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PubMed2004

SlidingBayes: exploring recombination using a sliding window approach based on Bayesian phylogenetic inference.

We developed a software tool (SlidingBayes) for recombination analysis based on Bayesian phylogenetic inference. Sliding-Bayes provides a powerful approach for detecting potential recombination, especially between highly divergent sequences and complex HIV-1 recombinants for which simpler methods like neighbor joining (NJ) may be less powerful. SlidingBayes guides Markov Chain Monte Carlo (MCMC) sampling performed by MrBayes in a sliding window across the alignment (Bayesian scanning). The tool can be used for nucleotide and amino acid sequences and combines all the modeling possibilities of MrBayes with the ability to plot the posterior probability support for clustering of various combinations of taxa.

Algorithms↗
PubMed2005

SCHIP: statistics for chromosome interphase positioning based on interchange data.

MOTIVATION: The position of chromosomes in the interphase nucleus is believed to be associated with a number of biological processes. Here, we present a web-based application that helps analyze the relative position of chromosomes during interphase in human cells, based on observed radiogenic chromosome aberrations. The inputs of the program are a table of yields of pairwise chromosome interchanges and a proposed chromosome geometric cluster. Each can either be uploaded or selected from provided datasets. The main outputs are P-values for the proposed chromosome clusters. SCHIP is designed to be used by a number of scientific communities interested in nuclear architecture, including cancer and cell biologists, radiation biologists and mathematical/computational biologists.

Chromosome Aberrations↗
PubMed1988

A linkage map of mouse chromosome 12: localization of Igh and effects of sex and interference on recombination.

Inheritance of restriction fragment length polymorphisms associated with four anonymous DNA markers (D12Nyu1, 2, 3 and 4), the Fos proto-oncogene, the Mtv-9 viral integration site, and the alpha 1-antitrypsin (Aat-1) and immunoglobulin heavy chain (Igh) gene families in the mouse has been followed in a backcross experiment. A Bayesian multilocus map-building strategy yielded the map: centromere-D12Nyu2-10 cM-D12Nyu1-2 cM-D12Nyu3-15 cM-Fos-1 cM-D12Nyu4-2 cM-Mtv-9-8 cM-Aat-1-17 cM-Igh-C. A map constructed from male meiotic data was substantially shorter than one constructed from female meiotic data. Significant interference was observed for the linkage group. Two groups of markers studied in recombinant inbred strains of mice could be interpolated into the map: Es-25, D12Nyu10, D12Nyu7 and Apob form a cluster proximal to D12Nyu2, and Ly-18, Ah, and D12Nyu5 form a cluster between D12Nyu2 and D12Nyu1. These data establish an unambiguously ordered linkage group including Igh and Aat-1 that spans most of chromosome 12.

Algorithms↗
PubMed1991

Inferences of species phylogeny in relation to segregation of ancient polymorphisms.

Standard formulas of gene frequency change under genetic drift are used to derive the probability of obtaining incorrect phylogenetic information for three species due to segregation of ancient polymorphisms. This probability depends upon the level of polymorphisms at the time of speciation and is generally quite high unless the two speciation events are far apart in time. If phylogenetic data from multiple loci are available, a likelihood ratio test can be used to reject the null hypothesis in favor of the best phylogeny. The appropriate null hypothesis is either a trichotomy or an alternative phylogeny, depending on the data set. The likelihood ratios required for accepting the best phylogeny are given. These ratios are obtained by exact enumeration when the number of loci is small (n less than 15) and by an asymptotic approach for larger n's. In general, more than five loci are needed to resolve the species phylogeny.

Alleles↗
PubMed1992

Theoretical study of near neutrality. II. Effect of subdivided population structure with local extinction and recolonization.

There are several unsolved problems concerning the model of nearly neutral mutations. One is the interaction of subdivided population structure and weak selection that spatially fluctuates. The model of nearly neutral mutations whose selection coefficient spatially fluctuates has been studied by adopting the island model with periodic extinction-recolonization. Both the number of colonies and the migration rate play significant roles in determining mutants' behavior, and selection is ineffective when the extinction-recolonization is frequent with low migration rate. In summary, the number of mutant substitutions decreases and the polymorphism increases by increasing the total population size, and/or decreasing the extinction-recolonization rate. However, by increasing the total size of the population, the mutant substitution rate does not become as low when compared with that in panmictic populations, because of the extinction-recolonization, especially when the migration rate is limited. It is also found that the model satisfactorily explains the contrasting patterns of molecular polymorphisms observed in sibling species of Drosophila, including heterozygosity, proportion of polymorphism and fixation index.

Animals↗
PubMed1992

On models of quantitative genetic variability: a stabilizing selection-balance model.

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.

Alleles↗
PubMed1999

Effect of selection against deleterious mutations on the decline in heterozygosity at neutral loci in closely inbreeding populations.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.

Animals↗
PubMed2003

Likelihood-based estimation of microsatellite mutation rates.

Microsatellites are widely used in genetic analyses, many of which require reliable estimates of microsatellite mutation rates, yet the factors determining mutation rates are uncertain. The most straightforward and conclusive method by which to study mutation is direct observation of allele transmissions in parent-child pairs, and studies of this type suggest a positive, possibly exponential, relationship between mutation rate and allele size, together with a bias toward length increase. Except for microsatellites on the Y chromosome, however, previous analyses have not made full use of available data and may have introduced bias: mutations have been identified only where child genotypes could not be generated by transmission from parents' genotypes, so that the probability that a mutation is detected depends on the distribution of allele lengths and varies with allele length. We introduce a likelihood-based approach that has two key advantages over existing methods. First, we can make formal comparisons between competing models of microsatellite evolution; second, we obtain asymptotically unbiased and efficient parameter estimates. Application to data composed of 118,866 parent-offspring transmissions of AC microsatellites supports the hypothesis that mutation rate increases exponentially with microsatellite length, with a suggestion that contractions become more likely than expansions as length increases. This would lead to a stationary distribution for allele length maintained by mutational balance. There is no evidence that contractions and expansions differ in their step size distributions.

Alleles↗
PubMed2005

Analysing the genetic control of peach fruit quality through an ecophysiological model combined with a QTL approach.

Ecophysiological models are increasingly expected to include genetic information via genotype-dependent parameters. These parameters could be considered as quantitative traits and submitted to analysis. A pre-existing ecophysiological model of fruit quality was used and the distribution of the genotypic parameters in a second backcross population derived from a clone of a wild peach (Prunus davidiana) and commercial nectarine varieties (P. persica (L.) Batsch) was analysed. The correlations between the two years of experimentation were higher for the genotypic parameters than for the quality traits commonly studied by breeders. The correlations between the genotypic parameters and the quality traits were low. Quantitative trait loci (QTLs) for the genotypic key parameters of the ecophysiological model were detected by linear regression. Co-locations of QTLs for parameters were observed as well as co-locations of QTLs for parameters and quality traits. The ecophysiological model and the results of the QTL analysis were combined by substituting each parameter in the model by the sum of QTL effects. This combined model can simulate the behaviour of genotypes carrying diverse combinations of alleles. The quality of this combined model was moderately suitable, but had some shortcomings. Improvements are suggested and further use of this combined model as a tool for breeders is discussed.

Agriculture↗
PubMed2005

A Bayesian model comparison approach to inferring positive selection.

A popular approach to detecting positive selection is to estimate the parameters of a probabilistic model of codon evolution and perform inference based on its maximum likelihood parameter values. This approach has been evaluated intensively in a number of simulation studies and found to be robust when the available data set is large. However, uncertainties in the estimated parameter values can lead to errors in the inference, especially when the data set is small or there is insufficient divergence between the sequences. We introduce a Bayesian model comparison approach to infer whether the sequence as a whole contains sites at which the rate of nonsynonymous substitution is greater than the rate of synonymous substitution. We incorporated this probabilistic model comparison into a Bayesian approach to site-specific inference of positive selection. Using simulated sequences, we compared this approach to the commonly used empirical Bayes approach and investigated the effect of tree length on the performance of both methods. We found that the Bayesian approach outperforms the empirical Bayes method when the amount of sequence divergence is small and is less prone to false-positive inference when the sequences are saturated, while the results are indistinguishable for intermediate levels of sequence divergence.

Bayes Theorem↗
PubMed2006

A combined empirical and mechanistic codon model.

The evolutionary selection forces acting on a protein are commonly inferred using evolutionary codon models by contrasting the rate of synonymous to nonsynonymous substitutions. Most widely used models are based on theoretical assumptions and ignore the empirical observation that distinct amino acids differ in their replacement rates. In this paper, we develop a general method that allows assimilation of empirical amino acid replacement probabilities into a codon-substitution matrix. In this way, the resulting codon model takes into account not only the transition-transversion bias and the nonsynonymous/synonymous ratio, but also the different amino acid replacement probabilities as specified in empirical amino acid matrices. Different empirical amino acid replacement matrices, such as secondary structure-specific matrices or organelle-specific matrices (e.g., mitochondria and chloroplasts), can be incorporated into the model, making it context dependent. Using a diverse set of coding DNA sequences, we show that the novel model better fits biological data as compared with either mechanistic or empirical codon models. Using the suggested model, we further analyze human immunodeficiency virus type 1 protease sequences obtained from drug-treated patients and reveal positive selection in sites that are known to confer drug resistance to the virus.

Amino Acid Substitution↗
PubMed1995

A novel measure of genetic distance for highly polymorphic tandem repeat loci.

Genetic distance measures are indicators of relatedness among populations or species and are useful for reconstructing the historic and phylogenetic relationships among such groups. Classical measures of genetic distance were developed to analyze biochemical and serological polymorphisms, systems which generally show limited variability. However, these traditional measures of genetic distance are inadequate for the analysis of certain classes of variable number tandem repeat (VNTR) loci, which have a larger number of alleles and higher levels of heterozygosity than traditional genetic markers. At the higher levels of heterozygosity observed at these loci, the standard measures of genetic distance are nonlinear and do not account for the mutational mechanisms of hypervariable loci. We have developed a measure of genetic distance, DSW, which is appropriate for the analysis of highly polymorphic DNA loci. Using computer simulations of diverging populations, we show that DSW conforms to linearity and that the variance is similar in magnitude to traditional measures of genetic distance. Comparisons of phylogenetic trees derived from the simulated divergence of human racial groups demonstrate that the branch lengths of trees prepared using DSW are more similar to the model tree than those generated using other measures. Finally, we demonstrate the applicability of DSW to evolutionary analysis by reconstructing the relationships among eight human populations using 14 microsatellite and STR loci. The phylogenetic trees generated using DSW are different from trees constructed with traditional measures and better reflect the well-documented ancient divergence of African and non-African populations.

Animals↗
PubMed2005

Adaptive walk on complex networks.

We investigate the properties of adaptive walks on an uncorrelated fitness landscape which is established in sequence spaces of complex structure. In particular, we perform numerical simulations of adaptive walks on random graphs and scale-free networks. For the former, we also derive some analytical approximations for the density of local optima of the fitness landscape and the mean length walk. We compare our results with those obtained for regular lattices. We obtain that the density of local optima decreases as 1/z, where z is the mean connectivity, for all networks we have investigated. In random graphs, the mean length walk L reaches the asymptotic value e - 1 for large z, which corresponds to the result for regular networks. Although we could not find an exact estimate, we derive an underestimated value for L. Unlike random graphs, scale-free networks show an upper asymptotic value of L.

Adaptation, Physiological↗
PubMedDate not supplied

A short proof that phylogenetic tree reconstruction by maximum likelihood is hard.

Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum likelihood tree is NP-hard by exploiting a connection between likelihood and parsimony observed by Tuffley and Steel.

Algorithms↗
PubMed2001

Estimating the frequency distribution of crossovers during meiosis from recombination data.

Estimation of tetrad crossover frequency distributions from genetic recombination data is a classic problem dating back to Weinstein (1936, Genetics 21, 155-199). But a number of important issues, such as how to specify the maximum number of crossovers, how to construct confidence intervals for crossover probabilities, and how to obtain correct p-values for hypothesis tests, have never been adequately addressed. In this article, we obtain some properties of the maximum likelihood estimate (MLE) for crossover probabilities that imply guidelines for choosing the maximum number of crossovers. We give these results for both normal meiosis and meiosis with nondisjunction. We also develop an accelerated EM algorithm to find the MLE more efficiently. We propose bootstrap-based methods to find confidence intervals and p-values and conduct simulation studies to check the validity of the bootstrap approach.

Algorithms↗
PubMed2002

Variable selection in high-dimensional multivariate binary data with application to the analysis of microbial community DNA fingerprints.

In order to understand the relevance of microbial communities on crop productivity, the identification and characterization of the rhizosphere soil microbial community is necessary. Characteristic profiles of the microbial communities are obtained by denaturing gradient gel electrophoresis (DGGE) of polymerase chain reaction (PCR) amplified 16S rDNA from soil extracted DNA. These characteristic profiles, commonly called community DNA fingerprints, can be represented in the form of high-dimensional binary vectors. We address the problem of modeling and variable selection in high-dimensional multivariate binary data and present an application of our methodology in the context of a controlled agricultural experiment.

Agriculture↗
PubMed2006

Statistical measures of the structure of genomic sequences: entropy, complexity, and position information.

Identifying regions of DNA with extreme statistical characteristics is an important aspect of the structural analysis of complete genomes. Linguistic methods, mainly based on estimating word frequency, can be used for this as they allow for the delineation of regions of low complexity. Low complexity may be due to biased nucleotide composition, by tandem- or dispersed repeats, by palindrome-hairpin structures, as well as by a combination of all these features. We developed software tools in which various numerical measures of text complexity are implemented, including combinatorial and linguistic ones. We also added Hurst exponent estimate to the software to measure dependencies in DNA sequences. By applying these tools to various functional genomic regions, we demonstrate that the complexity of introns and regulatory regions is lower than that of coding regions, whilst Hurst exponent is larger. Further analysis of promoter sequences revealed that the lower complexity of these regions is associated with long-range correlations caused by transcription factor binding sites.

Algorithms↗
PubMed2006

Comparison of statistical significance criteria.

We study and compare two classes of statistical criteria to assess the significance of exceptional words. Indeed, the Z-score-like criteria, or the normal approximation that is a strict equivalent, suffer from several drawbacks in terms of sensitivity and specificity. Thanks to the combinatorial structure of words, a computation of the exact P-value has been made possible by recent mathematical results. We study here the drawbacks of the Z-score, the choice of the threshold and the tightness to the P-value. A major conclusion is that the normal approximation is always very poor and overestimates statistical significance.

Algorithms↗