternative approaches may be slightly more powerful to detect certain type of alternatives, but much less powerful for others. Our results are illustrated by simulation studies and an application to a genetic linkage study of schizophrenia.     

Common pitfalls when testing additivity of treatment mixtures with chi‐square analyses

Studying interactions of multiple pesticides applied simultaneously in a mixture is a common task in phytopathology. Statistical methods are employed to test whether the treatment components influence each other's efficacy in a promotive or inhibitory way (synergistic or antagonistic interaction) or rather act independent of one another (additivity). The trouble is that widely used procedures based on chi‐square tests are often seriously flawed, either because people apply them in a preposterous way or because the method simply does not fit the problem at hand. Browsing recent volumes of entomological journals, we found that numerous researchers have (in all likelihood unwittingly) analysed their data as if they had had a sample size of 100 or, equally bad, a sample size of one! We show how to avoid such poor practices and further argue that chi‐square testing is, even if applied correctly (meaning that no technical errors are made), a limited purpose tool for assessing treatment interactions.     

Resolving genetic relationships with microsatellite markers: a parentage testing system for the swallow Hirundo rustica

Eight polymorphic microsatellite markers from the swallow were isolated and characterized. Extraordinary variability was revealed at the HrU6 locus with 45 different alleles scored among 46 unrelated individuals. The probability that the same genotype combination would occur in two random and unrelated individuals at six selected loci was as low as 1.3 × 10^-8 and the combined exclusion probability was 0.9996. Stable Mendelian inheritance was observed in about 1000 meioses. No significant linkage was revealed and for almost all combinations of marker-pairs, linkage closer than 5 cM could be excluded. At two loci, null (nonamplifying) alleles were encountered. Thirteen (30%) extra-pair offspring were identified in 5 (56%) broods when applying the marker set on a nearly complete swallow colony. We were able to identify a single male from the other families in the colony as the most likely father for nine of the 13 extra-pair offspring.