Seemingly unrelated measurement error models, with application to nutritional epidemiology

Motivated by an important biomarker study in nutritional epidemiology, we consider the combination of the linear mixed measurement error model and the linear seemingly unrelated regression model, hence Seemingly Unrelated Measurement Error Models. In our context, we have data on protein intake and energy (caloric) intake from both a food frequency questionnaire (FFQ) and a biomarker, and wish to understand the measurement error properties of the FFQ for each nutrient. Our idea is to develop separate marginal mixed measurement error models for each nutrient, and then combine them into a larger multivariate measurement error model: the two measurement error models are seemingly unrelated because they concern different nutrients, but aspects of each model are highly correlated. As in any seemingly unrelated regression context, the hope is to achieve gains in statistical efficiency compared to fitting each model separately. We show that if we employ a "full" model (fully parameterized), the combination of the two measurement error models leads to no gain over considering each model separately. However, there is also a scientifically motivated "reduced" model that sets certain parameters in the "full" model equal to zero, and for which the combination of the two measurement error models leads to considerable gain over considering each model separately, e.g., 40% decrease in standard errors. We use the Akaike information criterion to distinguish between the two possibilities, and show that the resulting estimates achieve major gains in efficiency. We also describe theoretical and serious practical problems with the Bayes information criterion in this context.     

Functional hierarchical models for identifying genes with different time-course expression profiles

Time-course studies of gene expression are essential in biomedical research to understand biological phenomena that evolve in a temporal fashion. We introduce a functional hierarchical model for detecting temporally differentially expressed (TDE) genes between two experimental conditions for cross-sectional designs, where the gene expression profiles are treated as functional data and modeled by basis function expansions. A Monte Carlo EM algorithm was developed for estimating both the gene-specific parameters and the hyperparameters in the second level of modeling. We use a direct posterior probability approach to bound the rate of false discovery at a pre-specified level and evaluate the methods by simulations and application to microarray time-course gene expression data on Caenorhabditis elegans developmental processes. Simulation results suggested that the procedure performs better than the two-way ANOVA in identifying TDE genes, resulting in both higher sensitivity and specificity. Genes identified from the C. elegans developmental data set show clear patterns of changes between the two experimental conditions.     

Parametric and nonparametric FDR estimation revisited

Nonparametric and parametric approaches have been proposed to estimate false discovery rate under the independent hypothesis testing assumption. The parametric approach has been shown to have better performance than the nonparametric approaches. In this article, we study the nonparametric approaches and quantify the underlying relations between parametric and nonparametric approaches. Our study reveals the conservative nature of the nonparametric approaches, and establishes the connections between the empirical Bayes method and p-value-based nonparametric methods. Based on our results, we advocate using the parametric approach, or directly modeling the test statistics using the empirical Bayes method.     

Accounting for variation of substitution rates through time in Bayesian phylogeny reconstruction of Sapotoideae (Sapotaceae)

We used Bayesian phylogenetic analysis of 5 kb of chloroplast DNA data from 68 Sapotaceae species to clarify phylogenetic relationships within Sapotoideae, one of the two major clades within Sapotaceae. Variation in substitution rates through time was shown to be a very important aspect of molecular evolution for this data set. Relative rates tests indicated that changes in overall rate have taken place in several lineages during the history of the group and Bayes factors strongly supported a covarion model, which allows the rate of a site to vary over time, over commonly used models that only allow rates to vary across sites. Rate variation over time was actually found to be a more important model component than rate variation across sites. The covarion model was originally developed for coding gene sequences and has so far only been tested for this type of data. The fact that it performed so well with the present data set, consisting mainly of data from noncoding spacer regions, suggests that it deserves a wider consideration in model based phylogenetic inference. Repeatability of phylogenetic results was very difficult to obtain with the more parameter rich models, and analyses with identical settings often supported different topologies. Overparameterization may be the reason why the MCMC did not sample from the posterior distribution in these cases. The problem could, however, be overcome by using less parameter rich evolutionary models, and adjusting the MCMC settings. The phylogenetic results showed that two taxa, previously thought to belong in Sapotoideae, are not part of this group. Eberhardtia aurata is the sister of the two major Sapotaceae clades, Chrysophylloideae and Sapotoideae, and Neohemsleya usambarensis belongs in Chrysophylloideae. Within Sapotoideae two clades, Sideroxyleae and Sapoteae, were strongly supported. Bayesian analysis of the character history of some floral morphological traits showed that the ancestral type of flower in Sapotoideae may have been characterized by floral parts (sepals, petals, stamens, and staminodes) in single whorls of five, entire corolla lobes, and seeds with an adaxial hilum.     

Non-monophyly of most supraspecific taxa of calcareous sponges (Porifera, Calcarea) revealed by increased taxon sampling and partitioned Bayesian analysis of ribosomal DNA

Calcareous sponges (Porifera, Calcarea) play an important role for our understanding of early metazoan evolution, since several molecular studies suggested their closer relationship to Eumetazoa than to the other two sponge 'classes,' Demospongiae and Hexactinellida. The division of Calcarea into the subtaxa Calcinea and Calcaronea is well established by now, but their internal relationships remain largely unresolved. Here, we estimate phylogenetic relationships within Calcarea in a Bayesian framework, using full-length 18S and partial 28S ribosomal DNA sequences. Both genes were analyzed separately and in combination and were further partitioned by stem and loop regions, the former being modelled to take non-independence of paired sites into account. By substantially increasing taxon sampling, we show that most of the traditionally recognized supraspecific taxa within Calcinea and Calcaronea are not monophyletic, challenging the existing classification system, while monophyly of Calcinea and Calcaronea is again highly supported.     

Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution

Summary We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85 , 1–11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.     

Fine-scale genetic population structure in a mobile marine mammal: inshore bottlenose dolphins in Moreton Bay, Australia

Highly mobile marine species in areas with no obvious geographic barriers are expected to show low levels of genetic differentiation. However, small‐scale variation in habitat may lead to resource polymorphisms and drive local differentiation by adaptive divergence. Using nuclear microsatellite genotyping at 20 loci, and mitochondrial control region sequencing, we investigated fine‐scale population structuring of inshore bottlenose dolphins (Tursiops aduncus) inhabiting a range of habitats in and around Moreton Bay, Australia. Bayesian structure analysis identified two genetic clusters within Moreton Bay, with evidence of admixture between them (F_ST = 0.05, P = 0.001). There was only weak isolation by distance but one cluster of dolphins was more likely to be found in shallow southern areas and the other in the deeper waters of the central northern bay. In further analysis removing admixed individuals, southern dolphins appeared genetically restricted with lower levels of variation (AR = 3.252, π = 0.003) and high mean relatedness (r = 0.239) between individuals. In contrast, northern dolphins were more diverse (AR = 4.850, π = 0.009) and were mixing with a group of dolphins outside the bay (microsatellite‐based STRUCTURE analysis), which appears to have historically been distinct from the bay dolphins (mtDNA Φ_ST = 0.272, P < 0.001). This study demonstrates the ability of genetic techniques to expose fine‐scale patterns of population structure and explore their origins and mechanisms. A complex variety of inter‐related factors including local habitat variation, differential resource use, social behaviour and learning, and anthropogenic disturbances are likely to have played a role in driving fine‐scale population structure among bottlenose dolphins in Moreton Bay.     

Influence of finite-sites mutation, population subdivision and sampling schemes on patterns of nucleotide polymorphism for species with molecular hyperdiversity

Molecular hyperdiversity has been documented in viruses, prokaryotes and eukaryotes. Such organisms undermine the assumptions of the infinite-sites mutational model, because multiple mutational events at a site comprise a non-negligible portion of polymorphisms. Moreover, different sampling schemes of individuals from species with subdivided populations can profoundly influence resulting patterns and interpretations of molecular variation. Inspired by molecular hyperdiversity in the nematode Caenorhabditis sp. 5, which exhibits average pairwise differences among synonymous sites of >5% as well as modest population structure, we investigated via coalescent simulation the joint effects of a finite-sites mutation (FSM) process and population subdivision on the variant frequency spectrum. From many demes interconnected through a stepping-stone migration model, we constructed local samples from a single deme, pooled samples from several demes and scattered samples of a single individual from numerous demes. Compared with a single panmictic population at equilibrium, we find that high population mutation rates induce a deficit of rare variants (positive Tajima's D) under a FSM model. Population structure also induces such a skew for local samples when migration is high and for pooled samples when migration is low. Contrasts of sampling schemes for C. sp. 5 imply high mutational input coupled with high migration. We propose that joint analysis of local, pooled and scattered samples for species with subdivided populations provides a means of improving inference of demographic history, by virtue of the partially distinct patterns of polymorphism that manifest when sequences are analyzed according to differing sampling schemes.     

Fine‐scale spatiotemporal patterns of genetic variation reflect budding dispersal coupled with strong natal philopatry in a cooperatively breeding mammal

The relatedness structure of animal populations is thought to be a critically important factor underlying the evolution of mating systems and social behaviours. While previous work has shown that population structure is shaped by many biological processes, few studies have investigated how these factors vary over time. Consequently, we explored the fine‐scale spatiotemporal genetic structure of an intensively studied population of cooperatively breeding banded mongooses (Mungos mungo) over a 10‐year period. Overall population structure was strong (average F_ST = 0.129) but groups with spatially overlapping territories were not more genetically similar to one another than noncontiguous groups. Instead, genetic differentiation was associated with historical group‐fission (budding) events, with new groups diverging from their parent groups over time. Within groups, relatedness was high within but not between the sexes, although the latter increased over time since group formation due to group founders being replaced by philopatric young. This trend was not mirrored by a decrease in average offspring heterozygosity over time, suggesting that close inbreeding may often be avoided, even when immigration into established groups is virtually absent and opportunities for extra‐group matings are rare. Fine‐scale spatiotemporal population structure could have important implications in social species, where relatedness between interacting individuals is a vital component in the evolution of patterns of inbreeding avoidance, reproductive skew and kin‐selected helping and harming.     

mmod: an R library for the calculation of population differentiation statistics

mmod is a library for the R programming language that allows the calculation of the population differentiation measures D_est, G″_ST and φ′_ST. R provides a powerful environment in which to conduct and record population genetic analyses but, at present, no R libraries provide functions for the calculation of these statistics from standard population genetic files. In addition to the calculation of differentiation measures, mmod can produce parametric bootstrap and jackknife samples of data sets for further analysis. By integrating with and complimenting the existing libraries adegenet and pegas , mmod extends the power of R as a population genetic platform.