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PubMedDate not supplied

A Bayesian model for detecting past recombination events in DNA multiple alignments.

Most phylogenetic tree estimation methods assume that there is a single set of hierarchical relationships among sequences in a data set for all sites along an alignment. Mosaic sequences produced by past recombination events will violate this assumption and may lead to misleading results from a phylogenetic analysis due to the imposition of a single tree along the entire alignment. Therefore, the detection of past recombination is an important first step in an analysis. A Bayesian model for the changes in topology caused by recombination events is described here. This model relaxes the assumption of one topology for all sites in an alignment and uses the theory of Hidden Markov models to facilitate calculations, the hidden states being the underlying topologies at each site in the data set. Changes in topology along the multiple sequence alignment are estimated by means of the maximum a posteriori (MAP) estimate. The performance of the MAP estimate is assessed by application of the model to data sets of four sequences, both simulated and real.

Bayes Theorem↗
PubMedDate not supplied

Reconstructing reticulate evolution in species-theory and practice.

We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison's approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing phylogenetic networks from two gene trees contained inside the network. We allow the network to have an arbitrary number of reticulations, but we limit the reticulation in the network so that the cycles in the network are node-disjoint ("galled"). Our second method is a polynomial time algorithm for constructing networks with one reticulation, where we allow for errors in the estimated gene trees. Using simulations, we demonstrate improved performance of this method over both NeighborNet and Maddison's method.

Computer Simulation↗
PubMed2005

There is no silver bullet--a guide to low-level data transforms and normalisation methods for microarray data.

To overcome random experimental variation, even for simple screens, data from multiple microarrays have to be combined. There are, however, systematic differences between arrays, and any bias remaining after experimental measures to ensure consistency needs to be controlled for. It is often difficult to make the right choice of data transformation and normalisation methods to achieve this end. In this tutorial paper we review the problem and a selection of solutions, explaining the basic principles behind normalisation procedures and providing guidance for their application.

Algorithms↗
PubMed2003

Combining multiple microarray studies and modeling interstudy variation.

We have established a method for systematic integration of multiple microarray datasets. The method was applied to two different sets of cancer profiling studies. The change of gene expression in cancer was expressed as 'effect size', a standardized index measuring the magnitude of a treatment or covariate effect. The effect sizes were combined to obtain the estimate of the overall mean. The statistical significance was determined by a permutation test extended to multiple datasets. It was shown that the data integration promotes the discovery of small but consistent expression changes with increased sensitivity and reliability. The effect size methods provided the efficient modeling framework for addressing interstudy variation as well. Based on the result of homogeneity tests, a fixed effects model was adopted for one set of datasets that had been created in controlled experimental conditions. By contrast, a random effects model was shown to be appropriate for the other set of datasets that had been published by independent groups. We also developed an alternative modeling procedure based on a Bayesian approach, which would offer flexibility and robustness compared to the classical procedure.

Algorithms↗
PubMed2003

R/qtl: QTL mapping in experimental crosses.

SUMMARY: R/qtl is an extensible, interactive environment for mapping quantitative trait loci (QTLs) in experimental populations derived from inbred lines. It is implemented as an add-on package for the freely-available statistical software, R, and includes functions for estimating genetic maps, identifying genotyping errors, and performing single-QTL and two-dimensional, two-QTL genome scans by multiple methods, with the possible inclusion of covariates. AVAILABILITY: The package is freely available at http://www.biostat.jhsph.edu/~kbroman/qtl.

Algorithms↗
PubMed2003

Normality of oligonucleotide microarray data and implications for parametric statistical analyses.

MOTIVATION: Experimental limitations have resulted in the popularity of parametric statistical tests as a method for identifying differentially regulated genes in microarray data sets. However, these tests assume that the data follow a normal distribution. To date, the assumption that replicate expression values for any gene are normally distributed, has not been critically addressed for Affymetrix GeneChip data. RESULTS: The normality of the expression values calculated using four different commercial and academic software packages was investigated using a data set consisting of the same target RNA applied to 59 human Affymetrix U95A GeneChips using a combination of statistical tests and visualization techniques. For the majority of probe sets obtained from each analysis suite, the expression data showed a good correlation with normality. The exception was a large number of low-expressed genes in the data set produced using Affymetrix Microarray Suite 5.0, which showed a striking non-normal distribution. In summary, our data provide strong support for the application of parametric tests to GeneChip data sets without the need for data transformation.

Algorithms↗
PubMed2004

On the significance of sequence alignments when using multiple scoring matrices.

MOTIVATION: Pairwise local sequence alignment is commonly used to search data bases for sequences related to some query sequence. Alignments are obtained using a scoring matrix that takes into account the different frequencies of occurrence of the various types of amino acid substitutions. Software like BLAST provides the user with a set of scoring matrices available to choose from, and in the literature it is sometimes recommended to try several scoring matrices on the sequences of interest. The significance of an alignment is usually assessed by looking at E-values and p-values. While sequence lengths and data base sizes enter the standard calculations of significance, it is much less common to take the use of several scoring matrices on the same sequences into account. Altschul proposed corrections of the p-value that account for the simultaneous use of an infinite number of PAM matrices. Here we consider the more realistic situation where the user may choose from a finite set of popular PAM and BLOSUM matrices, in particular the ones available in BLAST. It turns out that the significance of a result can be considerably overestimated, if a set of substitution matrices is used in an alignment problem and the most significant alignment is then quoted. RESULTS: Based on extensive simulations, we study the multiple testing problem that occurs when several scoring matrices for local sequence alignment are used. We consider a simple Bonferroni correction of the p-values and investigate its accuracy. Finally, we propose a more accurate correction based on extreme value distributions fitted to the maximum of the normalized scores obtained from different scoring matrices. For various sets of matrices we provide correction factors which can be easily applied to adjust p- and E-values reported by software packages.

Data Interpretation, Statistical↗
PubMed2004

Growing genetic regulatory networks from seed genes.

MOTIVATION: A number of models have been proposed for genetic regulatory networks. In principle, a network may contain any number of genes, so long as data are available to make inferences about their relationships. Nevertheless, there are two important reasons why the size of a constructed network should be limited. Computationally and mathematically, it is more feasible to model and simulate a network with a small number of genes. In addition, it is more likely that a small set of genes maintains a specific core regulatory mechanism. RESULTS: Subnetworks are constructed in the context of a directed graph by beginning with a seed consisting of one or more genes believed to participate in a viable subnetwork. Functionalities and regulatory relationships among seed genes may be partially known or they may simply be of interest. Given the seed, we iteratively adjoin new genes in a manner that enhances subnetwork autonomy. The algorithm is applied using both the coefficient of determination and the Boolean-function influence among genes, and it is illustrated using a glioma gene-expression dataset. AVAILABILITY: Software for the seed-growing algorithm will be available at the website for Probabilistic Boolean Networks: http://www2.mdanderson.org/app/ilya/PBN/PBN.htm

Algorithms↗
PubMed2004

Normalization of microarray data using a spatial mixed model analysis which includes splines.

MOTIVATION: Microarray experiments with thousands of genes on a slide and multiple slides used in any experimental set represent a large body of data with many sources of variation. The identification of such sources of variation within microarray experimental sets is critical for correct deciphering of desired gene expression differences. RESULTS: We describe new methods for the normalization using spatial mixed models which include splines and analysis of two-colour spotted microarrays for within slide variation and for a series of slides. The model typically explains 45-85% of the variation on a slide with only approximately 1% of the total degrees of freedom. The results from our methods compare favourably with those from intensity dependent normalization loess methods where we accounted for twice as much uncontrolled and unwanted variation on the slides. We have also developed an index for each EST that combines the various measures of the differential response into a single value that researchers can use to rapidly assess the genes of interest.

Algorithms↗
PubMed2004

Statistical detection of chromosomal homology using shared-gene density alone.

MOTIVATION: Over evolutionary time, various processes including point mutations and insertions, deletions and inversions of variable sized segments progressively degrade the homology of duplicated chromosomal regions making identification of the homologous regions correspondingly difficult. Existing algorithms that attempt to detect homology are based on shared-gene density and colinearity and possibly also strand information. RESULTS: Here, we develop a new algorithm for the statistical detection of chromosomal homology, CloseUp, which uses shared-gene density alone to fully exploit the observation that relaxing colinearity requirements in general is beneficial for homology detection and at the same time optimizes computation time. CloseUp has two components: the identification of candidate homologous regions followed by their statistical evaluation using Monte Carlo methods and data randomization. Using both artificial and real data, we compared CloseUp with two existing programs (ADHoRe and LineUp) for chromosomal homology detection and found that in general CloseUp compares favorably. AVAILABILITY: CloseUp and supplementary information are available at http://www.igb.uci.edu/servers/cgss.html CONTACT: pfbaldi@ics.uci.edu.

Algorithms↗
PubMed2004

Statistical evaluation and comparison of a pairwise alignment algorithm that a priori assigns the number of gaps rather than employing gap penalties.

MOTIVATION: Although pairwise sequence alignment is essential in comparative genomic sequence analysis, it has proven difficult to precisely determine the gap penalties for a given pair of sequences. A common practice is to employ default penalty values. However, there are a number of problems associated with using gap penalties. First, alignment results can vary depending on the gap penalties, making it difficult to explore appropriate parameters. Second, the statistical significance of an alignment score is typically based on a theoretical model of non-gapped alignments, which may be misleading. Finally, there is no way to control the number of gaps for a given pair of sequences, even if the number of gaps is known in advance. RESULTS: In this paper, we develop and evaluate the performance of an alignment technique that allows the researcher to assign a priori set of the number of allowable gaps, rather than using gap penalties. We compare this approach with the Smith-Waterman and Needleman-Wunsch techniques on a set of structurally aligned protein sequences. We demonstrate that this approach outperforms the other techniques, especially for short sequences (56-133 residues) with low similarity (<25%). Further, by employing a statistical measure, we show that it can be used to assess the quality of the alignment in relation to the true alignment with the associated optimal number of gaps. AVAILABILITY: The implementation of the described methods SANK_AL is available at http://cbbc.murdoch.edu.au/ CONTACT: matthew@cbbc.murdoch.edu.au.

Algorithms↗
PubMed2006

Simulated maximum likelihood method for estimating kinetic rates in gene expression.

MOTIVATION: Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. RESULTS: In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Algorithms↗
PubMed2006

Odds ratio based multifactor-dimensionality reduction method for detecting gene-gene interactions.

MOTIVATION: The identification and characterization of genes that increase the susceptibility to common complex multifactorial diseases is a challenging task in genetic association studies. The multifactor dimensionality reduction (MDR) method has been proposed and implemented by Ritchie et al. (2001) to identify the combinations of multilocus genotypes and discrete environmental factors that are associated with a particular disease. However, the original MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups in an ad hoc manner based on a simple comparison of the ratios of the number of cases and controls. Hence, the MDR approach is prone to false positive and negative errors when the ratio of the number of cases and controls in a combination of genotypes is similar to that in the entire data, or when both the number of cases and controls is small. Hence, we propose the odds ratio based multifactor dimensionality reduction (OR MDR) method that uses the odds ratio as a new quantitative measure of disease risk. RESULTS: While the original MDR method provides a simple binary measure of risk, the OR MDR method provides not only the odds ratio as a quantitative measure of risk but also the ordering of the multilocus combinations from the highest risk to lowest risk groups. Furthermore, the OR MDR method provides a confidence interval for the odds ratio for each multilocus combination, which is extremely informative in judging its importance as a risk factor. The proposed OR MDR method is illustrated using the dataset obtained from the CDC Chronic Fatigue Syndrome Research Group. AVAILABILITY: The program written in R is available.

Fatigue Syndrome, Chronic↗
PubMed2006

Indelign: a probabilistic framework for annotation of insertions and deletions in a multiple alignment.

MOTIVATION: A quantitative study of molecular evolutionary events such as substitutions, insertions and deletions from closely related genomes requires (1) an accurate multiple sequence alignment program and (2) a method to annotate the insertions and deletions that explain the 'gaps' in the alignment. Although the former requirement has been extensively addressed, the latter problem has received little attention, especially in a comprehensive probabilistic framework. RESULTS: Here, we present Indelign, a program that uses a probabilistic evolutionary model to compute the most likely scenario of insertions and deletions consistent with an input multiple alignment. It is also capable of modifying the given alignment so as to obtain a better agreement with the evolutionary model. We find close to optimal performance and substantial improvement over alternative methods, in tests of Indelign on synthetic data. We use Indelign to analyze regulatory sequences in Drosophila, and find an excess of insertions over deletions, which is different from what has been reported for neutral sequences. AVAILABILITY: The Indelign program may be downloaded from the website http://veda.cs.uiuc.edu/indelign/ SUPPLEMENTARY INFORMATION: Supplementary material is available at Bioinformatics online.

Algorithms↗
PubMed1999

Evolution of genetic variability and the advantage of sex and recombination in changing environments.

The role of recombination and sexual reproduction in enhancing adaptation and population persistence in temporally varying environments is investigated on the basis of a quantitative-genetic multilocus model. Populations are finite, subject to density-dependent regulation with a finite growth rate, diploid, and either asexual or randomly mating and sexual with or without recombination. A quantitative trait is determined by a finite number of loci at which mutation generates genetic variability. The trait is under stabilizing selection with an optimum that either changes at a constant rate in one direction, exhibits periodic cycling, or fluctuates randomly. It is shown by Monte Carlo simulations that if the directional-selection component prevails, then freely recombining populations gain a substantial evolutionary advantage over nonrecombining and asexual populations that goes far beyond that recognized in previous studies. The reason is that in such populations, the genetic variance can increase substantially and thus enhance the rate of adaptation. In nonrecombining and asexual populations, no or much less increase of variance occurs. It is explored by simulation and mathematical analysis when, why, and by how much genetic variance increases in response to environmental change. In particular, it is elucidated how this change in genetic variance depends on the reproductive system, the population size, and the selective regime, and what the consequences for population persistence are.

Animals↗
PubMed2000

Mutation-selection balance, dominance and the maintenance of sex.

A leading hypothesis for the evolutionary function of sex postulates that sex is an adaptation that purges deleterious mutations from the genome, thereby increasing the equilibrium mean fitness of a sexual population relative to its asexual competitor. This hypothesis requires two necessary conditions: first, the mutation rate per genome must be of order one, and, second, multiple mutations within a genome must act with positive epistasis, that is, two or more mutations of different genes must be more harmful together than if they acted independently. Here, by reconsidering the theory of mutation-selection balance at a single diploid gene locus, we demonstrate a significant advantage of sex due to nearly recessive mutations provided the mutation rate per genome is of order one. The assumption of positive epistasis is unnecessary, and multiple mutations may be assumed to act independently.

Animals↗
PubMed2001

Construction of a genetic linkage map in tetraploid species using molecular markers.

This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.

Algorithms↗
PubMed2001

The use of intraallelic variability for testing neutrality and estimating population growth rate.

To better understand the forces affecting individual alleles, we introduce a method for finding the joint distribution of the frequency of a neutral allele and the extent of variability at closely linked marker loci (the intraallelic variability). We model three types of intraallelic variability: (a) the number of nonrecombinants at a linked biallelic marker locus, (b) the length of a conserved haplotype, and (c) the number of mutations at a linked marker locus. If the population growth rate is known, the joint distribution provides the basis for a test of neutrality by testing whether the observed level of intraallelic variability is consistent with the observed allele frequency. If the population growth rate is unknown but neutrality can be assumed, the joint distribution provides the likelihood of the growth rate and leads to a maximum-likelihood estimate. We apply the method to data from published data sets for four loci in humans. We conclude that the Delta32 allele at CCR5 and a disease-associated allele at MLH1 arose recently and have been subject to strong selection. Alleles at PAH appear to be neutral and we estimate the recent growth rate of the European population to be approximately 0.027 per generation with a support interval of (0.017-0.037). Four of the relatively common alleles at CFTR also appear to be neutral but DeltaF508 appears to be significantly advantageous to heterozygous carriers.

Alleles↗