Homology in coding and non-coding DNA sequences: a parsimony perspective

Putative synapomorphy assessment (primary homology assessment) is distinct for DNA strings having a codon structure (hereafter, coding DNA) versus those lacking it (hereafter, non-coding DNA). The first requires the identification of a reading frame and of usually few in-frame insertions and deletions. In non-coding DNA, where length variation is much more common, putative synapomorphy assessment is considerably less straightforward and highly depends on the alignment method. Appreciating the existence of evolutionary constraints, alignments that consider patterns associated with specific putative evolutionary events are favored. Once the sequences have been aligned, the postulated putative evolutionary events need to be coded as an additional step. In order for the alignments and the alignment coding to be falsifiable, they should be carried out using justified and explicitly formulated criteria. Alternative coding methods for the most common patterns present in alignments of non-coding DNA are discussed here. Simpler putative synapomorphy assessment will not always correlate to more reliable phylogenetic information because simplicity does not necessarily correlate to the degree of homoplasy. The use of non-coding DNA can result in more laborious coding, but at the same time in more corroborated hypotheses, mirroring their accuracy for phylogenetic inference.     

Frequent inconsistency of parsimony under a simple model of cladogenesis

Although the conditions under which the parsimony method becomes inconsistent have been studied for almost two decades, the probability that the parsimony method would encounter conditions causing inconsistency under simple models of cladogenesis is unknown. Here, we examine the statistical behavior of the parsimony method under a birth-death model of cladogenesis, when the molecular clock holds. The parsimony method can become inconsistent a high proportion of the time even under this simple model of cladogenesis. When taxon sampling is poor or rates of evolution are high, the probability that parsimony will become inconsistent increases.     

Multi-species SIR models from a dynamical Bayesian perspective

Multi-species compartment epidemic models, such as the multi-species susceptible–infectious–recovered (SIR) model, are extensions of the classic SIR models, which are used to explore the transient dynamics of pathogens that infect multiple hosts in a large population. In this article, we propose a dynamical Bayesian hierarchical SIR (HSIR) model, to capture the stochastic or random nature of an epidemic process in a multi-species SIR (with recovered becoming susceptible again) dynamical setting, under hidden mass balance constraints. We call this a Bayesian hierarchical multi-species SIR (MSIR_B) model. Different from a classic multi-species SIR model (which we call MSIR_C), our approach imposes mass balance on the underlying true counts rather than, improperly, on the noisy observations. Moreover, the MSIR_B model can capture the discrete nature of, as well as uncertainties in, the epidemic process.     

Phylogenetic relationships and biogeography of the desert plant genus Fagonia (Zygophyllaceae), inferred by parsimony and Bayesian model averaging

Phylogenetic relationships within Fagonia were inferred from analyses of plastid trnL intron and nuclear ribosomal ITS DNA sequences. Sampling of the genus was nearly complete, including 32 of 34 species. Phylogenetic analysis was carried out using parsimony, and Bayesian model averaging. The latter method allows model-based inference while accounting for model-selection uncertainty, and is here used for the first time in phylogenetic analyses. All species of Fagonia in the Old World, except F. cretica, form a weakly supported clade, and all Fagonia species of the New World, except F. scoparia, are well supported as sister to the Old World clade. Fagonia scoparia, from Mexico, and F. cretica, from Northern Africa, are well supported as sisters to all other Fagonia species. Vicariance-dispersal analysis, using DIVA, indicated that the occurrences of Fagonia in South America and southern Africa are due to dispersals, and also, that the ancestor of Fagonia had a distribution compatible with the boreotropics hypothesis.     

A Bayesian two-level model for fluctuation assay

The fluctuation experiment is an essential tool for measuring microbial mutation rates in the laboratory. When inferring the mutation rate from an experiment, one assumes that the number of mutants in each test tube follows a common distribution. This assumption conceptually restricts the scope of applicability of fluctuation assay. We relax this assumption by proposing a Bayesian two-level model, under which an experiment-wide average mutation rate can be defined. The new model suggests a gamma mixture of the Luria-Delbrück distribution, which coincides with a recently discovered discrete distribution. While the mixture model is of considerable independent interest in fluctuation assay, it also offers a practical Markov chain Monte Carlo method for estimating mutation rates. We illustrate the Bayesian approach with a detailed analysis of an actual fluctuation experiment.     

A computationally efficient algorithm for genomic prediction using a Bayesian model

Background

Genomic prediction of breeding values from dense single nucleotide polymorphisms (SNP) genotypes is used for livestock and crop breeding, and can also be used to predict disease risk in humans. For some traits, the most accurate genomic predictions are achieved with non-linear estimates of SNP effects from Bayesian methods that treat SNP effects as random effects from a heavy tailed prior distribution. These Bayesian methods are usually implemented via Markov chain Monte Carlo (MCMC) schemes to sample from the posterior distribution of SNP effects, which is computationally expensive. Our aim was to develop an efficient expectation–maximisation algorithm (emBayesR) that gives similar estimates of SNP effects and accuracies of genomic prediction than the MCMC implementation of BayesR (a Bayesian method for genomic prediction), but with greatly reduced computation time.

Methods

emBayesR is an approximate EM algorithm that retains the BayesR model assumption with SNP effects sampled from a mixture of normal distributions with increasing variance. emBayesR differs from other proposed non-MCMC implementations of Bayesian methods for genomic prediction in that it estimates the effect of each SNP while allowing for the error associated with estimation of all other SNP effects. emBayesR was compared to BayesR using simulated data, and real dairy cattle data with 632 003 SNPs genotyped, to determine if the MCMC and the expectation-maximisation approaches give similar accuracies of genomic prediction.

Results

We were able to demonstrate that allowing for the error associated with estimation of other SNP effects when estimating the effect of each SNP in emBayesR improved the accuracy of genomic prediction over emBayesR without including this error correction, with both simulated and real data. When averaged over nine dairy traits, the accuracy of genomic prediction with emBayesR was only 0.5% lower than that from BayesR. However, emBayesR reduced computing time up to 8-fold compared to BayesR.

Conclusions

The emBayesR algorithm described here achieved similar accuracies of genomic prediction to BayesR for a range of simulated and real 630 K dairy SNP data. emBayesR needs less computing time than BayesR, which will allow it to be applied to larger datasets.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0082-4) contains supplementary material, which is available to authorized users.     

A method for constructing maximum parsimony ancestral amino acid sequences on a given network

A solution is presented for the problem of how to find ancestral codons which minimize the number of mutations over a given network of species for which character-states of aligned amino acid sequences among the contemporary species are known. Three theorems which allow this “maximum parsimony” problem to be solved are proved; then the use of these theorems in finding maximum parsimony ancestral codons is illustrated on a network of chicken and mammalian alpha globin amino acid sequences at two alignment positions.     

Links between maximum likelihood and maximum parsimony under a simple model of site substitution

Stochastic models of nucleotide substitution are playing an increasingly important role in phylogenetic reconstruction through such methods as maximum likelihood. Here, we examine the behaviour of a simple substitution model, and establish some links between the methods of maximum parsimony and maximum likelihood under this model.     

The phylogeny of early eureptiles: comparing parsimony and Bayesian approaches in the investigation of a basal fossil clade

For the first time the phylogenetic relationships of early eureptiles, consisting of captorhinids, diapsids, and protorothyridids, are investigated in a modern phylogenetic context using both parsimony and Bayesian approaches. Ninety parsimony-informative characters and 25 taxa were included in the analyses. The Bayesian analysis was run with and without a gamma-shape parameter allowing for variable rates across characters. In addition, we ran two more Bayesian analyses that included 42 autapomorphies and thus parsimony-uninformative characters in order to test the effect of variable branch lengths. The different analyses largely converged to the same topology, suggesting that the protorothyridid Coelostegus is the sister taxon of all other eureptiles and that the remaining protorothyridids are paraphyletic. Also, there is a close relationship between diapsids and Anthracodromeus, Cephalerpeton, and Protorothyris, a grouping of Thuringothyris with captorhinids, and a variable position of the protorothyridids Brouffia, Hylonomus, and Paleothyris. The lack of resolution in some parts of the tree might be due to hard polytomies and short divergence times between the respective taxa. The tree topology is consistent with the hypothesis that the temporal fenestrations of diapsid reptiles appear to be the consequence of a more lightly built skeleton, indicating a significant ecological shift in the early stages of diapsid evolution. Bayesian analysis is a very useful additional approach in studies of fossil taxa in which more traditional statistical support like the bootstrap is often weak. However, the exclusive use of the Mk model appears suitable only if autapomorphic characters are included, whereas the Mk+gamma model performed well with or without autapomorphies.     

A Bayesian estimation approach for the mortality in a stage-structured demographic model

Journal of Mathematical Biology - Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be...     

A Bayesian antedependence model for whole genome prediction

Hierarchical mixed effects models have been demonstrated to be powerful for predicting genomic merit of livestock and plants, on the basis of high-density single-nucleotide polymorphism (SNP) marker panels, and their use is being increasingly advocated for genomic predictions in human health. Two particularly popular approaches, labeled BayesA and BayesB, are based on specifying all SNP-associated effects to be independent of each other. BayesB extends BayesA by allowing a large proportion of SNP markers to be associated with null effects. We further extend these two models to specify SNP effects as being spatially correlated due to the chromosomally proximal effects of causal variants. These two models, that we respectively dub as ante-BayesA and ante-BayesB, are based on a first-order nonstationary antedependence specification between SNP effects. In a simulation study involving 20 replicate data sets, each analyzed at six different SNP marker densities with average LD levels ranging from r(2) = 0.15 to 0.31, the antedependence methods had significantly (P < 0.01) higher accuracies than their corresponding classical counterparts at higher LD levels (r(2) > 0. 24) with differences exceeding 3%. A cross-validation study was also conducted on the heterogeneous stock mice data resource (http://mus.well.ox.ac.uk/mouse/HS/) using 6-week body weights as the phenotype. The antedependence methods increased cross-validation prediction accuracies by up to 3.6% compared to their classical counterparts (P < 0.001). Finally, we applied our method to other benchmark data sets and demonstrated that the antedependence methods were more accurate than their classical counterparts for genomic predictions, even for individuals several generations beyond the training data.     

A flexible Bayesian model for studying gene-environment interaction

An important follow-up step after genetic markers are found to be associated with a disease outcome is a more detailed analysis investigating how the implicated gene or chromosomal region and an established environment risk factor interact to influence the disease risk. The standard approach to this study of gene–environment interaction considers one genetic marker at a time and therefore could misrepresent and underestimate the genetic contribution to the joint effect when one or more functional loci, some of which might not be genotyped, exist in the region and interact with the environment risk factor in a complex way. We develop a more global approach based on a Bayesian model that uses a latent genetic profile variable to capture all of the genetic variation in the entire targeted region and allows the environment effect to vary across different genetic profile categories. We also propose a resampling-based test derived from the developed Bayesian model for the detection of gene–environment interaction. Using data collected in the Environment and Genetics in Lung Cancer Etiology (EAGLE) study, we apply the Bayesian model to evaluate the joint effect of smoking intensity and genetic variants in the 15q25.1 region, which contains a cluster of nicotinic acetylcholine receptor genes and has been shown to be associated with both lung cancer and smoking behavior. We find evidence for gene–environment interaction (P-value = 0.016), with the smoking effect appearing to be stronger in subjects with a genetic profile associated with a higher lung cancer risk; the conventional test of gene–environment interaction based on the single-marker approach is far from significant.     

A hierarchical Bayesian model for next-generation population genomics

The demography of populations and natural selection shape genetic variation across the genome and understanding the genomic consequences of these evolutionary processes is a fundamental aim of population genetics. We have developed a hierarchical Bayesian model to quantify genome-wide population structure and identify candidate genetic regions affected by selection. This model improves on existing methods by accounting for stochastic sampling of sequences inherent in next-generation sequencing (with pooled or indexed individual samples) and by incorporating genetic distances among haplotypes in measures of genetic differentiation. Using simulations we demonstrate that this model has a low false-positive rate for classifying neutral genetic regions as selected genes (i.e., Φ(ST) outliers), but can detect recent selective sweeps, particularly when genetic regions in multiple populations are affected by selection. Nonetheless, selection affecting just a single population was difficult to detect and resulted in a high false-negative rate under certain conditions. We applied the Bayesian model to two large sets of human population genetic data. We found evidence of widespread positive and balancing selection among worldwide human populations, including many genetic regions previously thought to be under selection. Additionally, we identified novel candidate genes for selection, several of which have been linked to human diseases. This model will facilitate the population genetic analysis of a wide range of organisms on the basis of next-generation sequence data.