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Evolutionary and statistical properties of three genetic distances.

Many genetic distances have been developed to summarize allele frequency differences between populations. I review the evolutionary and statistical properties of three popular genetic distances: DS, DA, and theta;, using computer simulation of two simple evolutionary histories: an isolation model of population divergence and an equilibrium migration model. The effect of effective population size, mutation rate, and mutation mechanism upon the parametric value between pairs of populations in these models explored, and the unique properties of each distance are described. The effect of these evolutionary parameters on study design is also investigated and similar results are found for each genetic distance in each model of evolution: large sample sizes are warranted when populations are relatively genetically similar; and loci with more alleles produce better estimates of genetic distance.

Computer Simulation↗

A modified algorithm for the improvement of composite interval mapping.

Composite interval mapping (CIM) is the most commonly used method for mapping quantitative trait loci (QTL) with populations derived from biparental crosses. However, the algorithm implemented in the popular QTL Cartographer software may not completely ensure all its advantageous properties. In addition, different background marker selection methods may give very different mapping results, and the nature of the preferred method is not clear. A modified algorithm called inclusive composite interval mapping (ICIM) is proposed in this article. In ICIM, marker selection is conducted only once through stepwise regression by considering all marker information simultaneously, and the phenotypic values are then adjusted by all markers retained in the regression equation except the two markers flanking the current mapping interval. The adjusted phenotypic values are finally used in interval mapping (IM). The modified algorithm has a simpler form than that used in CIM, but a faster convergence speed. ICIM retains all advantages of CIM over IM and avoids the possible increase of sampling variance and the complicated background marker selection process in CIM. Extensive simulations using two genomes and various genetic models indicated that ICIM has increased detection power, a reduced false detection rate, and less biased estimates of QTL effects.

Algorithms↗

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.

Alleles↗

Comparative F statistics analysis of the genetic structure of ten Spanish dog breeds.

The genetic structure and relationships among 10 Spanish dog breeds have been studied by using F statistics. Data came from 21 structural genic loci that codify for blood-soluble proteins and enzymes detected by electrophoresis. Of the 21 loci, 11 were found to be polymorphic. The study was done at three levels of hierarchical differentiation: ancestral trunks, breeds, and subpopulations. The deficit of heterozygotes was estimated at the subpopulation, breed, and ancestral trunk levels, with values of 4.0%, 6.5%, and 11.2%, respectively. In the whole population, the deficit of heterozygotes was about 17%. The proportion of genetic variability attributable to differences between subpopulations, breeds, and ancestral trunks was estimated to be 14.2%, 9.9%, and 6.9%, respectively. The dendrogram, obtained by using values of genic differentiation (FST) as a measure of the genetic distance among populations, is topologically identical to the one obtained using Nei's index of distance, which indicates a high correlation (r = .99) between both distances. These racial groupings, however, differ from the grouping obtained from historical, archeological, and morphological data.

Animals↗

Predicting response to selection on a quantitative trait: a comparison between models for mixed-mating populations.

Two different theoretical frameworks have been developed to predict response to selection in a mixed mating population (in which reproduction occurs by a mixture of outcrossing and self-fertilization). The genotypic covariance model (GCM) and the structured linear model (SLM) rely on the same assumptions regarding quantitative trait inheritance, but use different genetic summary statistics. Here, we demonstrate the algebraic relationships between the various genetic metrics used in each theory. This is accomplished by reformulating the GCM in terms of the Wright-Kempthorne equation. We use stochastic simulations to investigate the relative accuracy of each theory for a range of selfing rates. The SLM is generally more accurate than the GCM, the most pronounced differences emerging in simulations with inbreeding depression for fitness. In fact, with strong inbreeding depression and high selfing rates, evolution can occur opposite the direction predicted by the GCM. The simulations also indicate that direct application of random mating models to partially selfing populations can produce very inaccurate predictions if quantitative trait loci exhibit dominance.

Animals↗

Genetic diversity and population structure of Elytrigia pycnantha (Godr.) (Triticeae) in Mont Saint-Michel Bay using microsatellite markers.

During the last decade, an invasive wheatgrass species (Elytrigia pycnantha) has colonized the low salt marshes of the Mont Saint Michel Bay resulting in an accelerated change in the vegetation. This study was conducted using microgeographical genetic diversity in order to understand the genetic structure of this invasive and clonal species. Genetic variation and population structure of fifteen populations collected in high and low marsh habitats around the Bay were analyzed using five microsatellite loci. Because E. pycnantha is an allohexaploid, the application of standard genetic diversity statistics was not possible; we chose to summarize genetic diversity using statistics calculated from banding phenotypes. The mean number of alleles per locus was 10.2, the mean number of different alleles per sample was 6.87. The mean number of allelic phenotypes across all populations was 7.21. The mean value of genetic diversity for the species, calculated as the average number of alleles by which pairs of individuals differ, was H's = 1.91 and H't = 2.04. Little genetic differentiation among populations was detected (0.067). The association between pairwise genetic differentiation and geographic distances exhibited no evidence for isolation by distance. A geographical pattern of population differentiation, where a single population GI was clearly separated from the remaining population groups (considered as a metapopulation), was revealed by principal component analysis (PCA), and we propose that this is because GI represents a new genotype.

Ecosystem↗

Impact of pharmacogenetics on toxicological studies. Statistical implications.

Genetic differences in response to chemicals are probably ubiquitous. The implications of such genetic differences for the design of toxicological experiments is reviewed. The inclusion of genetic differences as factors in factorial experimental designs is illustrated by an experiment to investigate differences between inbred strains of mice in the length of anaesthesia following the administration of pentobarbitone to control and phenobarbitone pre-treated animals. The effects of including genetic differences as a factor in the standard toxicological studies such as the long-term rodent carcinogenicity bioassay (LTRCB) are reviewed. Such designs are likely to result in more chemicals being identified as carcinogens based upon the criteria of a positive result in the LTRCB. However, they are unlikely to provide any improvement in the estimation of risk to the human population from low level exposures to the chemicals because of the limitations of the existing extrapolation methods. Information on the degree of genetic variability in response to chemical exposure should, though, help in the more qualitative biologically-based risk assessment approaches favoured by some toxicologists. The presence of genetic differences in response also provides potential models for investigation of the mechanisms underlying toxicological responses.

Animals↗

Robust genetic linkage analysis based on a score test of homogeneity: the weighted pairwise correlation statistic.

In testing genetic linkage using large or complex pedigrees, robust methods may be preferred to the Lod-score method. The affected-pedigree-member method is robust but does not use the information available in nonaffected subjects, which results in a loss of power. We propose a new test of genetic linkage based on a score test of homogeneity derived from a random effect model. The statistic is simple and uses only pairs of subjects. In contrast with the affected-pedigree-method, it uses all the available pairs and does not depend on the marker alleles frequencies. A rank version of this weighted pairwise correlation statistic is proposed, its exact first and second moment derived. We show that for age-dependent diseases, it provides a simple nonparametric test.

Age of Onset↗

Education and certification of genetic counselors.

Genetic counseling is defined by the American Society of Human Genetics as a communication process which deals with the human problems associated with the occurrence, or risk of occurrence, of a genetic disorder in a family. The first graduate program (Master's degree) in genetic counseling started in 1969 at Sarah Lawrence College, NY, USA, while in 1979 the National Society of Genetic Counseling (NSGC) was established. Today, there are 29 programs in U.S.A. offering a Master's degree in Genetic Counseling, five programs in Canada, one in Mexico, one in England and one in S. Africa. Most of these graduate programs offer two year training, consisting of graduate courses, seminars, research and practical training. Emphasis is given in human physiology, biochemistry, clinical genetics, cytogenetics, molecular and biochemical genetics, population genetics and statistics, prenatal diagnosis, teratology and genetic counseling in relation to psychosocial and ethical issues. Certification for eligible candidates is available through the American Board of Medical Genetics (ABMG). Requirements for certification include a master's degree in human genetics, training at sites accredited by the ABMG, documentation of genetic counseling experience, evidence of continuing education and successful completion of a comprehensive ABMG certification examination. As professionals, genetic counselors should maintain expertise, should insure mechanisms for professional advancement and should always maintain the ability to approach their patients.

Counseling↗

Peopling of northern North America: clues from genetic studies.

The paper reviews the archaeological evidence for the length of human occupation in N. America and raises the question whether single or multiple movements of people out of Asia into America occurred, pointing out that considerable genetic variation can occur in small isolated populations in relatively short periods of time. The entire subarctic culture area is populated by speakers of either Athapascan or Algonkian language families. The archaeologic record for tracing the origin of these linguistic groups depends on items of material culture and these have been used to trace the origin of the modern peoples back for a few thousand years. Comparison between groups based on genetic data suffers from unevenness of the data for various Athapascan-and Algonkian-speaking groups. The problem is made more difficult by the smallness of populations and inadequate sample size. The gene diversity measure H of Nei has been used on data for the Athapaskan Dogrib. It suggests that there was probably significant gene diversity present in sub-arctic groups in pre-contact times. Probably this is true also for the Algonkians as typified by the Ojibwa. Examination of the apportioned gene diversity shows that the bulk of the diversity exists within groups rather than between groups. Genetic clues to the peopling of the Americas derive from specific marker genes and from genetic distance statistics. The distribution of the Dia and the GmZa; b03st alleles suggest that Athapaskan genetic links are towards the Bering Sea area while Algonkian connections are towards the south. Nei's genetic distance statistic was calculated for 13 populations using 14 blood group and enzyme loci. The dendrogram derived from the D matrix shows that Eskimos and Chukchi cluster together, and the Athapaskans are closer to the Eskimos than are the Algonkians. These relationships could be valid if the origin of Eskimos goes back to a population of Asiatic Beringia and that populations north of the late Wisconsin ice sheets included a group that led to the Athapaskans whilst populations south of the Wisconsin ice sheet led to the Algonkians.

Anthropology, Physical↗

A statistical model and analysis for genetic and environmental effects in responses from twin-family studies.

A statistical model and analysis for genetic and environmental effects in twin-family data are presented. The model is used to derive expressions for phenotypic correlations of 22 essential pair relationships in twin-family units. The analysis proceeds in two steps. First, differential effects of sex, generation, and sex-zygosity of twin-family units and correlations due to cluster sampling are eliminated from correlation data. Then, estimates and tests of model parameters are calculated from the adjusted data. The theory and methods were developed for a Swedish twin-family study of many behaviors possibly related to the smoking habit. There, it is important to screen for behaviors that clearly are under genetic control and to assess relative influences of various biological and social environments on the development of all behaviors. Height data from the Swedish study are used to illustrate concepts and methods presented in this paper.

Body Height↗

Comments on the statistical aspects of the NRC's report on DNA typing.

The goal of the NRC report on DNA typing was to answer a "crescendo of questions concerning DNA typing," many of them in the areas of population genetics and statistics. Unfortunately, few of these questions were answered adequately. In lieu of answering these questions, the panel proposed another conservative method of forensic inference, the "ceiling principle." Aside from its extreme conservativeness, this new method is difficult to justify because it is based on inadequate population genetics and statistical theory. Moreover, in its ultimate implementation, the panel's method will depend on a population genetics study whose rationale is questionable. In this article, we elaborate some of the general comments we made about the NRC report in a recent article [1]. Specifically we cover three topics. First we question the statistical basis for the ceiling principle, showing that the empirical results that motivated the method are likely to be misinterpreted and showing, by power calculations, that the effects of population substructure cannot be substantial. Second, we show that the study design to determine "ceiling" allele frequencies has several undesirable statistical properties. Finally, we discuss the estimation of handling errors from the statistical perspective, a subject treated inadequately by the report.

DNA Fingerprinting↗

Use of max and min scores for trend tests for association when the genetic model is unknown.

In case-control studies, the Cochran-Armitage (CA) trend test is powerful for detection of an association between a risk allele and a marker. To apply this test, a score should be assigned to the genotypes based on the genetic model. When the underlying genetic model is unknown, the trend test statistic is a function of the score. In this paper, simple procedures are given to obtain two scores (max and min), which respectively maximize and minimize the CA trend test statistics for genetic associations. These two scores can be used to examine the effect of the choice of scores on the test of no association. When the CA trend test statistic with the max (or min) score is less (or greater) than a prespecified value, the conclusion is clear: we will accept (or reject) the null hypothesis of no association for any scores used. When this value is less than the CA trend test statistic with the max score but greater than the one with the min score, the decision of whether or not to reject the null hypothesis depends on the choice of scores. In this situation, the CA trend test with a prespecified score cannot be used without careful scientific justification of the choice of scores. The use of max and min scoring schemes is applied to a real data set.

Case-Control Studies↗

Measurement of genetic structure within populations using Moran's spatial autocorrelation statistics.

Spatial structure of genetic variation within populations, an important interacting influence on evolutionary and ecological processes, can be analyzed in detail by using spatial autocorrelation statistics. This paper characterizes the statistical properties of spatial autocorrelation statistics in this context and develops estimators of gene dispersal based on data on standing patterns of genetic variation. Large numbers of Monte Carlo simulations and a wide variety of sampling strategies are utilized. The results show that spatial autocorrelation statistics are highly predictable and informative. Thus, strong hypothesis tests for neutral theory can be formulated. Most strikingly, robust estimators of gene dispersal can be obtained with practical sample sizes. Details about optimal sampling strategies are also described.

Biological Evolution↗

Hitchhiking mapping--functional genomics from the population genetics perspective.

Several statistical tests based on population genetic theory are used to identify genes that have recently acquired a beneficial mutation. Here, I describe the extension of these tests to a multilocus approach for a genome-wide survey for genes that have been under recent positive selection. As this strategy could potentially identify genes with weak phenotypic effects, it will be very useful in population genetic approaches aimed at understanding adaptation processes in natural populations. Furthermore, this 'hitchhiking mapping' could also help in the functional characterization of genomes.

Animals↗