Nonparametric Convergence Assessment for MCMC Model Selection

Do Mothers or Children Lead the Dance? Disentangling Individual and Influence Effects During Conflict

Are mother-child conflict discussions shaped by time-varying, reciprocal influences, even after accounting for stable contributions from each individual? Mothers were filmed discussing a conflict for 5 min, separately with their younger (ages 5-9, N = 217) and older (ages 7-13, N = 220) children. Each person's conflict constructiveness was coded in 20-s intervals and data were analyzed using dynamic structural equation modeling, which separates individual and influence effects. Children influenced their mothers' behavior under certain conditions, with evidence for developmental differences in the magnitude and direction of influence, whereas mothers did not influence their children under any circumstance. Results are discussed in the context of child effects on parent behavior and changes in parenting across middle childhood.

Temporal modelling of ballast water discharge and ship-mediated invasion risk to Australia

Biological invasions have the potential to cause extensive ecological and economic damage. Maritime trade facilitates biological invasions by transferring species in ballast water, and on ships' hulls. With volumes of maritime trade increasing globally, efforts to prevent these biological invasions are of significant importance. Both the International Maritime Organization and the Australian government have developed policy seeking to reduce the risk of these invasions. In this study, we constructed models for the transfer of ballast water into Australian waters, based on historic ballast survey data. We used these models to hindcast ballast water discharge over all vessels that arrived in Australian waters between 1999 and 2012. We used models for propagule survival to compare the risk of ballast-mediated propagule transport between ecoregions. We found that total annual ballast discharge volume into Australia more than doubled over the study period, with the vast majority of ballast water discharge and propagule pressure associated with bulk carrier traffic. As such, the ecoregions suffering the greatest risk are those associated with the export of mining commodities. As global marine trade continues to increase, effective monitoring and biosecurity policy will remain necessary to combat the risk of future marine invasion events.

Bayesian model comparison in genetic association analysis: linear mixed modeling and SNP set testing

We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for Single Nucleotide Polymorphism (SNP) set analysis in genetic association studies. We derive a class of analytic approximate Bayes factors and illustrate their connections with a variety of frequentist test statistics, including the Wald statistic and the variance component score statistic. Taking advantage of Bayesian model averaging and hierarchical modeling, we demonstrate some distinct advantages and flexibilities in the approaches utilizing the derived Bayes factors in the context of genetic association studies. We demonstrate our proposed methods using real or simulated numerical examples in applications of single SNP association testing, multi-locus fine-mapping and SNP set association testing.

Bayesian QTL analyses using pedigreed families of an outcrossing species, with application to fruit firmness in apple

Proof of concept of Bayesian integrated QTL analyses across pedigree-related families from breeding programs of an outbreeding species. Results include QTL confidence intervals, individuals' genotype probabilities and genomic breeding values. Bayesian QTL linkage mapping approaches offer the flexibility to study multiple full sib families with known pedigrees simultaneously. Such a joint analysis increases the probability of detecting these quantitative trait loci (QTL) and provide insight of the magnitude of QTL across different genetic backgrounds. Here, we present an improved Bayesian multi-QTL pedigree-based approach on an outcrossing species using progenies with different (complex) genetic relationships. Different modeling assumptions were studied in the QTL analyses, i.e., the a priori expected number of QTL varied and polygenic effects were considered. The inferences include number of QTL, additive QTL effect sizes and supporting credible intervals, posterior probabilities of QTL genotypes for all individuals in the dataset, and QTL-based as well as genome-wide breeding values. All these features have been implemented in the FlexQTL(™) software. We analyzed fruit firmness in a large apple dataset that comprised 1,347 individuals forming 27 full sib families and their known ancestral pedigrees, with genotypes for 87 SSR markers on 17 chromosomes. We report strong or positive evidence for 14 QTL for fruit firmness on eight chromosomes, validating our approach as several of these QTL were reported previously, though dispersed over a series of studies based on single mapping populations. Interpretation of linked QTL was possible via individuals' QTL genotypes. The correlation between the genomic breeding values and phenotypes was on average 90 %, but varied with the number of detected QTL in a family. The detailed posterior knowledge on QTL of potential parents is critical for the efficiency of marker-assisted breeding.

Fast food in ant communities: how competing species find resources

An understanding of foraging behavior is crucial to understanding higher level community dynamics; in particular, there is a lack of information about how different species discover food resources. We examined the effect of forager number and forager discovery capacity on food discovery in two disparate temperate ant communities, located in Texas and Arizona. We defined forager discovery capacity as the per capita rate of resource discovery, or how quickly individual ants arrived at resources. In general, resources were discovered more quickly when more foragers were present; this was true both within communities, where species identity was ignored, as well as within species. This pattern suggests that resource discovery is a matter of random processes, with ants essentially bumping into resources at a rate mediated by their abundance. In contrast, species that were better discoverers, as defined by the proportion of resources discovered first, did not have higher numbers of mean foragers. Instead, both mean forager number and mean forager discovery capacity determined discovery success. The Texas species used both forager number and capacity, whereas the Arizona species used only forager capacity. There was a negative correlation between a species' prevalence in the environment and the discovery capacity of its foragers, suggesting that a given species cannot exploit both high numbers and high discovery capacity as a strategy. These results highlight that while forager number is crucial to determining time to discovery at the community level and within species, individual forager characteristics influence the outcome of exploitative competition in ant communities.

Using biological knowledge to discover higher order interactions in genetic association studies

The recent successes of genome-wide association studies (GWAS) have revealed that many of the replicated findings have explained only a small fraction of the heritability of common diseases. One hypothesis that investigators have suggested is that higher order interactions between SNPs or SNPs and environmental risk factors may account for some of this missing heritability. Searching for these interactions poses great statistical and computational challenges. In this article, we propose a novel method that addresses these challenges by incorporating external biological knowledge into a fully Bayesian analysis. The method is designed to be scalable for high-dimensional search spaces (where it supports interactions of any order) because priors that use such knowledge focus the search in regions that are more biologically plausible and avoid having to enumerate all possible interactions. We provide several examples based on simulated data demonstrating how external information can enhance power, specificity, and effect estimates in comparison to conventional approaches based on maximum likelihood estimates. We also apply the method to data from a GWAS for breast cancer, revealing a set of interactions enriched for the Gene Ontology terms growth, metabolic process, and biological regulation.

A Beta-mixture model for assessing genetic population structure

An important fraction of recently generated molecular data is dominant markers. They contain substantial information about genetic variation but dominance makes it impossible to apply standard techniques to calculate measures of genetic differentiation, such as F-statistics. In this article, we propose a new Bayesian beta-mixture model that more accurately describes the genetic structure from dominant markers and estimates multiple F(ST) s from the sample. The model also has important application for codominant markers and single-nucleotide polymorphism (SNP) data. The number of F(ST)  is assumed unknown beforehand and follows a random distribution. The reversible jump algorithm is used to estimate the unknown number of multiple F(ST) s. We evaluate the performance of three split proposals and the overall performance of the proposed model based on simulated dominant marker data. The model could reliably identify and estimate a spectrum of degrees of genetic differentiation present in multiple loci. The estimates of F(ST) s also incorporate uncertainty about the magnitude of within-population inbreeding coefficient. We illustrate the method with two examples, one using dominant marker data from a rare orchid and the other using codominant marker data from human populations.

Probabilistic inference of transcription factor binding from multiple data sources

An important problem in molecular biology is to build a complete understanding of transcriptional regulatory processes in the cell. We have developed a flexible, probabilistic framework to predict TF binding from multiple data sources that differs from the standard hypothesis testing (scanning) methods in several ways. Our probabilistic modeling framework estimates the probability of binding and, thus, naturally reflects our degree of belief in binding. Probabilistic modeling also allows for easy and systematic integration of our binding predictions into other probabilistic modeling methods, such as expression-based gene network inference. The method answers the question of whether the whole analyzed promoter has a binding site, but can also be extended to estimate the binding probability at each nucleotide position. Further, we introduce an extension to model combinatorial regulation by several TFs. Most importantly, the proposed methods can make principled probabilistic inference from multiple evidence sources, such as, multiple statistical models (motifs) of the TFs, evolutionary conservation, regulatory potential, CpG islands, nucleosome positioning, DNase hypersensitive sites, ChIP-chip binding segments and other (prior) sequence-based biological knowledge. We developed both a likelihood and a Bayesian method, where the latter is implemented with a Markov chain Monte Carlo algorithm. Results on a carefully constructed test set from the mouse genome demonstrate that principled data fusion can significantly improve the performance of TF binding prediction methods. We also applied the probabilistic modeling framework to all promoters in the mouse genome and the results indicate a sparse connectivity between transcriptional regulators and their target promoters. To facilitate analysis of other sequences and additional data, we have developed an on-line web tool, ProbTF, which implements our probabilistic TF binding prediction method using multiple data sources. Test data set, a web tool, source codes and supplementary data are available at: http://www.probtf.org.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a "metachain" to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely.