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[Stabilizing selection and linkage disequilibrium].

An approach to the investigation of the evolution of quantitative traits on the basis of analysis of two-locus marginal systems dynamics has been developed. It has been shown that under stabilizing selection the "quasi-stationary" state is quickly reached and maintained continuously. The "quasi-stationary" state is characterized by small changes in allele frequencies and by linkage disequilibrium that significantly decreases genotypic variance. Equations defining the role of linkage disequilibrium in the stationary state of mutation-selection balance are derived.

Alleles↗

A class of tests for linkage using affected pedigree members.

We describe a class of nonparametric tests for linkage between a marker and a gene assumed to exist and to govern susceptibility to a disease. The tests are formed by assigning a score to each possible pattern of marker allele sharing (identity-by-descent) among affected pedigree members, and then averaging the scores over all patterns compatible with the observed marker genotype and genealogical relationship of the affected members. Different score functions give different tests. One function, which examines marker allele similarity across pairs of affected pedigree members, gives a test similar to that of Fimmers et al. (1989, in Multipoint Mapping and Linkage Based on Affected Pedigree Members: Genetic Analysis Workshop, R. C. Elston, M. A. Spence, S. E. Hodge, and J. W. MacCluer (eds), 123-128; City: Alan R. Liss). A second function examines allele similarity across arbitrary subsets, not just pairs, of affected members. The resulting test can be more powerful than the one based solely on pairs of affected members. The approach has several advantages: it does not require knowledge of the mode of disease inheritance; it does not require unambiguous determination of identity-by-descent at the marker; it does not suffer from variability due to chance allele similarity among affected members who are unrelated, such as spouses; it allows marker genotypes of unaffected members to contribute information on allele sharing among the affected; it permits calculation of exact P-values. Computational requirements limit the tests to many pedigrees with few (< 16) affected members.

Alleles↗

Deleterious mutations in animal mitochondrial DNA.

A simple neutral model predicts that the ratio of non-synonymous to synonymous fixed differences between species will be the same as the ratio of non-synonymous to synonymous polymorphisms within species. This prediction is tested with existing mitochondrial datasets from 25 animal species. In slightly over half of the studies, the ratio of replacement to silent polymorphisms within species is significantly greater than the ratio of replacement to silent fixed differences between species. These observations are best explained by a substantial number of mildly deleterious amino acid mutations that contribute to heterozygosity but rarely become fixed.

Animals↗

The fate of competing beneficial mutations in an asexual population.

In sexual populations, beneficial mutations that occur in different lineages may be recombined into a single lineage. In asexual populations, however, clones that carry such alternative beneficial mutations compete with one another and, thereby, interfere with the expected progression of a given mutation to fixation. From theoretical exploration of such 'clonal interference', we have derived (1) a fixation probability for beneficial mutations, (2) an expected substitution rate, (3) an expected coefficient of selection for realized substitutions, (4) an expected rate of fitness increase, (5) the probability that a beneficial mutation transiently achieves polymorphic frequency (> or = 1%), and (6) the probability that a beneficial mutation transiently achieves majority status. Based on (2) and (3), we were able to estimate the beneficial mutation rate and the distribution of mutational effects from changes in mean fitness in an evolving E. coli population.

Computer Simulation↗

The amount and pattern of DNA polymorphism under the neutral mutation hypothesis.

The amount and pattern of DNA polymorphism can give useful information on the maintenance mechanism of genetic variation at the DNA level. In this note we have shown the amount and pattern of DNA polymorphism expected under the neutral theory. The amount of DNA polymorphism can be estimated from the average number of nucleotide differences per site, the proportion of segregating sites, and so on. We have shown how to estimate theta from these quantities, where theta = 4Nv, N is the effective population size and v is the mutation rate per site per generation. We have also shown the expectations of the nucleotide variation within and between allelic classes.

Base Sequence↗

Genetic factors in susceptibility to death: a comparative analysis of bivariate survival models.

BACKGROUND: Molecular epidemiological studies of aging and longevity are focused on evaluating the effects of single genes on susceptibility to disease and death. The effects of all genetic factors on susceptibility can be evaluated from the analysis of survival data on related individuals. METHOD: The analyses of survival data on Danish monozygotic (MZ) and dizygotic (DZ) twins are performed using gamma, inverse Gaussian and three-parameter correlated frailty models. The semiparametric representations of the respective models are used to obtain maximum likelihood estimates of model parameters. The results are compared using the likelihood ratio test. RESULTS: The survival of Danish MZ and DZ twins can be characterised by the same marginal hazards and identical univariate frailty distributions for any of the three frailty models. In all three cases the genetic influence on frailty is statistically significant. CONCLUSION: All three models can be used to study genetic effects on susceptibility. The gamma and inverse Gaussian frailty models fit the Danish twin data equally well. Our analyses show that for the Danish twin data these two models are preferable to the three-parameter model.

Cohort Studies↗

Locally weighted transmission/disequilibrium test for genetic association analysis.

The transmission/disequilibrium test statistic has been used for assessing genetic association in affected-parent trios. In the presence of multiple tightly linked marker loci where local dependency may exist, haplotypes are reconstructed statistically to estimate the joint effects of these markers. In this manuscript, we propose an alternative to the haplotype approach by taking a weighted average of multiple loci, where the weight is proportional to the product of (1-2X recombination fraction) and the linkage disequilibrium between markers. As an illustration, we applied the method to the simulated Aipotu data.

Genome-Wide Association Study↗

Robust genomic control for association studies.

Population-based case-control studies are a useful method to test for a genetic association between a trait and a marker. However, the analysis of the resulting data can be affected by population stratification or cryptic relatedness, which may inflate the variance of the usual statistics, resulting in a higher-than-nominal rate of false-positive results. One approach to preserving the nominal type I error is to apply genomic control, which adjusts the variance of the Cochran-Armitage trend test by calculating the statistic on data from null loci. This enables one to estimate any additional variance in the null distribution of statistics. When the underlying genetic model (e.g., recessive, additive, or dominant) is known, genomic control can be applied to the corresponding optimal trend tests. In practice, however, the mode of inheritance is unknown. The genotype-based chi (2) test for a general association between the trait and the marker does not depend on the underlying genetic model. Since this general association test has 2 degrees of freedom (df), the existing formulas for estimating the variance factor by use of genomic control are not directly applicable. By expressing the general association test in terms of two Cochran-Armitage trend tests, one can apply genomic control to each of the two trend tests separately, thereby adjusting the chi (2) statistic. The properties of this robust genomic control test with 2 df are examined by simulation. This genomic control-adjusted 2-df test has control of type I error and achieves reasonable power, relative to the optimal tests for each model.

Case-Control Studies↗

Resistance or emigration: response of the high-alpine plant Eritrichium nanum (L.) Gaudin to the ice age within the Central Alps.

Two main possibilities regarding glacial survival of the mountain flora of the Alps during the Quaternary have been discussed: the tabula rasa and the nunatak hypotheses. Eritrichium nanum (L.) Gaudin (Boraginaceae) is a perennial cushion plant, occurring at high elevations of the Central Alps and having a preference for extreme habitats. It belongs to a group of high-alpine plants, for which in situ glacial survival on nunataks is ecologically possible. By investigating 20 populations of E. nanum of potential nunatak and peripheral refugial regions using amplified fragment length polymorphism, considerable genetic differences between populations from the Central Alps and populations from peripheral refugia were detected; hence, the latter probably did not serve as potential sources for the re-colonization of the Central Alps after glaciation. Genetic variation was hierarchically structured (AMOVA), and three genetically distinct regions could be identified in the Central Alps. Two of these, the Penninic and Rhaetic Alps, correspond to nunatak regions proposed in the biogeographic literature. Populations from the Lepontic Alps formed a third genetic group. Genetic correlation (Mantel statistics) was highest within populations, with a modest decline among populations within specific nunatak regions and a negative correlation outside the genetic influence of specific nunatak regions. In situ glacial survival in E. nanum could be a model for the Quaternary history of other alpine plants, especially those that also occur at high elevations and in similar habitats.

Altitude↗

A unified statistical model for functional mapping of environment-dependent genetic expression and genotype x environment interactions for ontogenetic development.

The effects of quantitative trait loci (QTL) on phenotypic development may depend on the environment (QTL x environment interaction), other QTL (genetic epistasis), or both. In this article, we present a new statistical model for characterizing specific QTL that display environment-dependent genetic expressions and genotype x environment interactions for developmental trajectories. Our model was derived within the maximum-likelihood-based mixture model framework, incorporated by biologically meaningful growth equations and environment-dependent genetic effects of QTL, and implemented with the EM algorithm. With this model, we can characterize the dynamic patterns of genetic effects of QTL governing growth curves and estimate the global effect of the underlying QTL during the course of growth and development. In a real example with rice, our model has successfully detected several QTL that produce differences in their genetic expression between two contrasting environments. These detected QTL cause significant genotype x environment interactions for some fundamental aspects of growth trajectories. The model provides the basis for deciphering the genetic architecture of trait expression adjusted to different biotic and abiotic environments and genetic relationships for growth rates and the timing of life-history events for any organism.

Chromosome Mapping↗

Thermometers: something for statistical geneticists to think about.

In human genetics, we measure the strength of statistical evidence using a variety of maximized likelihood ratios, LODs, and empirical p values. I argue here that these statistics have highly undesirable properties as evidence measures when applied to complex disorders. Among other deficiencies, I show that when following up on an interesting finding, they will tend to erroneously indicate diminished evidence as more data are considered (e.g., the LOD will tend to go down at a linked locus as the sample size increases). This violates a fundamental assumption underlying standard linkage and association designs in which we first scan the genome for our best signals, and then follow up at those genomic positions with additional data. I argue here for a coherent theoretical approach to formalizing statistical evidence measures, and derive a set of minimal requirements that any evidence measure should meet, drawing heavily on an analogy with the thermometer. I speculate that measures of evidence that come closer to meeting these requirements will do a better job of finding and characterizing genes, and I propose an alternative evidence metric as a step in this direction.

Genetic Linkage↗

An algorithm for molecular dissection of tumor progression.

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.

Algorithms↗

Anthropometric and genetic distance between Gonds of Central India.

A morphological and genetic study was undertaken on five Gondi-speaking populations of Central India (Andhra Pradesh and Maharashtra States). There has been no systematic biological study on this large Dravidian-speaking tribal group, 4 million in number, amounting to 13% of the total tribal population of India. Data was collected on 16 anthropometric measurements and seven genetic markers (blood groups, hemoglobin, G6PD and plasma protein polymorphisms) on the Raj Gonds, Kolams, Manne, Koyas and Plains Maria Gonds. Various genetic distance measures such as Mahalanobis's D2 and Nei's and Sanghvi's measures and cluster analysis techniques were used to determine the relationship between these groups based on anthropometrics and genetic variables. The statistical analysis revealed the Gonds to be a heterogenous group in both morphology and genetic characteristics. The morphological and genetic distances between these five groups when projected graphically revealed that the spatial distribution of these Gonds generally corresponds to their present geographical distribution. However, the actual relationships among each of the Gond populations show differences when based on these two biological variables, the possible reasons for this being discussed in the paper. The emphasis of this study is on the importance of geographical proximity in producing morphological and genetic similarity between populations, brought about by a short distance as well as similar geographical factors (such as soil, terrain, flora, etc.) drawing these populations together under a common ecocultural umbrella.

Anthropometry↗

BAPS 2: enhanced possibilities for the analysis of genetic population structure.

UNLABELLED: Bayesian statistical methods based on simulation techniques have recently been shown to provide powerful tools for the analysis of genetic population structure. We have previously developed a Markov chain Monte Carlo (MCMC) algorithm for characterizing genetically divergent groups based on molecular markers and geographical sampling design of the dataset. However, for large-scale datasets such algorithms may get stuck to local maxima in the parameter space. Therefore, we have modified our earlier algorithm to support multiple parallel MCMC chains, with enhanced features that enable considerably faster and more reliable estimation compared to the earlier version of the algorithm. We consider also a hierarchical tree representation, from which a Bayesian model-averaged structure estimate can be extracted. The algorithm is implemented in a computer program that features a user-friendly interface and built-in graphics. The enhanced features are illustrated by analyses of simulated data and an extensive human molecular dataset. AVAILABILITY: Freely available at http://www.rni.helsinki.fi/~jic/bapspage.html.

Algorithms↗

Role of gene expression microarray analysis in finding complex disease genes.

The promise of gene expression studies using microarray technology has inspired much new hope for finding complex diseases genes. It has become clear that complex diseases result from collective actions of many genetic and nongenetic factors. Therefore, genetic dissection of complex diseases should be carried out in a global context. The technology of gene expression microarray analysis (GEMA) can provide such global information on transcription activities of essentially all genes simultaneously. It is hoped that this promising technology can be applied to samples drawn from large-scale, well-defined genetic epidemiological studies and help us untangle the web of pathways leading to complex diseases. However, extremely noisy GEMA data pose serious challenges in terms of the statistical methodologies needed. Extensive work is needed in order to respond to the challenges before one can fully utilize the potential power provided by GEMA. We begin in this paper by identifying several statistical problems related to the application of GEMA to genetic epidemiological analysis, and consider study designs that might benefit from this promising new technology. While it is still too early to tell how much of the enormous potential of GEMA will be realized ultimately, its success will probably depend most critically on the ability of statistical genetics to rise to the challenge of mining information from a sea of noise.

Gene Expression↗

Incorporating individual error rate into association test of unmatched case-control design.

OBJECTIVES: Genotyping error commonly occurs and could reduce the power and bias statistical inference in genetics studies. In addition to genotypes, some automated biotechnologies also provide quality measurement of each individual genotype. We studied the relationship between the quality measurement and genotyping error rate. Furthermore, we propose two association tests incorporating the genotyping quality information with the goal to improve statistical power and inference. METHODS: 50 pairs of DNA sample duplicates were typed for 232 SNPs by BeadArray technology. We used scatter plot, smoothing function and generalized additive models to investigate the relationship between genotype quality score (q) and inconsistency rate (ĩ) among duplicates. We constructed two association tests: (1) weighted contingency table test (WCT) and (2) likelihood ratio test (LRT) to incorporate individual genotype error rate (epsilon(i)), in unmatched case-control setting. RESULTS: In the 50 duplicates, we found q and ĩ were in strong negative association, suggesting the genotypes with low quality score were more likely to be mistyped. The WCT improved the statistical power and partially corrects the bias in point estimation. The LRT offered moderate power gain, but was able to correct the bias in odds ratio estimation. The two new methods also performed favorably in some scenarios when epsilon(i) was mis-specified. CONCLUSIONS: With increasing number of genetic studies and application of automated genotyping technology, there is a growing need to adequately account for individual genotype error rate in statistical analysis. Our study represents an initial step to address this need and points out a promising direction for further research.

Case-Control Studies↗