Bayesian inference for identifying interaction rules in moving animal groups

The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of "universal" classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed.     

A gene frequency model for QTL mapping using Bayesian inference

Background

Information for mapping of quantitative trait loci (QTL) comes from two sources: linkage disequilibrium (non-random association of allele states) and cosegregation (non-random association of allele origin). Information from LD can be captured by modeling conditional means and variances at the QTL given marker information. Similarly, information from cosegregation can be captured by modeling conditional covariances. Here, we consider a Bayesian model based on gene frequency (BGF) where both conditional means and variances are modeled as a function of the conditional gene frequencies at the QTL. The parameters in this model include these gene frequencies, additive effect of the QTL, its location, and the residual variance. Bayesian methodology was used to estimate these parameters. The priors used were: logit-normal for gene frequencies, normal for the additive effect, uniform for location, and inverse chi-square for the residual variance. Computer simulation was used to compare the power to detect and accuracy to map QTL by this method with those from least squares analysis using a regression model (LSR).

Results

To simplify the analysis, data from unrelated individuals in a purebred population were simulated, where only LD information contributes to map the QTL. LD was simulated in a chromosomal segment of 1 cM with one QTL by random mating in a population of size 500 for 1000 generations and in a population of size 100 for 50 generations. The comparison was studied under a range of conditions, which included SNP density of 0.1, 0.05 or 0.02 cM, sample size of 500 or 1000, and phenotypic variance explained by QTL of 2 or 5%. Both 1 and 2-SNP models were considered. Power to detect the QTL for the BGF, ranged from 0.4 to 0.99, and close or equal to the power of the regression using least squares (LSR). Precision to map QTL position of BGF, quantified by the mean absolute error, ranged from 0.11 to 0.21 cM for BGF, and was better than the precision of LSR, which ranged from 0.12 to 0.25 cM.

Conclusions

In conclusion given a high SNP density, the gene frequency model can be used to map QTL with considerable accuracy even within a 1 cM region.     

Gene selection using a two-level hierarchical Bayesian model

SUMMARY: The fundamental problem of gene selection via cDNA data is to identify which genes are differentially expressed across different kinds of tissue samples (e.g. normal and cancer). cDNA data contain large number of variables (genes) and usually the sample size is relatively small so the selection process can be unstable. Therefore, models which incorporate sparsity in terms of variables (genes) are desirable for this kind of problem. This paper proposes a two-level hierarchical Bayesian model for variable selection which assumes a prior that favors sparseness. We adopt a Markov chain Monte Carlo (MCMC) based computation technique to simulate the parameters from the posteriors. The method is applied to leukemia data from a previous study and a published dataset on breast cancer. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

Quantitative trait nucleotide analysis using Bayesian model selection

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.     

QTL mapping in outbred half-sib families using Bayesian model selection

In this article, we propose a model selection method, the Bayesian composite model space approach, to map quantitative trait loci (QTL) in a half-sib population for continuous and binary traits. In our method, the identity-by-descent-based variance component model is used. To demonstrate the performance of this model, the method was applied to map QTL underlying production traits on BTA6 in a Chinese half-sib dairy cattle population. A total of four QTLs were detected, whereas only one QTL was identified using the traditional least square (LS) method. We also conducted two simulation experiments to validate the efficiency of our method. The results suggest that the proposed method based on a multiple-QTL model is efficient in mapping multiple QTL for an outbred half-sib population and is more powerful than the LS method based on a single-QTL model.     

Gene networks inference using dynamic Bayesian networks

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.     

Ecological boundary detection using Carlin–Chib Bayesian model selection

Sharp ecological transitions in space (ecotones, edges, boundaries) often are where ecologically important events occur, such as elevated or reduced biodiversity or altered ecological functions (e.g. changes in productivity, pollination rates or parasitism loads, nesting success). While human observers often identify these transitions by using intuitive or gestalt assignments (e.g. the boundary between a remnant woodland patch and the surrounding farm paddock seems obvious), it is clearly desirable to make statistical assessments based on measurements. These assessments often are straightforward to make if the data are univariate, but identifying boundaries or transitions using compositional or multivariate data sets is more difficult. There is a need for an intermediate step in which pairwise similarities between points or temporal samples are computed. Here, I describe an approach that treats points along a transect as alternative hypotheses (models) about the location of the boundary. Carlin and Chib (1995) introduced a Bayesian technique for comparing non‐hierarchical models, which I adapted to compute the probabilities of each boundary location (i.e. a model) relative to the ensemble of models constituting the set of possible points of the boundary along the transect. Several artificial data sets and two field data sets (on vegetation and soils and on cave‐dwelling invertebrates and microclimates) are used to illustrate the approach. The method can be extended to cases in with several boundaries along a gradient, such as where there is an ecotone of non‐zero thickness.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Development of computational tools for the inference of protein interaction specificity rules and functional annotation using structural information

Relatively few protein structures are known, compared to the enormous amount of sequence data produced in the sequencing of different genomes, and relatively few protein complexes are deposited in the PDB with respect to the great amount of interaction data coming from high-throughput experiments (two-hybrid or affinity purification of protein complexes and mass spectrometry). Nevertheless, we can rely on computational techniques for the extraction of high-quality and information-rich data from the known structures and for their spreading in the protein sequence space. We describe here the ongoing research projects in our group: we analyse the protein complexes stored in the PDB and, for each complex involving one domain belonging to a family of interaction domains for which some interaction data are available, we can calculate its probability of interaction with any protein sequence. We analyse the structures of proteins encoding a function specified in a PROSITE pattern, which exhibits relatively low selectivity and specificity, and build extended patterns. To this aim, we consider residues that are well-conserved in the structure, even if their conservation cannot easily be recognized in the sequence alignment of the proteins holding the function. We also analyse protein surface regions and, through the annotation of the solvent-exposed residues, we annotate protein surface patches via a structural comparison performed with stringent parameters and independently of the residue order in the sequence. Local surface comparison may also help in identifying new sequence patterns, which could not be highlighted with other sequence-based methods.     

Bayesian inference of fine-scale recombination rates using population genomic data

Recently, several statistical methods for estimating fine-scale recombination rates using population samples have been developed. However, currently available methods that can be applied to large-scale data are limited to approximated likelihoods. Here, we developed a full-likelihood Markov chain Monte Carlo method for estimating recombination rate under a Bayesian framework. Genealogies underlying a sampling of chromosomes are effectively modelled by using marginal individual single nucleotide polymorphism genealogies related through an ancestral recombination graph. The method is compared with two existing composite-likelihood methods using simulated data.Simulation studies show that our method performs well for different simulation scenarios. The method is applied to two human population genetic variation datasets that have been studied by sperm typing. Our results are consistent with the estimates from sperm crossover analysis.     

Genetic parameters for five traits in Africanized honeybees using Bayesian inference

Heritability and genetic correlations for honey (HP) and propolis production (PP), hygienic behavior (HB), syrup-collection rate (SCR) and percentage of mites on adult bees (PMAB) of a population of Africanized honeybees were estimated. Data from 110 queen bees over three generations were evaluated. Single and multi-trait models were analyzed by Bayesian Inference using MTGSAM. The localization of the hive was significant for SCR and HB and highly significant for PP. Season-year was highly significant only for SCR. The number of frames with bees was significant for HP and PP, including SCR. The heritability estimates were 0.16 for HP, 0.23 for SCR, 0.52 for HB, 0.66 for PP, and 0.13 for PMAB. The genetic correlations were positive among productive traits (PP, HP and SCR) and negative between productive traits and HB, except between PP and HB. Genetic correlations between PMAB and other traits, in general, were negative, except with PP. The study permitted to identify honeybees for improved propolis and honey production. Hygienic behavior may be improved as a consequence of selecting for improved propolis production. The rate of syrup consumption and propolis production may be included in a selection index to enhance honeybee traits.     

Implementing relevance feedback in ligand-based virtual screening using Bayesian inference network

Recently, the use of the Bayesian network as an alternative to existing tools for similarity-based virtual screening has received noticeable attention from researchers in the chemoinformatics field. The main aim of the Bayesian network model is to improve the retrieval effectiveness of similarity-based virtual screening. To this end, different models of the Bayesian network have been developed. In our previous works, the retrieval performance of the Bayesian network was observed to improve significantly when multiple reference structures or fragment weightings were used. In this article, the authors enhance the Bayesian inference network (BIN) using the relevance feedback information. In this approach, a few high-ranking structures of unknown activity were filtered from the outputs of BIN, based on a single active reference structure, to form a set of active reference structures. This set of active reference structures was used in two distinct techniques for carrying out such BIN searching: reweighting the fragments in the reference structures and group fusion techniques. Simulated virtual screening experiments with three MDL Drug Data Report data sets showed that the proposed techniques provide simple ways of enhancing the cost-effectiveness of ligand-based virtual screening searches, especially for higher diversity data sets.     

Analyzing tropical forest tree species abundance distributions using a nonneutral model and through approximate Bayesian inference

The neutral theory of biodiversity challenges the classical niche-based view of ecological communities, where species attributes and environmental conditions jointly determine community composition. Functional equivalence among species, as assumed by neutral ecological theory, has been recurrently falsified, yet many patterns of tropical tree communities appear consistent with neutral predictions. This may mean that neutral theory is a good first-approximation theory or that species abundance data sets contain too little information to reject neutrality. Here we present a simple test of neutrality based on species abundance distributions in ecological communities. Based on this test, we show that deviations from neutrality are more frequent than previously thought in tropical forest trees, especially at small spatial scales. We then develop a nonneutral model that generalizes Hubbell's dispersal-limited neutral model in a simple way by including one additional parameter of frequency dependence. We also develop a statistical method to infer the parameters of this model from empirical data by approximate Bayesian computation. In more than half of the permanent tree plots, we show that our new model fits the data better than does the neutral model. Finally, we discuss whether observed deviations from neutrality may be interpreted as the signature of environmental filtering on tropical tree species abundance distributions.