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PubMed2001

Allelic association and disease mapping.

The application of allelic association to map genes for complex traits, particularly using high-density maps of single nucleotide polymorphisms in candidate regions, is an area of very active research. Here we present some aspects of the methodology and applications to both major gene mapping, which illustrates the effectiveness of the method, and oligogenes, where methods are still in flux and for which there have been relatively few successes to date. Several important considerations emerge, including the selection of the optimal metric for measuring association and the importance of modelling the decline in association with distance given the variability in association in a candidate region. The Malecot model of association with distance is shown to have a resolution of greater than 50 kilobases but the available evidence suggests that considerably higher resolution might be achieved with dense single nucleotide polymorphism (SNP) maps.

Alleles↗
PubMed2000

Fels-Rand: an Xlisp-Stat program for the comparative analysis of data under phylogenetic uncertainty.

MOTIVATION: Currently available programs for the comparative analysis of phylogenetic data do not perform optimally when the phylogeny is not completely specified (i.e. the phylogeny contains polytomies). Recent literature suggests that a better way to analyse the data would be to create random trees from the known phylogeny that are fully-resolved but consistent with the known tree. A computer program is presented, Fels-Rand, that performs such analyses. A randomisation procedure is used to generate trees that are fully resolved but whose structure is consistent with the original tree. Statistics are then calculated on a large number of these randomly-generated trees. Fels-Rand uses the object-oriented features of Xlisp-Stat to manipulate internal tree representations. Xlisp-Stat's dynamic graphing features are used to provide heuristic tools to aid in analysis, particularly outlier analysis. The usefulness of Xlisp-Stat as a system for phylogenetic computation is discussed. AVAILABILITY: Available from the author or at http://www.uq.edu.au/~ansblomb/Fels-Rand.sit.hqx. Xlisp-Stat is available from http://stat.umn.edu/~luke/xls/xlsinfo/xlsinfo.html. CONTACT: s.blomberg@abdn.ac.uk

Algorithms↗
PubMed2001

A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes.

MOTIVATION: DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. RESULTS: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t -test, provide a systematic inference approach that compares favorably with simple t -test or fold methods, and partly compensate for the lack of replication.

Bayes Theorem↗
PubMed1992

Extendable words in nucleotide sequences.

Previous statistical analyses revealed several peculiarities of nucleotide sequences that preclude their description by existing models and thus allow one to distinguish DNA and RNA sequences from random A,T,G,C-texts. This is a consequence of the unusual distribution of certain words in nucleotide sequences: while the distribution of (most) words is consistent with Markov models of small orders, the distribution of certain words cannot be described by any previous model (anomalies in distribution of homonucleotide/homopurine/homopyrimidine runs, complementary and mirror palindromes, and non-stationary words). In this work we introduce a probabilistic approach that is partly motivated by analogy with linguistics. We also describe another important feature of DNA/RNA sequences: anomalies in distribution of words of poor nucleotide composition. We show that some classes of these words are the major obstacle for the simple Markov description of nucleotide sequences.

Base Sequence↗
PubMed2003

PopHist: inferring population history from the spectrum of allele frequencies.

SUMMARY: PopHist is a computer program that uses the frequency spectrum of alleles to: (a) estimate maximum likelihood parameters describing a population's history; and (b) compare alternative hypotheses about population history using likelihood ratio tests. The program uses the matrix coalescent, a method for calculating theoretical frequency spectra that can be applied to sets of unlinked sites. AVAILABILITY: Source code and documentation are available at http://mombasa.anthro.utah.edu/wooding/PopHist

Algorithms↗
PubMed2003

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.

Algorithms↗
PubMed2005

apTreeshape: statistical analysis of phylogenetic tree shape.

apTreeshape is a R package dedicated to simulation and analysis of phylogenetic tree topologies using statistical imbalance measures. It is a companion library of the R package 'ape', which provides additional functions for reading, plotting, manipulating phylogenetic trees and for connecting to public phylogenetic tree databases. One strength of the package is to include appropriate corrections of classical shape statistics as well as new tests based on the statistical theory of likelihood ratios.

Algorithms↗
PubMed2005

Improving missing value estimation in microarray data with gene ontology.

MOTIVATION: Gene expression microarray experiments produce datasets with frequent missing expression values. Accurate estimation of missing values is an important prerequisite for efficient data analysis as many statistical and machine learning techniques either require a complete dataset or their results are significantly dependent on the quality of such estimates. A limitation of the existing estimation methods for microarray data is that they use no external information but the estimation is based solely on the expression data. We hypothesized that utilizing a priori information on functional similarities available from public databases facilitates the missing value estimation. RESULTS: We investigated whether semantic similarity originating from gene ontology (GO) annotations could improve the selection of relevant genes for missing value estimation. The relative contribution of each information source was automatically estimated from the data using an adaptive weight selection procedure. Our experimental results in yeast cDNA microarray datasets indicated that by considering GO information in the k-nearest neighbor algorithm we can enhance its performance considerably, especially when the number of experimental conditions is small and the percentage of missing values is high. The increase of performance was less evident with a more sophisticated estimation method. We conclude that even a small proportion of annotated genes can provide improvements in data quality significant for the eventual interpretation of the microarray experiments. AVAILABILITY: Java and Matlab codes are available on request from the authors. SUPPLEMENTARY MATERIAL: Available online at http://users.utu.fi/jotatu/GOImpute.html.

Algorithms↗
PubMed2006

Variance stabilization and normalization for one-color microarray data using a data-driven multiscale approach.

MOTIVATION: Many standard statistical techniques are effective on data that are normally distributed with constant variance. Microarray data typically violate these assumptions since they come from non-Gaussian distributions with a non-trivial mean-variance relationship. Several methods have been proposed that transform microarray data to stabilize variance and draw its distribution towards the Gaussian. Some methods, such as log or generalized log, rely on an underlying model for the data. Others, such as the spread-versus-level plot, do not. We propose an alternative data-driven multiscale approach, called the Data-Driven Haar-Fisz for microarrays (DDHFm) with replicates. DDHFm has the advantage of being 'distribution-free' in the sense that no parametric model for the underlying microarray data is required to be specified or estimated; hence, DDHFm can be applied very generally, not just to microarray data. RESULTS: DDHFm achieves very good variance stabilization of microarray data with replicates and produces transformed intensities that are approximately normally distributed. Simulation studies show that it performs better than other existing methods. Application of DDHFm to real one-color cDNA data validates these results. AVAILABILITY: The R package of the Data-Driven Haar-Fisz transform (DDHFm) for microarrays is available in Bioconductor and CRAN.

Algorithms↗
PubMed2003

A Bayesian approach to disease gene location using allelic association.

A Bayesian approach to analysing data from family-based association studies is developed. This permits direct assessment of the range of possible values of model parameters, such as the recombination frequency and allelic associations, in the light of the data. In addition, sophisticated comparisons of different models may be handled easily, even when such models are not nested. The methodology is developed in such a way as to allow separate inferences to be made about linkage and association by including theta, the recombination fraction between the marker and disease susceptibility locus under study, explicitly in the model. The method is illustrated by application to a previously published data set. The data analysis raises some interesting issues, notably with regard to the weight of evidence necessary to convince us of linkage between a candidate locus and disease.

Alleles↗
PubMed1986

The evolution of self-regulated transposition of transposable elements.

This paper examines the conditions under which self-regulated rates of transposition can evolve in populations of transposable elements infecting sexually reproducing hosts. Models of the evolution of both cis-acting regulation (transposition immunity) and trans-acting regulation (transposition repression) are analyzed. The potential selective advantage to regulation is assumed to be derived from the deleterious effects of mutations associated with the insertion of newly replicated elements. It is shown that both types of regulation can easily evolve in hosts with low rates of genetic recombination per generation, such as bacteria or bacterial plasmids. Conditions are much more restrictive in organisms with relatively free recombination. In haploids, the main selective force promoting regulation is the induction of lethal or sterile mutations by transposition; in diploids, a sufficiently high frequency of dominant lethal or sterile mutations associated with transpositions is required. Data from Drosophila and maize suggest that this requirement can sometimes be met. Coupling of regulatory effects across different families of elements would also aid the evolution of regulation. The selective advantages of restricting transposition to the germ line and of excising elements from somatic cells are discussed.

Animals↗
PubMed1991

A maximum likelihood method for estimating genome length using genetic linkage data.

The genetic length of a genome, in units of Morgans or centimorgans, is a fundamental characteristic of an organism. We propose a maximum likelihood method for estimating this quantity from counts of recombinants and nonrecombinants between marker locus pairs studied from a backcross linkage experiment, assuming no interference and equal chromosome lengths. This method allows the calculation of the standard deviation of the estimate and a confidence interval containing the estimate. Computer simulations have been performed to evaluate and compare the accuracy of the maximum likelihood method and a previously suggested method-of-moments estimator. Specifically, we have investigated the effects of the number of meioses, the number of marker loci, and variation in the genetic lengths of individual chromosomes on the estimate. The effect of missing data, obtained when the results of two separate linkage studies with a fraction of marker loci in common are pooled, is also investigated. The maximum likelihood estimator, in contrast to the method-of-moments estimator, is relatively insensitive to violation of the assumptions made during analysis and is the method of choice. The various methods are compared by application to partial linkage data from Xiphophorus.

Animals↗
PubMed1992

Polymorphism and balancing selection at major histocompatibility complex loci.

Amino acid replacements in the peptide-binding region (PBR) of the functional major histocompatibility complex (Mhc) genes appear to be driven by balancing selection. Of the various types of balancing selection, we have examined a model equivalent to overdominance that confers heterozygote advantage. As discussed by A. Robertson, overdominance selection tends to maintain alleles that have more or less the same degree of heterozygote advantage. Because of this symmetry, the model makes various testable predictions about the genealogical relationships among different alleles and provides ways of analyzing DNA sequences of Mhc alleles. In this paper, we analyze DNA sequences of 85 alleles at the HLA-A, -B, -C, -DRB1 and -DQB1 loci with respect to the number of alleles and extent of nucleotide differences at the PBR, as well as at the synonymous (presumably neutral) sites. Theory suggests that the number of alleles that differ at the sites targeted by selection (presumably the nonsynonymous sites in the PBR) should be equal to the mean number of nucleotide substitutions among pairs of alleles. We also demonstrate that the nucleotide substitution rate at the targeted sites relative to that of neutral sites may be much larger than 1. The predictions of the presented model are in surprisingly good agreement with the actual data and thus provide means for inferring certain population parameters. For overdominance selection in a finite population at equilibrium, the product of selection intensity (s) against homozygotes and the effective population size (N) is estimated to be 350-3000, being largest at the B locus and smallest at the C locus. We argue that N is of the order of 10(5) and s is several percent at most, if the mutation rate per site per generation is 10(-8).

Alleles↗
PubMed1992

Inferring selective history from multilocus frequency data: Wright meets the Hamiltonian.

We describe a method to study characteristics of the dynamics of multilocus population genetic models without specifying the form of selection a priori. Our approach consists of specifying initial and final genotypic frequencies (either completely or partially) and then determining the minimum time to go from the initial condition to the final condition according to a continuous time genetic model, with arbitrary constraints on the strength and possibly the form of selection. In analyzing a two-locus, two-allele model with this approach, we show that--so long as r is not much larger than s--substantial linkage disequilibrium can be generated from an initial state of linkage equilibrium in a few hundred generations. We also show that unless recombination is much larger than selection, there is only weak dependence on r of the minimum time to reach a specified state. Thus, similar strengths of selection can lead to similar levels of disequilibrium over a fixed time and a range of small recombination rates. This implies that, within the level of a single gene, selection cannot in general be assumed to lead to any particular relationship between recombination rate and levels of disequilibrium. We indicate a number of other ways in which our method can be useful in asking theoretical questions and in interpreting data.

Alleles↗
PubMed1992

Estimation of levels of gene flow from DNA sequence data.

We compare the utility of two methods for estimating the average levels of gene flow from DNA sequence data. One method is based on estimating FST from frequencies at polymorphic sites, treating each site as a separate locus. The other method is based on computing the minimum number of migration events consistent with the gene tree inferred from their sequences. We compared the performance of these two methods on data that were generated by a computer simulation program that assumed the infinite sites model of mutation and that assumed an island model of migration. We found that in general when there is no recombination, the cladistic method performed better than FST while the reverse was true for rates of recombination similar to those found in eukaryotic nuclear genes, although FST performed better for all recombination rates for very low levels of migration (Nm = 0.1).

Computer Simulation↗
PubMed1995

Testing heterozygote excess and deficiency.

Currently used tests of Hardy-Weinberg proportions do not take into account the nature of the alternative hypothesis, which is generally a heterozygote deficiency. Different exact tests, appropriate for small sample size and large number of alleles, are proposed in this perspective, and their properties are evaluated by power comparisons. Some tests are found to be close to optimal for the detection of inbreeding or heterozygote excess, one of which is a score test closely related to Robertson and Hill's estimator of the inbreeding coefficient. This test is also easily applied to multiple samples. Such tests are not always the most appropriate if alternative hypotheses differ from those considered here.

Alleles↗