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PubMed2003

RNA-based phylogenetic methods: application to mammalian mitochondrial RNA sequences.

The PHASE software package allows phylogenetic tree construction with a number of evolutionary models designed specifically for use with RNA sequences that have conserved secondary structure. Evolution in the paired regions of RNAs occurs via compensatory substitutions, hence changes on either side of a pair are correlated. Accounting for this correlation is important for phylogenetic inference because it affects the likelihood calculation. In the present study we use the complete set of tRNA and rRNA sequences from 69 complete mammalian mitochondrial genomes. The likelihood calculation uses two evolutionary models simultaneously for different parts of the sequence: a paired-site model for the paired sites and a single-site model for the unpaired sites. We use Bayesian phylogenetic methods and a Markov chain Monte Carlo algorithm is used to obtain the most probable trees and posterior probabilities of clades. The results are well resolved for almost all the important branches on the mammalian tree. They support the arrangement of mammalian orders within the four supra-ordinal clades that have been identified by studies of much larger data sets mainly comprising nuclear genes. Groups such as the hedgehogs and the murid rodents, which have been problematic in previous studies with mitochondrial proteins, appear in their expected position with the other members of their order. Our choice of genes and evolutionary model appears to be more reliable and less subject to biases caused by variation in base composition than previous studies with mitochondrial genomes.

Animals↗

PubMed2006

Estimating in real time the efficacy of measures to control emerging communicable diseases.

Controlling an emerging communicable disease requires prompt adoption of measures such as quarantine. Assessment of the efficacy of these measures must be rapid as well. In this paper, the authors present a framework to monitor the efficacy of control measures in real time. Bayesian estimation of the reproduction number R (mean number of cases generated by a single infectious person) during an outbreak allows them to judge rapidly whether the epidemic is under control (R < 1). Only counts and time of onset of symptoms, plus tracing information from a subset of cases, are required. Markov chain Monte Carlo and Monte Carlo sampling are used to infer the temporal pattern of R up to the last observation. The operating characteristics of the method are investigated in a simulation study of severe acute respiratory syndrome-like outbreaks. In this particular setting, control measures lacking efficacy (R > or = 1.1) could be detected after 2 weeks in at least 70% of the epidemics, with less than a 5% probability of a wrong conclusion. When control measures are efficacious (R = 0.5), this situation may be evidenced in 68% of the epidemics after 2 weeks and 92% of the epidemics after 3 weeks, with less than a 5% probability of a wrong conclusion.

Animals↗

PubMed2006

Phylogenetic relationships and historical biogeography of neotropical parrots (Psittaciformes: Psittacidae: Arini) inferred from mitochondrial and nuclear DNA sequences.

Previous hypotheses of phylogenetic relationships among Neotropical parrots were based on limited taxon sampling and lacked support for most internal nodes. In this study we increased the number of taxa (29 species belonging to 25 of the 30 genera) and gene sequences (6388 base pairs of RAG-1, cyt b, NADH2, ATPase 6, ATPase 8, COIII, 12S rDNA, and 16S rDNA) to obtain a stronger molecular phylogenetic hypothesis for this group of birds. Analyses of the combined gene sequences using maximum likelihood and Bayesian methods resulted in a well-supported phylogeny and indicated that amazons and allies are a sister clade to macaws, conures, and relatives, and these two clades are in turn a sister group to parrotlets. Key morphological and behavioral characters used in previous classifications were mapped on the molecular tree and were phylogenetically uninformative. We estimated divergence times of taxa using the molecular tree and Bayesian and penalized likelihood methods that allow for rate variation in DNA substitutions among sites and taxa. Our estimates suggest that the Neotropical parrots shared a common ancestor with Australian parrots 59 Mya (million of years ago; 95% credibility interval (CrI) 66, 51 Mya), well before Australia separated from Antarctica and South America, implying that ancestral parrots were widespread in Gondwanaland. Thus, the divergence of Australian and Neotropical parrots could be attributed to vicariance. The three major clades of Neotropical parrots originated about 50 Mya (95% CrI 57, 41 Mya), coinciding with periods of higher sea level when both Antarctica and South America were fragmented with transcontinental seaways, and likely isolated the ancestors of modern Neotropical parrots in different regions in these continents. The correspondence between major paleoenvironmental changes in South America and the diversification of genera in the clade of amazons and allies between 46 and 16 Mya suggests they diversified exclusively in South America. Conversely, ancestors of parrotlets and of macaws, conures, and allies may have been isolated in Antarctica and/or the southern cone of South America, and only dispersed out of these southern regions when climate cooled and Antarctica became ice-encrusted about 35 Mya. The subsequent radiation of macaws and their allies in South America beginning about 28 Mya (95% CrI 22, 35 Mya) coincides with the uplift of the Andes and the subsequent formation of dry, open grassland habitats that would have facilitated ecological speciation via niche expansion from forested habitats.

Animals↗

PubMed2005

Stochastic models for horizontal gene transfer: taking a random walk through tree space.

Horizontal gene transfer (HGT) plays a critical role in evolution across all domains of life with important biological and medical implications. I propose a simple class of stochastic models to examine HGT using multiple orthologous gene alignments. The models function in a hierarchical phylogenetic framework. The top level of the hierarchy is based on a random walk process in "tree space" that allows for the development of a joint probabilistic distribution over multiple gene trees and an unknown, but estimable species tree. I consider two general forms of random walks. The first form is derived from the subtree prune and regraft (SPR) operator that mirrors the observed effects that HGT has on inferred trees. The second form is based on walks over complete graphs and offers numerically tractable solutions for an increasing number of taxa. The bottom level of the hierarchy utilizes standard phylogenetic models to reconstruct gene trees given multiple gene alignments conditional on the random walk process. I develop a well-mixing Markov chain Monte Carlo algorithm to fit the models in a Bayesian framework. I demonstrate the flexibility of these stochastic models to test competing ideas about HGT by examining the complexity hypothesis. Using 144 orthologous gene alignments from six prokaryotes previously collected and analyzed, Bayesian model selection finds support for (1) the SPR model over the alternative form, (2) the 16S rRNA reconstruction as the most likely species tree, and (3) increased HGT of operational genes compared to informational genes.

Archaea↗

PubMed2006

Bayesian multivariate hierarchical transformation models for ROC analysis.

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.

Bayes Theorem↗

PubMed2005

Inferring genetic regulatory logic from expression data.

MOTIVATION: High-throughput molecular genetics methods allow the collection of data about the expression of genes at different time points and under different conditions. The challenge is to infer gene regulatory interactions from these data and to get an insight into the mechanisms of genetic regulation. RESULTS: We propose a model for genetic regulatory interactions, which has a biologically motivated Boolean logic semantics, but is of a probabilistic nature, and is hence able to confront noisy biological processes and data. We propose a method for learning the model from data based on the Bayesian approach and utilizing Gibbs sampling. We tested our method with previously published data of the Saccharomyces cerevisiae cell cycle and found relations between genes consistent with biological knowledge.

Bayes Theorem↗

PubMed2004

Multiple origins of parasitism in lice.

A major fraction of the diversity of insects is parasitic, as herbivores, parasitoids or vertebrate ectopara sites. Understanding this diversity requires information on the origin of parasitism in various insect groups. Parasitic lice (Phthiraptera) are the only major group of insects in which all members are permanent parasites of birds or mammals. Lice are classified into a single order but are thought to be closely related to, or derived from, book lice and bark lice (Psocoptera). Here, we use sequences of the nuclear 18S rDNA gene to investigate the relationships among Phthiraptera and Psocoptera and to identify the origins of parasitism in this group (termed Psocodea). Maximum-likelihood (ML), Bayesian ML and parsimony analyses of these data indicate that lice are embedded within the psocopteran infraorder Nanopsocetae, making the order Psocoptera paraphyletic (i.e. does not contain all descendants of a single common ancestor). Furthermore, one family of Psocoptera, Liposcelididae, is identified as the sister taxon to the louse suborder Amblycera, making parasitic lice (Phthiraptera) a polyphyletic order (i.e. descended from two separate ancestors). We infer from these results that parasitism of vertebrates arose twice independently within Psocodea, once in the common ancestor of Amblycera and once in the common ancestor of all other parasitic lice.

Animals↗

PubMedDate not supplied

Lung cancer mortality in a district of La Spezia (Italy) exposed to air pollution from industrial plants.

AIMS AND BACKGROUND: In the last decades, many epidemiological studies have implicated outdoor environmental carcinogens in the onset of lung cancer. The present investigation evaluated lung cancer mortality in two areas of the Province of La Spezia (Northern Italy) exposed to environmental pollution emitted by a coal-fired power station and other industrial sources, including a waste incinerator. METHODS: In the two exposed areas, lung cancer mortality risk for the 1988-1996 calendar period was evaluated using the whole Province population as referent. The corresponding relative risks (RR) were estimated after controlling for age structure, urban/rural gradient and deprivation factors (occupation, education, home ownership, housing conditions and family structure) by a Poisson regression modeling. The geographic pattern of risk for the whole province was evaluated via the Besag, York and Mollié (BYM) bayesian model. RESULTS: Persons living in urban areas showed the highest rates in both sexes. No statistically significant risk excess was found in the two exposed areas among males, after excluding rural and semi-rural zones from the analyses (RR = 1.03 and RR = 0.77). In contrast, a risk excess was observed for females in both exposed areas, which remained elevated and statistically significant (P <0.05) after restriction to urban/semi-urban municipalities and after controlling for deprivation factors (RR = 1.54 and RR = 2.14, respectively). Bayesian mapping confirmed the rural/urban gradient and the risk excess observed in females near the industrial sites. CONCLUSIONS: The risk observed among females is consistent with pollution measurements and with other epidemiologic findings, whereas a strong confounding from occupational exposures and smoking habit could account for the lack of an excess risk in males. However, the ecologic nature of this investigation prevented drawing a causal inference. The pollution-related risk observed in the female gender is an important clue that deserves further epidemiologic attention.

Adult↗

PubMed2004

Molecular phylogeny of Trichomonadidae family inferred from ITS-1, 5.8S rRNA and ITS-2 sequences.

The Trichomonads have been the subject of several molecular studies that reported some discrepancies both at the lower and higher taxonomic levels. The purpose of this study was to make an extensive phylogenetic analysis of the Trichomonadidae using ITS-1/5.8S/ITS-2 sequences, to better understand its phylogeny and the usefulness of this marker. ITS-1/5.8S/ITS-2 sequences of 36 strains from 14 species belonging to Trichomonadidae and Monocercomonadidae were analysed, in which 20 were newly determined. Maximum likelihood, maximum parsimony, neighbour joining, and Bayesian phylogenetic methods were employed in order to reconstruct and compare the evolutionary history of this group. Tetratrichomonas gallinarum and four strains of Tetratrichomonas sp. isolated from bull genital organs were found closely related, confirming the classification of the latter, probably as a new species. The monophyly of Tritrichomonadinae and Trichomonadinae subfamilies were corroborated, with the exclusion of Trichomitus batrachorum from the latter since it grouped consistently with Hypotrichomonas acosta. Tritrichomonas foetus, Tritrichomonas suis and potentially also Tritrichomonas mobilensis seemed to correspond to the same species. Monocercomonas sp. and Ditrichomonas honigbergii emerged as independent lineages, with their phylogenetic positions undetermined. Neither Trichomonadidae nor Monocercomonadidae were supported as monophyletic groups. The ITS-1/5.8S/ITS-2 seems to be a reliable locus for phylogenetic studies in the Trichomonadida, mainly at lower taxonomic levels, and at least up to the family level.

Animals↗

PubMed2004

Preliminary phylogeny of Valerianaceae (Dipsacales) inferred from nuclear and chloroplast DNA sequence data.

Valerianaceae is a relatively small (ca. 350 species), but morphologically diverse angiosperm clade. Sequence data from the entire ndhF gene, the trnL-F intergenic spacer region, the trnL intron, the matK region, the rbcL-atpB intergenic spacer region and internal transcribed spacer (ITS) region of nuclear ribosomal DNA were collected for 21 taxa within Dipsacaceae and Valerianaceae (1 and 20, respectively). These data were included in several phylogenetic analyses with previously published sequences from Dipsacales. Results from these analyses (maximum parsimony, maximum likelihood, and Bayesian analysis) are in strong agreement with many of the conclusions from previous studies, most importantly: (1) Valerianaceae is sister to Dipsacaceae; (2) Triplostegia is more closely related to species of Dipsacaceae than to Valerianaceae; and (3) Valeriana appears not to be monophyletic, with Valeriana celtica falling outside the remainder of the species of Valeriana sampled here (with very strong support). With the exception of V. celtica, these data support two major clades within Valeriana; one that is exclusively New World and another that is distributed in both the Old and New World. Although the species of Valerianaceae and its sister group Dipsacaceae plus Triplostegia, are widely distributed in the Northern Hemisphere, and the data imply that Valerianaceae diversified initially in Asia (the Himalayan Patrinia and Nardostachys falling at the base of the clade), the center of modern species diversity for the group is in the Andes of South America with as many as 175 species restricted to that region. Although the exclusively South American taxa form a clade in the chloroplast and combined ITS and chloroplast analyses, support values tend to be low. Future studies will need to include additional data, in the form of both characters and taxa, before any strong conclusions about the character evolution, diversification, and biogeography of the South American valerians can be made.

Bayes Theorem↗

PubMed2003

Coding of the contrasts in natural images by visual cortex (V1) neurons: a Bayesian approach.

Individual V1 neurons respond dynamically over only limited ranges of stimulus contrasts, yet we can discriminate contrasts over a wide range. Different V1 neurons cover different parts of the contrast range, and the information they provide must be pooled somehow. We describe a probabilistic pooling model that shows that populations of neurons with contrast responses like those in cat and monkey V1 would most accurately code contrasts in the range actually found in natural scenes. The pooling equation is similar to Bayes's equation; however, explicit inclusion of prior probabilities in the inference increases coding accuracy only slightly.

Animals↗

PubMed2005

Bayesian analysis for generalized linear models with nonignorably missing covariates.

We propose Bayesian methods for estimating parameters in generalized linear models (GLMs) with nonignorably missing covariate data. We show that when improper uniform priors are used for the regression coefficients, phi, of the multinomial selection model for the missing data mechanism, the resulting joint posterior will always be improper if (i) all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism, or (ii) at least one of the covariates is continuous and unbounded. This impropriety will result regardless of whether proper or improper priors are specified for the regression parameters, beta, of the GLM or the parameters, alpha, of the covariate distribution. To overcome this problem, we propose a novel class of proper priors for the regression coefficients, phi, in the selection model for the missing data mechanism. These priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a Gibbs sampling scheme that leads to accelerated convergence. In addition, we extend the model assessment criterion of Chen, Dey, and Ibrahim (2004a, Biometrika 91, 45-63), called the weighted L measure, to GLMs and missing data problems as well as extend the deviance information criterion (DIC) of Spiegelhalter et al. (2002, Journal of the Royal Statistical Society B 64, 583-639) for assessing whether the missing data mechanism is ignorable or nonignorable. A novel Markov chain Monte Carlo sampling algorithm is also developed for carrying out posterior computation. Several simulations are given to investigate the performance of the proposed Bayesian criteria as well as the sensitivity of the prior specification. Real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods.

Bayes Theorem↗

PubMed1993

Drug delivery optimization through Bayesian networks: an application to erythropoietin therapy in uremic anemia.

This paper describes how Bayesian networks can be used in combination with compartmental models to plan recombinant human erythropoietin delivery in the treatment of anemia of chronic uremic patients. Past measurements of hemoglobin concentration in a patient during the therapy can be exploited to adjust the parameters of a compartmental model of erythropoiesis. This adaptive process provides more accurate patient-specific predictions, and hence a more rational dosage planning. Inferences are performed by using a stochastic simulation algorithm called Gibbs sampling. We describe a drug delivery optimization protocol based on our approach. Some results obtained on real data are presented.

Adult↗

PubMedDate not supplied

A genetic and spatial Bayesian analysis of mastitis resistance.

A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.

Animals↗

PubMed2026

Cell Type-Resolved Causal Inference and Spatial Transcriptomic Integration Reveal Immune-Specific Genetic Drivers of Autoimmune and Malignant Thyroid Disease.

BACKGROUND: Thyroid diseases, including autoimmune thyroid disease (AITD) and thyroid cancer, are characterized by immune dysregulation, yet the cell type-specific genetic mechanisms underlying these conditions remain poorly understood. Most genome-wide association studies (GWAS) have relied on bulk tissue expression quantitative trait loci (eQTL), which cannot resolve the heterogeneity of immune cell populations. METHODS: We performed two-sample Mendelian randomization (MR) analyses using single-cell cis-eQTLs from 14 immune cell subtypes (OneK1K cohort) as instrumental variables against GWAS summary statistics for four thyroid outcomes: autoimmune hyperthyroidism, autoimmune hypothyroidism, thyroid cancer and autoimmune thyroiditis. Causal associations were validated through Bayesian colocalization, phenome-wide association analysis (PheWAS) and multi-layered transcriptomic validation encompassing spatial transcriptomics of AITD tissue (GSE248205), bulk RNA-seq of thyroid cancer (GSE3678) and single-cell RNA-seq of thyroid tumours (GSE250521). gsMap spatial LD score regression was applied to map disease heritability onto spatial tissue architecture. RESULTS: We identified six Bonferroni-significant causal gene-cell type pairs for autoimmune hyperthyroidism, including protective effects of ABHD16A in naïve/immature B cells (OR = 0.440), HIST1H3H in CD8 NC T cells (OR = 0.324), HMGN4 in NK recruiting cells (OR = 0.556) and ZKSCAN4 in CD8 S100B T cells (OR = 0.427), with five pairs showing strong colocalization (PP.H4 ≥ 86%). Three pairs reached significance for autoimmune hypothyroidism, including a risk association of HLA-F in CD4 NC T cells (OR = 1.139). For autoimmune thyroiditis, FAM134B/RETREG1 showed consistent suggestive protective associations across both CD4 and CD8 NC T cells (PP.H4 ≥ 90% for both), suggesting a possible involvement of ER phagy regulation in thyroiditis susceptibility. Thyroid cancer showed a suggestive association with HLA-G in classical monocytes (OR = 1.899, PP.H4 = 53%). Spatial transcriptomic validation demonstrated progressive immune infiltration from control tissue to Graves' disease to Hashimoto's thyroiditis (7.7%-15.7%, 46.1%-54.1%, respectively) and strong spatial correlation between target gene expression and corresponding cell type enrichment (e.g., plasma cell-HLA-DQB1: r = 0.491, p < 10-300). HLA-G was independently validated in thyroid cancer bulk (log2fc = 0.542, p = 9.51 × 10-3, AUC = 0.857) and single-cell datasets. PheWAS revealed no significant associations detected for the core candidates. gsMap identified significant enrichment of autoimmune hypothyroidism heritability in gastrointestinal tract, adrenal gland and adipose tissue (all Bonferroni p < 0.002). CONCLUSIONS: This study establishes a multi-scale analytical framework integrating cell type-resolved genetic inference with spatial tissue validation, revealing distinct immunogenetic architectures underlying autoimmune versus malignant thyroid disease. Protective genetic programs in autoimmune hyperthyroidism converge on chromatin remodelling (HIST1H3H, HMGN4, ZKSCAN4) and lipid metabolism (ABHD16A) across lymphocyte subsets, whereas thyroid cancer risk involves immune escape mediated by HLA-G in myeloid cells. The ER-phagy receptor RETREG1 represents a candidate pathway warranting further investigation in autoimmune thyroiditis. These findings provide genetically supported, cell type-specific therapeutic targets and demonstrate a generalizable strategy for dissecting the immune-mediated mechanisms of complex thyroid diseases.

Mendelian randomization↗

PubMed2005

Multiple independent losses of photosynthesis and differing evolutionary rates in the genus Cryptomonas (Cryptophyceae): combined phylogenetic analyses of DNA sequences of the nuclear and the nucleomorph ribosomal operons.

In this study, evidence for at least three independent losses of photosynthesis in the freshwater cryptophyte genus Cryptomonas is presented. The phylogeny of the genus was inferred by molecular phylogenetic analyses of the nuclear internal transcribed spacer 2 (nuclear ITS2), partial nuclear large subunit ribosomal DNA (LSU rDNA), and nucleomorph small subunit ribosomal DNA (SSU rDNA, NM). Both concatenated and single data sets were used. In all data sets, the colorless Cryptomonas strains formed three different lineages, always supported by high bootstrap values (maximum parsimony, neighbor joining and maximum likelihood) and posterior probabilities (Bayesian analyses). The three leukoplast-bearing lineages displayed differing degrees of accelerated evolutionary rates in nuclear and nucleomorph rDNA. Also an increase in A + T-content in highly variable regions of the nucleomorph SSU rDNA was observed in one of the leukoplast-bearing lineages.

Base Composition↗

PubMed2005

Long-oligomer microarray profiling in Neurospora crassa reveals the transcriptional program underlying biochemical and physiological events of conidial germination.

To test the inferences of spotted microarray technology against a biochemically well-studied process, we performed transcriptional profiling of conidial germination in the filamentous fungus, Neurospora crassa. We first constructed a 70 base oligomer microarray that assays 3366 predicted genes. To estimate the relative gene expression levels and changes in gene expression during conidial germination, we analyzed a circuit design of competitive hybridizations throughout a time course using a Bayesian analysis of gene expression level. Remarkable consistency of mRNA profiles with previously published northern data was observed. Genes were hierarchically clustered into groups with respect to their expression profiles over the time course of conidial germination. A functional classification database was employed to characterize the global picture of gene expression. Consensus motif searches identified a putative regulatory component associated with genes involved in ribosomal biogenesis. Our transcriptional profiling data correlate well with biochemical and physiological processes associated with conidial germination and will facilitate functional predictions of novel genes in N.crassa and other filamentous ascomycete species. Furthermore, our dataset on conidial germination allowed comparisons to transcriptional mechanisms associated with germination processes of diverse propagules, such as teliospores of the phytopathogenic fungus Ustilago maydis and spores of the social amoeba Dictyostelium discoideum.

Animals↗

PubMed2006

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.

Bayes Theorem↗