The prior probabilities of phylogenetic trees

Bayesian methods have become among the most popular methods in phylogenetics, but theoretical opposition to this methodology remains. After providing an introduction to Bayesian theory in this context, I attempt to tackle the problem mentioned most often in the literature: the “problem of the priors”—how to assign prior probabilities to tree hypotheses. I first argue that a recent objection—that an appropriate assignment of priors is impossible—is based on a misunderstanding of what ignorance and bias are. I then consider different methods of assigning prior probabilities to trees. I argue that priors need to be derived from an understanding of how distinct taxa have evolved and that the appropriate evolutionary model is captured by the Yule birth–death process. This process leads to a well-known statistical distribution over trees. Though further modifications may be necessary to model more complex aspects of the branching process, they must be modifications to parameters in an underlying Yule model. Ignoring these Yule priors commits a fallacy leading to mistaken inferences both about the trees themselves and about macroevolutionary processes more generally.     

Developmental Genetics and Morphological Evolution of Flowering Plants, Especially Bladderworts (Utricularia): Fuzzy Arberian Morphology Complements Classical Morphology

This review compares new developmental models on flowering andother vascular plants with evolutionary hypotheses formulatedby Agnes Arber (1879–1960) and like-minded botanists.Special emphasis is laid on philosophical basics such as perspectivism,pluralism about evolutionary modelling, continuum way of thinking,and fuzzy logic. Arber's perspective is best labelled as F uzzyA rberian M orphology (FAM Approach). Its proponents (‘FAMmers’)treat structural categories (e.g. ‘roots’, ‘shoots’,‘stems’, ‘leaves’, ‘stipules’)in vascular plants as concepts with fuzzy borderlines allowingintermediates (including transitional forms, developmental mosaics).The FAM Approach complements Cla ssical Plant M orphology (ClaMApproach), which is the traditional approach in botany. ClaMproponents (‘ClaMmers’) postulate that the structuralcategories of vascular plants are regarded as concepts withclear-cut borderlines and without intermediates. However, duringthe evolution of vascular plants, the root-shoot distinctionand the stem-leaf distinction have become blurred several timesdue to developmental changes, resulting in organs with uniquecombinations of features. This happened, for example, in thebladderworts (Utricularia, Lentibulariaceae). When focusingon the ‘leaf’, the FAM Approach is identical toArber's ‘partial-shoot theory of the leaf’ and Sinha's‘leaf shoot continuum model’. A compound leaf canrepeat the developmental pathway of the whole shoot, at leastto some degree. For example, compound leaves of Chisocheton(Meliaceae)with indeterminate apical growth and three-dimensional branchingmay be seen as developmental mosaics sharing some growth processeswith whole shoots! We focus here on the FAM Approach becausethis perspective is especially promising for developmental geneticistsstudying flowering and other vascular plants. Copyright 2001Annals of Botany Company Review, body plan, developmental mosaics, leaf development, history of botany, homeosis, homeotic genes, Lentibulariaceae, morphological evolution, process morphology, stipules, Utricularia, flowering plants     

Philosophical Aspects of Measurements, Equations and Inferences in Plant Growth Studies

Growth analysis is based on equations that are ‘identities’because they are algebraically self-evident, whereas the moredeterministic models of plant growth are based on ‘conditionalequations’ that represent quantitative hypotheses. Growthanalytical studies consequently focus on the values of the componentsand not on the validity of the equations, whereas ‘validation’is a prime concern for other growth models. Implications ofmeasurement theory, of dependent and independent variables andof compensating components arise in the use of both types ofequation for quantifying growth. There is now available a rangeof approaches, from traditional growth analysis, through variousdevelopments of growth analysis including light conversion analysis,to complex mechanistic models of growth. Growth analysis, yield component analysis, light conversion analysis, mathematical models, measurement theory, derived quantities, independent variables, equations of growth     

Plant Morphology: The Historic Concepts of Wilhelm Troll, Walter Zimmermann and Agnes Arber

Recent molecular systematic and developmental genetic findingshave drawn attention to plant morphology as a discipline dealingwith the phenotypic appearance of plant forms. However, sincedifferent terms and conceptual frameworks have evolved overa period of more than 200 years, it is reasonable to surveythe history of plant morphology; this is the first of two paperswith this aim. The present paper deals with the historic conceptsof Troll, Zimmermann and Arber, which are based on Goethe'smorphology. Included are contrasting views of ‘unity anddiversity’, ‘position and process’, and ‘morphologyand phylogeny’, which, in part, are basic views of currentplant morphology, phylogenetic systematics and developmentalgenetics. Wilhelm Troll established the ‘type concept’and the ‘principle of variable proportions’. Hehas provided the most comprehensive overview of the positionalrelations of plant forms. Agnes Arber started from the universaldynamics of life and attempted to describe all structures asprocesses. She paid attention to ‘repetitive branching’,‘differential growth’, and ‘parallelism’.As a result she has recently been rediscovered by developmentalbotanists. Walter Zimmermann rejected any metaphysical influenceon plant form and instead called for objective procedures. Hewas mainly interested in phylogenetic ‘character transformation’and the ‘reconstruction of genealogical lines’.Guided by the example of flower-like inflorescences, a futurepaper will deal with functional and developmental constraintsinfluencing plant forms. Recent morphological concepts (‘trialectical’,‘continuum’/‘fuzzy’, ‘processmorphology’) will be discussed and related to currentmorphological and developmental genetic research. Copyright2001 Annals of Botany Company Plant form, plant morphology, natural philosophy, homology, phylogeny, Goethe, Troll, Arber, Zimmermann, typology, character transformation, differential growth, complementarity     

Testing a molecular clock without an outgroup: derivations of induced priors on branch-length restrictions in a Bayesian framework

We propose a Bayesian method for testing molecular clock hypotheses for use with aligned sequence data from multiple taxa. Our method utilizes a nonreversible nucleotide substitution model to avoid the necessity of specifying either a known tree relating the taxa or an outgroup for rooting the tree. We employ reversible jump Markov chain Monte Carlo to sample from the posterior distribution of the phylogenetic model parameters and conduct hypothesis testing using Bayes factors, the ratio of the posterior to prior odds of competing models. Here, the Bayes factors reflect the relative support of the sequence data for equal rates of evolutionary change between taxa versus unequal rates, averaged over all possible phylogenetic parameters, including the tree and root position. As the molecular clock model is a restriction of the more general unequal rates model, we use the Savage-Dickey ratio to estimate the Bayes factors. The Savage-Dickey ratio provides a convenient approach to calculating Bayes factors in favor of sharp hypotheses. Critical to calculating the Savage-Dickey ratio is a determination of the prior induced on the modeling restrictions. We demonstrate our method on a well-studied mtDNA sequence data set consisting of nine primates. We find strong support against a global molecular clock, but do find support for a local clock among the anthropoids. We provide mathematical derivations of the induced priors on branch length restrictions assuming equally likely trees. These derivations also have more general applicability to the examination of prior assumptions in Bayesian phylogenetics.     

Inference on fractal processes using multiresolution approximation

We consider Bayesian inference via Markov chain Monte Carlofor a variety of fractal Gaussian processes on the real line.These models have unknown parameters in the covariance matrix,requiring inversion of a new covariance matrix at each Markovchain Monte Carlo iteration. The processes have no suitableindependence properties so this becomes computationally prohibitive.We surmount these difficulties by developing a computationalalgorithm for likelihood evaluation based on a ‘multiresolutionapproximation’ to the original process. The method iscomputationally very efficient and widely applicable, makinglikelihood-based inference feasible for large datasets. A simulationstudy indicates that this approach leads to accurate estimatesfor underlying parameters in fractal models, including fractionalBrownian motion and fractional Gaussian noise, and functionalparameters in the recently introduced multifractional Brownianmotion. We apply the method to a variety of real datasets andillustrate its application to prediction and to model selection.     

An evaluation of prior influence on the predictive ability of Bayesian model averaging

Model averaging is gaining popularity among ecologists for making inference and predictions. Methods for combining models include Bayesian model averaging (BMA) and Akaike’s Information Criterion (AIC) model averaging. BMA can be implemented with different prior model weights, including the Kullback–Leibler prior associated with AIC model averaging, but it is unclear how the prior model weight affects model results in a predictive context. Here, we implemented BMA using the Bayesian Information Criterion (BIC) approximation to Bayes factors for building predictive models of bird abundance and occurrence in the Chihuahuan Desert of New Mexico. We examined how model predictive ability differed across four prior model weights, and how averaged coefficient estimates, standard errors and coefficients’ posterior probabilities varied for 16 bird species. We also compared the predictive ability of BMA models to a best single-model approach. Overall, Occam’s prior of parsimony provided the best predictive models. In general, the Kullback–Leibler prior, however, favored complex models of lower predictive ability. BMA performed better than a best single-model approach independently of the prior model weight for 6 out of 16 species. For 6 other species, the choice of the prior model weight affected whether BMA was better than the best single-model approach. Our results demonstrate that parsimonious priors may be favorable over priors that favor complexity for making predictions. The approach we present has direct applications in ecology for better predicting patterns of species’ abundance and occurrence.     

Voigt and Reuss Models for Predicting Changes in Young's Modulus of Dehydrating Plant Organs

A general modelling approach was used to predict the changesresulting from dehydration in the Young's modulus (E) of a tereteorgan with a simple anatomy (e.g. hypodermis of thick-walledtissue surrounding a parenchymatous core of ground tissue).Two general anatomical models were investigated: (1) an ‘apoplastmodel’ in which each cross section through the organ wasconsidered as a composite elastic material consisting of a solid(cell wall) and liquid (protoplasm) phase; and (2) a ‘core-rindmodel’ in which the organ consisted of a thick-walledand a thin-walled tissue. For each of these two anatomical models,two composite material models were considered, i.e. a Voigtor Reuss equation was used to predict the changes in E attendingdehydration. The predictions from the variants of the generalmodel were evaluated on the basis of observed changes in E ascylindrical segments of the pseudopetioles of Spathiphyllumwere allowed to desiccate at room temperature. Statistical comparisonsbetween predicted and observed values of E revealed that oneof the simple variants of the model, the ‘Voigt apoplastmodel’, was the most successful in predicting the observedtrend seen in the changes in E. However, when the Voigt andReuss apoplast models were combined, the ‘hybrid’model provided estimates of changes in E that were statisticallyindistinguishable from those observed. Based on the hybrid model,it was estimated that roughly 76.7% of the tissues with a representativeSpathiphyllum pscudopetiole operated according to a Voigt apoplastmodel. Young's modulus, dehydration, plant tissues     

An automated computer vision and roboticsbased technique for 3-D flexible biomolecular docking and matching

The generation of binding modes between two molecules, alsoknown as molecular docking, is a key problem in rational drugdesign and biomolecular recognition. Docking a ligand, e.g.,a drug molecule or a protein molecule, to a protein receptor,involves recognition of molecular surfaces as molecules interactat their surface. Recent studies report that the activity ofmany molecules induces conformational transitions by ‘hinge-bending’,which involves movements of relatively rigid parts with respectto each other. In ligand–receptor binding, relative rotationalmovements of molecu–lar substructures about their commonhinges have been observed. For automatically predicting flexiblemolecular interactions, we adapt a new technique developed inComputer Vision and Robotics for the efficient recognition ofpartially occluded articulated objects. These type of objectsconsist of rigid parts which are connected by rotary joints(hinges). Our approach is based on an extension and generalizationof the Geometric Hashing and Generalized Hough Transform paradigmfor rigid object recognition. Unlike other techniques whichmatch each part individually, our approach exploits forcefullyand efficiently enough the fact that the different rigid partsdo belong to the same flexible molecule. We show experimentalresults obtained by an implementation of the algorithm for rigidand flexible docking. While the ‘correct’, crystal–boundcomplex is obtained with a small RMSD, additional, predictive‘high scoring’ binding modes are generated as well.The diverse applications and implications of this general, powerfultool are discussed     

Integrating biological knowledge into variable selection: an empirical Bayes approach with an application in cancer biology

ABSTRACT: BACKGROUND: An important question in the analysis of biochemical data is that of identifying subsets of molecular variables that may jointly influence a biological response. Statistical variable selection methods have been widely used for this purpose. In many settings, it may be important to incorporate ancillary biological information concerning the variables of interest. Pathway and network maps are one example of a source of such information. However, although ancillary information is increasingly available, it is not always clear how it should be used nor how it should be weighted in relation to primary data. RESULTS: We put forward an approach in which biological knowledge is incorporated using informative prior distributions over variable subsets, with prior information selected and weighted in an automated, objective manner using an empirical Bayes formulation. We employ continuous, linear models with interaction terms and exploit biochemically-motivated sparsity constraints to permit exact inference. We show an example of priors for pathway- and network-based information and illustrate our proposed method on both synthetic response data and by an application to cancer drug response data. Comparisons are also made to alternative Bayesian and frequentist penalised-likelihood methods for incorporating network-based information. CONCLUSIONS: The empirical Bayes method proposed here can aid prior elicitation for Bayesian variable selection studies and help to guard against mis-specification of priors. Empirical Bayes, together with the proposed pathway-based priors, results in an approach with a competitive variable selection performance. In addition, the overall procedure is fast, deterministic, and has very few user-set parameters, yet is capable of capturing interplay between molecular players. The approach presented is general and readily applicable in any setting with multiple sources of biological prior knowledge.     

Cultivar Differences in the Performance of Bean Seedlings at Suboptimal Temperatures

Growth analysis of plants raised under controlled environments(10–5, 12, 15, 18 and 20 °C, and 21 h photoperiod)was used to examine whether varietal differences in the minimumgermination temperature of four bean cultivars persist duringgrowth at suboptimal temperatures. A method to estimate theminimum vegetative growth temperature, based on axis relativegrowth rate, was developed. In order to compensate for ontogeneticdrift, the harvests were conducted at the same stage of developmentof the plants. Axis relative growth rates, reduction rates ofthe cotyledons and other growth parameters were calculated inorder to compare the cultivars. Cultivar ‘Marschall’showed better growth potential at 12 °C than the others,‘Pergousa‘ at 15 °C, and ‘Marschall’,‘Olsok’ and ‘Pergousa’ at 18 and 20°C. The effect of temperature on axis RGR was similar for‘Marschall’, ‘Olsok’ and ‘Pergousa’(Q₁₀ = 2·1) and more pronounced than for ‘Processor’(Q₁₀ = 1·3). Although there were significant differencesin the growth parameters among the cultivars within each temperatureused, the differences did not correspond with the differencesduring germination at low temperatures. The minimum vegetativegrowth temperature was close to 10 °C for all the cultivarstested. Phaseolus vulgaris L., beans, suboptimum temperature, growth analysis, minimum germination temperature, minimum vegetative growth temperature     

Notes on Contagious Distributions in Plant Populations

Past experience has shown that the Poisson series is often inadequateas a model for describing plant populations. Various alternativetwo-parameter models have been suggested in place of the Poissonseries, but they all depend on assumptions which may or maynot hold. In this paper a different approach is put forwardin that attention is concentrated on the mean number of plantsper quadrat and an index of ‘clumping’ or ‘contagiousness’.Examples are given as to the use of these concepts to test fordifferences between the distribution of a plant in two localitiesor between two plants in the same locality.     

The Photosynthetic Net Carbon Dioxide Exchange Potential in Conventional and 'Leafless' Phenotypes of Pisum sativum L. in Relation to Foliage Area, Dry Matter Production and Seed Yield

The effect of the ‘leafless’ mutation (in whichtendrils replace leaflets and the stipules are reduced to avestigial form) upon foliage area, photosynthetic net CO₂ uptakepotential, dry matter production and seed yield in Pisum sativumwas studied by comparing two near-isogenic lines of genotypeafafstst and ++++. The mutation is of potential agronomic valuein that it offers improved lodging resistance, crop drying andharvester throughput. In the conventional phenotype the total foliage area of themain axis attained a plateau (456 cm²) at day 56 from seedlingemergence, whereas corresponding values for the ‘leafless’mutant showed a total area of 208 cm² at day 68 with no indicationof a plateau. The agronomic consequence of this is discussed.During the vegetative phase of the plant the maximum CO₂ uptakepotential in the fully expanded conventional leaf was 8·5mg CO₂ leaf^–1 h^–1 and in the ‘leafless’mutant this value was 7·0 mg CO₂ leaf^–1 h^–1.For most ‘leaves’ of the latter phenotype this valuewas between 30 and 60 per cent less than for their conventionalcounterpart. There was a consistently higher photosyntheticpotential per unit area in tendrils of the ‘leafless’mutant than in leaflets of the conventional phenotype. The respectivemean specific values for the two phenotypes were 53 and 37 mgCO₂ dm^–2 h^–1. The problem of obtaining a meaningfulsurface area value for tendrils is discussed and the cylindricalnature of tendrils is taken into account. The ‘leafless’ mutant consistently accumulated 50per cent less dry matter than did conventional plants in theperiod from seedling emergence to anthesis and yield of maturedry seed per plant showed a reduction of 50 per cent both inseed number and total seed weight. The implications for future breeding and selection programmesaimed at haulm reduction are discussed in relation to evaluatingthe ability of the background genotype to produce adequate tendrilsin the presence of afafstst. Triticum aestivum, wheat, callus culture, organogenesis     

On null hypotheses in survival analysis

The conventional nonparametric tests in survival analysis, such as the log‐rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby, we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. As an illustration, we apply our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomized controlled trial.     

CORRECTIONS, VOLUME 29

Part 1, under the frontispiece portrait of Dr. N. B. Eales,the words ‘President 1948–1951’ should havebeen added. Page 103, line 49, for ‘Newton Collection’ read‘Norman Collection (Canon Norman)’. 185, line 37, for ‘capillaris’ read ‘capillacca’. 188, Table 1, for ‘bemoralis’. read ‘nemoralis’. 188, Table 2, for ‘Cochlicella acuta (Müll)? ventrosa(Fér.)’ read ‘Cochlicella ventrosa (Fér.)’. 191, line 24, for ‘araheo-’ read ‘archeo-’.     

The conflation of ignorance and knowledge in the inference of clade posteriors

The objective Bayesian approach relies on the construction of prior distributions that reflect ignorance. When topologies are considered equally probable a priori, clades cannot be. Shifting justifications have been offered for the use of uniform topological priors in Bayesian inference. These include: (i) topological priors do not inappropriately influence Bayesian inference when they are uniform; (ii) although clade priors are not uniform, their undesirable influence is negated by the likelihood function, even when data sets are small; and (iii) the influence of nonuniform clade priors is an appropriate reflection of knowledge. The first two justifications have been addressed previously: the first is false, and the second was found to be questionable. The third and most recent justification is inconsistent with the first two, and with the objective Bayesian philosophy itself. Thus, there has been no coherent justification for the use of nonflat clade priors in Bayesian phylogenetics. We discuss several solutions: (i) Bayesian inference can be abandoned in favour of other methods of phylogenetic inference; (ii) the objective Bayesian philosophy can be abandoned in favour of a subjective interpretation; (iii) the topology with the greatest posterior probability, which is also the tree of greatest marginal likelihood, can be accepted as optimal, with clade support estimated using other means; or (iv) a Bayes factor, which accounts for differences in priors among competing hypotheses, can be used to assess the weight of evidence in support of clades.
©The Willi Hennig Society 2009     

Fast Bayesian inference in large Gaussian graphical models

Despite major methodological developments, Bayesian inference in Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and conditional independence structures between variables by multiple testing, which bypasses the exploration of the model space. Specifically, we introduce closed‐form Bayes factors under the Gaussian conjugate model to evaluate the null hypotheses of marginal and conditional independence between variables. Their computation for all pairs of variables is shown to be extremely efficient, thereby allowing us to address large problems with thousands of nodes as required by modern applications. Moreover, we derive exact tail probabilities from the null distributions of the Bayes factors. These allow the use of any multiplicity correction procedure to control error rates for incorrect edge inclusion. We demonstrate the proposed approach on various simulated examples as well as on a large gene expression data set from The Cancer Genome Atlas.     

Characterization of RNA-dependent RNA Polymerases in Healthy and Tobacco Mosaic Virus-infected Tomato Plants

Healthy tomato plants were shown to contain high levels of RNA-dependentRNA polymerase activity, mainly in a ‘soluble’ form,but also partly in a ‘ bound’ form. The ‘bound’enzyme was solublized by EDTA treatment. Both forms of enzymewere partially purified and characterized. The ion and pH optimaof the two forms were identical at all stages of purification.Both enzymes exhibited uridylyl transferase activity, whichmade up 35 per cent of total incorporation. Infection with tobacco mosaic virus (TMV) increased activityof ‘soluble’ enzyme by twofold, and of solubilized‘bound’ enzyme by less than twofold. Uridylyl transferaseactivity was also increased by infection. General propertiesof the enzymes were unaltered by infection with one exception:in the presence of TMV RNA as added template, the ‘soluble’enzyme from infected plants incorporated ³H-UTP into productswith the electrophoretic properties and RNase sensitivitiesexpected for replicative form and replicative intermediate ofTMV. ‘Soluble’ enzyme from healthy plants, and solublized‘ bound’ enzyme from either healthy or infectedplants did not synthesize these products. The ‘soluble’ and solubilized ‘bound’enzymes behaved differently on ion-exchange chromatography.Under the conditions used, ‘soluble’ enzyme didnot bind to the column, whereas solublized ‘bound’enzyme did. No differences in chromatographic behaviour werefound between enzymes from healthy or infected plants. Withboth ‘soluble’ and solublized ‘bound’enzymes, the uridylyl transferase activity co-chromatographedwith the polymerase activity. Tomato, Lycopersicon esculentum, RNA-dependent RNA polymerase, tobacco mosaic virus, tobacco mosaic virus replicase     

Concentration-dependent changes of perceived odor quality

In order to assess the dependence of perceived odor qualityon odorant concentration, we studied 21 subjects. For eightsubjects all possible pairs from a pool of six odorants at threedecimal dilutions were presented, and subjects were requestedto state whether members of the pair were qualitatively ‘similar’or ‘different’ It was found that while pairs withthe same odorant at identical concentrations were judged ‘similar’in >90% of the cases by all subjects, scores went down to10% ‘similar’ judgements in some cases when thesame odorant was presented at a 100-fold concentration difference.Large time-invariable differences were found among subjectsand among odorants. For the additional 13 subjects, all possiblepairs from a pool of four odorants at three decimal dilutionswere presented. Subjects were instructed to state whether membersof the pair were qualitatively ‘same’ or ‘different’,and were also requested to rank the degree of difference ona visual analogue scale. Results for this group were, in general,similar to the results of the former group of subjects and goodagreement between the two tasks was found. The results suggestthat variations in olfactory stimulus magnitude may be perceivedas quality differences, as previously shown for vision and audition.     

Relative Sensitivity and Tolerance of some Gladiolus Cultivars to Sulphur Dioxide

Five Gladiolus cultivars, namely ‘Aldebaran’, ‘BrightEye’, ‘Illusion’, ‘Manisha’ and‘Manmohan’, were exposed to 1 and 2 µg l^–1sulphur dioxide to test their relative-sensitivity toleranceto the pollutant Plants were fumigated experimentally for 2h daily Foliar injury symptoms were observed first in ‘Manisha’followed by ‘Aldebaran’ and ‘Illusion’at the higher dose Photosynthetic pigments and leaf extractpH were significantly decreased, particularly in ‘Manisha’and ‘Illusion’ Overall disturbances in the plantmetabolism due to SO₂ treatment led to retarded growth of plants,as evident from decreased shoot length and phytomass valuesThe order of sensitivity of the five Gladiolus cultivars toSO₂ was as follows, with the greatest first Manisha, Illusion,Aldebaran, Bright Eye, Manmohan Cultivars, Gladiolus, sensitivity, sulphur dioxide, tolerance