Bayesian hierarchical modeling for time course microarray experiments

Time course microarray experiments designed to characterize the dynamic regulation of gene expression in biological systems are becoming increasingly important. One critical issue that arises when examining time course microarray data is the identification of genes that show different temporal expression patterns among biological conditions. Here we propose a Bayesian hierarchical model to incorporate important experimental factors and to account for correlated gene expression measurements over time and over different genes. A new gene selection algorithm is also presented with the model to simultaneously identify genes that show changes in expression among biological conditions, in response to time and other experimental factors of interest. The algorithm performs well in terms of the false positive and false negative rates in simulation studies. The methodology is applied to a mouse model time course experiment to correlate temporal changes in azoxymethane-induced gene expression profiles with colorectal cancer susceptibility.     

Inferring population trends for the world's largest fish from mark-recapture estimates of survival

1. Precise estimates of demographic rates are key components of population models used to predict the effects of stochastic environmental processes, harvest scenarios and extinction probability. 2. We used a 12-year photographic identification library of whale sharks from Ningaloo Reef, Western Australia to construct Cormack-Jolly-Seber (CJS) model estimates of survival within a capture-mark-recapture (CMR) framework. Estimated survival rates, population structure and assumptions regarding age at maturity, longevity and reproduction frequency were combined in a series of age-classified Leslie matrices to infer the potential trajectory of the population. 3. Using data from 111 individuals, there was evidence for time variation in apparent survival (phi) and recapture probability (p). The null model gave a phi of 0.825 (95% CI: 0.727-0.893) and p = 0.184 (95% CI: 0.121-0.271). The model-averaged annual phi ranged from 0.737 to 0.890. There was little evidence for a sex effect on survival. 4. Using standardized total length as a covariate in the CMR models indicated a size bias in phi. Ignoring the effects of time, a 5-m shark has a phi = 0.59 and a 9 m shark has phi = 0.81. 5. Of the 16 model combinations considered, 10 (63%) indicated a decreasing population (lambda < 1). For models based on age at first reproduction (alpha) of 13 years, the mean age of reproducing females at the stable age distribution (A) ranged from 15 to 23 years, which increased to 29-37 years when alpha was assumed to be 25. 6. All model scenarios had higher total elasticities for non-reproductive female survival [E(s(nr))] compared to those for reproductive female survival [E(s(r))]. 7. Assuming relatively slow, but biologically realistic, vital rates (alpha = 25 and biennial reproduction) and size-biased survival probabilities, our results suggest that the Ningaloo Reef population of whale sharks is declining, although more reproductive data are clearly needed to confirm this conclusion. Combining relatively precise survival estimates from CMR studies with realistic assumptions of other vital rates provides a useful heuristic framework for determining the vulnerability of large oceanic predators for which few direct data exist.     

Comparison of breeding value prediction for two traits in a Nellore-Angus crossbred population using different Bayesian modeling methodologies

The objectives of this study were to 1) compare four models for breeding value prediction using genomic or pedigree information and 2) evaluate the impact of fixed effects that account for family structure. Comparisons were made in a Nellore-Angus population comprising F₂, F₃ and half-siblings to embryo transfer F₂ calves with records for overall temperament at weaning (TEMP; n = 769) and Warner-Bratzler shear force (WBSF; n = 387). After quality control, there were 34,913 whole genome SNP markers remaining. Bayesian methods employed were BayesB ($\tilde{\pi }$ = 0.995 or 0.997 for WBSF or TEMP, respectively) and BayesC (π = 0 and $\tilde{\pi }$), where $\tilde{\pi }$ is the ideal proportion of markers not included. Direct genomic values (DGV) from single trait Bayesian analyses were compared to conventional pedigree-based animal model breeding values. Numerically, BayesC procedures (using $\tilde{\pi }$) had the highest accuracy of all models for WBSF and TEMP ($\widehat{\rho }$_gĝ = 0.843 and 0.923, respectively), but BayesB had the least bias (regression of performance on prediction closest to 1, $\widehat{\beta }$_y,x = 2.886 and 1.755, respectively). Accounting for family structure decreased accuracy and increased bias in prediction of DGV indicating a detrimental impact when used in these prediction methods that simultaneously fit many markers.     

Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data

Summary .  We study quantile regression (QR) for longitudinal measurements with nonignorable intermittent missing data and dropout. Compared to conventional mean regression, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. We account for the within-subject correlation by introducing a   ℓ₂   penalty in the usual QR check function to shrink the subject-specific intercepts and slopes toward the common population values. The informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects. We assess the performance of the proposed method using simulation studies, and illustrate it with data from a pediatric AIDS clinical trial.     

Estimation of population size based on additive hazards models for continuous-time recapture experiments

We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous-time capture-recapture experiment, and then construct a Horvitz-Thompson-type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed .5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.     

The one‐inflated positive Poisson mixture model for use in population size estimation

The one‐inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz–Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture–recapture data: one‐inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data‐generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one‐inflation.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods

Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.     

Testing for genetic evidence of population expansion and contraction: an empirical analysis of microsatellite DNA variation using a hierarchical Bayesian model

The role of past climatic change in shaping the distributions of tropical rain forest vertebrates is central to long-standing hypotheses about the legacy of the Quaternary ice ages. One approach to testing such hypotheses is to use genetic data to infer the demographic history of codistributed species. Population genetic theory that relates the structure of allelic genealogies to historical changes in effective population size can be used to detect a past history of demographic expansion or contraction. The fruit bats Cynopterus sphinx and C. brachyotis (Chiroptera: Pteropodidae) exhibit markedly different distribution patterns across the Indomalayan region and therefore represent an exemplary species pair to use for such tests. The purpose of this study was to test alternative hypotheses about historical patterns of demographic expansion and contraction in C. sphinx and C. brachyotis using a coalescent-based analysis of microsatellite variation. Specifically, we used a hierarchical Bayesian model based on Markov chain Monte Carlo simulations to estimate the posterior distribution of genealogical and demographic parameters. The results revealed strong evidence for population contraction in both species. Evidence for a population contraction in C. brachyotis was expected on the basis of biogeographic considerations. However, similar evidence for population contraction in C. sphinx does not support the hypothesis that this species underwent a pronounced range expansion during the late Quaternary. Genetic evidence for population decline may reflect the consequences of habitat destruction on a more recent time scale.     

Accounting for heterogeneity when estimating stopover duration,timing and population size of red knots along the Luannan Coast of Bohai Bay,China

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Assessing population size and structure for Andean Condor Vultur gryphus in Bolivia using a photographic ‘capture‐recapture’ method

The Andean Condor Vultur gryphus is a globally threatened and declining species. Problems of surveying Andean Condor populations using traditional survey methods are particularly acute in Bolivia, largely because only few roosts are known there. However, similar to other vulture species, Andean Condors aggregate at animal carcasses, and are individually recognizable due to unique morphological characteristics (size and shape of male crests and pattern of wing coloration). This provided us with an opportunity to use a capture‐recapture (‘sighting‐resighting’) modelling framework to estimate the size and structure of an Andean Condor population in Bolivia using photographs of individuals taken at observer‐established feeding stations. Between July and December 2014, 28 feeding stations were established in five different zones throughout the eastern Andean region of Bolivia, where perched and flying Andean Condors were photographed. Between one and 57 (mean = 20.2 ± 14.6 sd) Andean Condors were recorded visiting each feeding station and we were able to identify 456 different individuals, comprising 134 adult males, 40 sub‐adult males, 79 juvenile males, 80 adult females, 30 sub‐adult females and 93 juvenile females. Open population capture‐recapture models produced population estimates ranging from 52 ± 14 (se) individuals to 678 ± 269 individuals across the five zones, giving a total of 1388 ± 413 sd individuals, which is roughly 20% of the estimated Andean Condor global population. Future trials of this method need to consider explicitly knowledge of Andean Condor movements and home‐ranges, habitat preferences when selecting suitable sites as feeding stations, juvenile movements and other behaviours. Sighting‐resighting methods have considerable potential to increase the accuracy of surveys of Andean Condors and other bird species with unique individual morphological characteristics.