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The evolution of unisexuality in Calligrapha leaf beetles: molecular and ecological insights on multiple origins via interspecific hybridization.

Interspecific hybridization is a well-established cause of unisexual origins in vertebrates. This mechanism is also suspected in other apomictic taxa, but compelling evidence is rare. Here, we evaluate this mechanism and other hypotheses for the evolutionary origins of unisexuality through an investigation of Calligrapha leaf beetles. This group provides an intriguing subject for studies of unisexual evolution because it presents a rare insect example of multiple apomictic thelytokous species within a primarily bisexual genus. To investigate unisexual evolution, this study conducts the first molecular systematic analysis of Calligrapha. This involved the collection and analysis of about 3000 bp of DNA sequences--representing RNA and protein-coding loci from mitochondrial and nuclear genomes--from 54 specimens of 25 Calligrapha species, including four unisexual tetraploid taxa. Phylogenetic and molecular clock analyses indicated independent and single evolutionary origins of each of these unisexual species during the Pleistocene. Significant phylogenetic incongruence was detected between mitochondrial and nuclear datasets and found to be especially associated with the asexual taxa. This pattern is expected when unisexual lineages arise via interspecific hybridization and thus represent genetic mosaics that possess certain nuclear alleles from the paternal species lineage and mitochondrial DNA (mtDNA) alleles from the maternal parent. Analyzing the mtDNA and nuclear relatedness of unisexuals with corresponding haplotypes of bisexual Calligrapha species allowed the putative identification of these maternal and paternal species lineages for each unisexual species. Strong phenotypic similarities between unisexual taxa and their paternal parent species supported a model that involves both backcrosses of interspecific hybrids with a paternal parent and unreduced gametes. This model accounts for the origins of apomixis, polyploidy, and an overrepresentation of paternal nuclear alleles (and associated phenotypes) in unisexuals. This model is also consistent with the tetraploid karyotypes of unisexual Calligrapha, in which three sets of chromosomes (of presumed paternal ancestry) are quite morphologically homogeneous compared to the fourth. Especially intriguing was a consistent association of unisexual species with the host plant of the paternal parent but never with the maternal host. The statistical implausibility of these patterns occurring by chance further supports our inference of parental species. Moreover, it points to a potentially critical role for host-association in the formation and preservation of unisexual lineages. These findings suggest that ecological factors are critical for the diversification of unisexual as well as bisexual taxa and thus point out new research directions in the area of ecological speciation.

Animals↗

Little loss of information due to unknown phase for fine-scale linkage-disequilibrium mapping with single-nucleotide-polymorphism genotype data.

We present the results of a simulation study that indicate that true haplotypes at multiple, tightly linked loci often provide little extra information for linkage-disequilibrium fine mapping, compared with the information provided by corresponding genotypes, provided that an appropriate statistical analysis method is used. In contrast, a two-stage approach to analyzing genotype data, in which haplotypes are inferred and then analyzed as if they were true haplotypes, can lead to a substantial loss of information. The study uses our COLDMAP software for fine mapping, which implements a Markov chain-Monte Carlo algorithm that is based on the shattered coalescent model of genetic heterogeneity at a disease locus. We applied COLDMAP to 100 replicate data sets simulated under each of 18 disease models. Each data set consists of haplotype pairs (diplotypes) for 20 SNPs typed at equal 50-kb intervals in a 950-kb candidate region that includes a single disease locus located at random. The data sets were analyzed in three formats: (1). as true haplotypes; (2). as haplotypes inferred from genotypes using an expectation-maximization algorithm; and (3). as unphased genotypes. On average, true haplotypes gave a 6% gain in efficiency compared with the unphased genotypes, whereas inferring haplotypes from genotypes led to a 20% loss of efficiency, where efficiency is defined in terms of root mean integrated square error of the location of the disease locus. Furthermore, treating inferred haplotypes as if they were true haplotypes leads to considerable overconfidence in estimates, with nominal 50% credibility intervals achieving, on average, only 19% coverage. We conclude that (1). given appropriate statistical analyses, the costs of directly measuring haplotypes will rarely be justified by a gain in the efficiency of fine mapping and that (2). a two-stage approach of inferring haplotypes followed by a haplotype-based analysis can be very inefficient for fine mapping, compared with an analysis based directly on the genotypes.

Algorithms↗

Saturation kinetics in hepatic drug removal: a statistical approach to functional heterogeneity.

Extraction of drugs and other substrates from blood passing through the intact liver (or other capillary beds), inferred from samples taken at the organ inlet and outlet, is influenced by two kinds of heterogeneity of capillaries: transverse and longitudinal with respect to the direction of blood flow. The transverse heterogeneity is exemplified by arteriovenous shunts of the extracting system; the longitudinal one by zones of liver function. These two clinically interesting examples are among transverse and longitudinal distributions of capillary properties that can be inferred from the way the organ transforms the influx of a substance (or of a pair of substances interacting via liver cells) into the outflux over a range of input concentrations or of rates of blood flow. Mathematical and statistical ideas recently developed to implement this program in terms of saturation kinetics of uptake are reviewed and elucidated in relation to key experiments, data analysis, and statistical hypothesis testing.

Animals↗

Issues in analyzing data: experiences with three data bases.

Analytic issues in stroke data base research are reviewed, drawing upon relevant experiences in the analyses of three observational data bases from a variety of clinical fields. The specifics of the data base construct, statistical issues and variations in possible interpretations of results are discussed. Responsible analyses of and conservative inferences from observational data bases are stressed.

Acquired Immunodeficiency Syndrome↗

Comparative roles of the atrial septal aneurysm versus patent foramen ovale in systemic embolization with inferences from neonatal studies.

Patent foramen ovale (PFO) and atrial septal aneurysm (ASA) have a significant statistical relation to ischemic strokes in adults. We reviewed their prevalence in 106 echocardiograms of neonates. Although all normal neonates have PFO, only 4% had ASA. From fetal and neonatal echocardiograms, we conclude that ASAs are more likely to be caused by inadequate size of the PFO, but the ASA can act as a funnel, enhancing the chances of paradoxic embolization in the presence of a PFO. There is no convincing evidence that an ASA alone causes strokes in adults; the confounder is probably atrial fibrillation.

Adult↗

Statistical analysis of intraclass correlations from multiple samples with applications to arterial blood pressure data.

We consider inference procedures on intraclass correlations for unbalanced data from several multivariate normal populations. We derive several tests, including ones based on Fisher's variance stabilizing transformation and Neyman's score functions, to test the homogeneity of intraclass correlations. We illustrate the methodology with an example that uses arterial blood pressure data collected by Miall and Oldham and we compare the procedures in terms of their empirical levels and powers with a Monte Carlo simulation study. We recommend the use of Neyman's C(alpha) test and a test based on the ANOVA estimators of the intraclass correlations as they hold their significance levels and give consistently higher powers.

Adult↗

Design and analysis of clinical trials with a bivariate failure time endpoint, with application to AIDS Clinical Trials Group Study A5142.

This paper investigates the use of a bivariate endpoint in clinical trials of antiretroviral drugs to treat infection with the HIV. While they provide the most reliable information about treatment effects, clinical events such AIDS or death are relatively rare among newly treated patients with HIV infection. As a result, surrogate endpoints, such as time to virological failure and time to regimen termination, are generally used in place of clinical endpoints in studies that enroll patients without previous treatment experience. Because no surrogate endpoint has been completely validated (i.e., shown to capture the full effect of treatment on clinical endpoint), it may be preferable to base treatment decisions on more than one surrogate. In this paper, we consider the bivariate endpoint of time to virological failure and time to regimen termination. Analysis of a bivariate endpoint requires appropriate statistical methods that maintain the experimentwise type I error rate when making simultaneous inference with respect to each endpoint. This article outlines such methods and compares their small sample properties using the simulation study that was executed for the purpose of designing a current AIDS clinical trial.

Anti-HIV Agents↗

Navigating Sampling Bias in Discrete Phylogeographic Analysis: Assessing the Performance of an Adjusted Bayes Factor.

Bayesian phylogeographic inference is widely used in molecular epidemiological studies to reconstruct the dispersal history of pathogens. Discrete phylogeographic analysis treats geographic locations as discrete traits and infers lineage transition events among them, and is typically followed by a Bayes factor (BF) test to assess the statistical support. In the standard BF (BFstd) test, the relative abundance of the involved trait states is not considered, which can be problematic in the case of unbalanced sampling. Existing methods to correct sampling bias in discrete phylogeographic analyses using continuous-time Markov chain (CTMC) model, often require additional epidemiological information to balance the sampling effort among locations. As such data is not necessarily available, alternative approaches that rely solely on available genomic data are needed. In this perspective, we assess the performance of a modification of the BFstd, the adjusted Bayes factor (BFadj), which incorporates information on the relative abundance of samples by location when inferring support for transition events and root location inference without requiring additional data. Using a simulation framework, we assess the statistical performance of BFstd and BFadj under varying levels of sampling bias, estimating their type I and type II error rates. Our results show that BFadj complements the BFstd by reducing type I errors at the cost increasing type II errors for inferred transition events, while improving type I and type II errors in root location inference. Our findings provide guidelines for implementing the complementary BFadj to detect and mitigate sampling bias in discrete phylogeographic inference using CTMC modeling.

Bayes Theorem↗

Inferring causal relationships among intermediate phenotypes and biomarkers: a case study of rheumatoid arthritis.

MOTIVATION: Genetic association analysis is based on statistical correlations which do not assign any cause-to-effect arrows between the two correlated variables. Normally, such assignment of cause and effect label is not necessary in genetic analysis since genes are always the cause and phenotypes are always the effect. However, among intermediate phenotypes and biomarkers, assigning cause and effect becomes meaningful, and causal inference can be useful. RESULTS: We show that causal inference is possible by an example in a study of rheumatoid arthritis. With the help of genotypic information, the shared epitope, the causal relationship between two biomarkers related to the disease, anti-cyclic citrullinated peptide (anti-CCP) and rheumatoid factor (RF) has been established. We emphasize the fact that third variable must be a genotype to be able to resolve potential ambiguities in causal inference. Two non-trivial conclusions have been reached by the causal inference: (1) anti-CCP is a cause of RF and (2) it is unlikely that a third confounding factor contributes to both anti-CCP and RF.

Arthritis, Rheumatoid↗

Modelling covariance structure in the analysis of repeated measures data.

The term 'repeated measures' refers to data with multiple observations on the same sampling unit. In most cases, the multiple observations are taken over time, but they could be over space. It is usually plausible to assume that observations on the same unit are correlated. Hence, statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit. Until recently, analysis techniques available in computer software only offered the user limited and inadequate choices. One choice was to ignore covariance structure and make invalid assumptions. Another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses. Ignoring covariance structure may result in erroneous inference, and avoiding it may result in inefficient inference. Recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model. The MIXED procedure of the SAS((R)) System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modelling the covariance structure is a major hurdle in the use of PROC MIXED. However, once the covariance structure is modelled, inference about fixed effects proceeds essentially as when using PROC GLM. An example from the pharmaceutical industry is used to illustrate how to choose a covariance structure. The example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects. In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structure.

Analysis of Variance↗

Higher-order probabilistic perceptrons as Bayesian inference engines.

An explicit structural connection is established between the Bayes optimal classifier operating on K binary input variables and a corresponding two-layer perceptron having normalized output activities and couplings from input to output units of all orders up to K. With suitable modification of connection weights and biases, such a higher-order probabilistic perceptron should in principle be able to learn the statistics of the classification problem and match the a posteriori probabilities given by Bayes optimal inference. Specific training algorithms are developed that allow this goal to be approximated in a controlled variational sense. An application to the task of discriminating between stable and unstable nuclides in nuclear physics yields network models with predictive performance comparable to the best that has been achieved with conventional multilayer perceptrons containing only pairwise connections.

Journal Article↗

Statistical analysis of longitudinal psychiatric data with dropouts.

Longitudinal studies are used in psychiatric research to address outcome changes over time within and between individuals. However, because participants may drop out of a study prematurely, ignoring the nature of dropout often leads to biased inference, and in turn, wrongful conclusions. The purpose of the present paper is: (1) to review several dropout processes, corresponding inferential issues and recent methodological advances; (2) to evaluate the impact of assumptions regarding the dropout processes on inference by simulation studies and an illustrative example using psychiatric data; and (3) to provide a general strategy for practitioners to perform analyses of longitudinal data with dropouts, using software available commercially or in the public domain. The statistical methods used in this paper are maximum likelihood, multiple imputation and semi-parametric regression methods for inference, as well as Little's test and index of sensitivity to nonignorability (ISNI) for assessing statistical dropout mechanisms. We show that accounting for the nature of the dropout process influences results and that sensitivity analysis is useful in assessing the robustness of parameter estimates and related uncertainties. We conclude that recording the causes of dropouts should be an integral part of any statistical analysis with longitudinal psychiatric data, and we recommend performing a sensitivity analysis when the exact nature of the dropout process cannot be discerned.

Antidepressive Agents↗

Comments about Joint Modeling of Cluster Size and Binary and Continuous Subunit-Specific Outcomes.

In longitudinal studies and in clustered situations often binary and continuous response variables are observed and need to be modeled together. In a recent publication Dunson, Chen, and Harry (2003, Biometrics 59, 521-530) (DCH) propose a Bayesian approach for joint modeling of cluster size and binary and continuous subunit-specific outcomes and illustrate this approach with a developmental toxicity data example. In this note we demonstrate how standard software (PROC NLMIXED in SAS) can be used to obtain maximum likelihood estimates in an alternative parameterization of the model with a single cluster-level factor considered by DCH for that example. We also suggest that a more general model with additional cluster-level random effects provides a better fit to the data set. An apparent discrepancy between the estimates obtained by DCH and the estimates obtained earlier by Catalano and Ryan (1992, Journal of the American Statistical Association 87, 651-658) is also resolved. The issue of bias in inferences concerning the dose effect when cluster size is ignored is discussed. The maximum-likelihood approach considered herein is applicable to general situations with multiple clustered or longitudinally measured outcomes of different type and does not require prior specification and extensive programming.

Animals↗

Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon.

Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.

Biological Evolution↗

Genetic analysis of complex demographic scenarios: spatially expanding populations of the cane toad, Bufo marinus.

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm, to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker, demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

Animals↗

Robust inference for event probabilities with non-Markov event data.

Multistate event data, in which a single subject is at risk for multiple events, is common in biomedical applications. This article considers nonparametric estimation of the vector of probabilities of state membership at time t. Estimators, derived under the Markov assumption, have been shown (Datta and Satten, 2001, Statistics and Probability Letters 55, 403-411) to be consistent for data that is non-Markov. Inference, however, must take into account possibly non-Markov transitions when constructing confidence bands for event curves. We develop robust confidence bands for these curves, evaluate them via simulation, and illustrate the method on two datasets.

AIDS-Related Opportunistic Infections↗

Gapped alignment of protein sequence motifs through Monte Carlo optimization of a hidden Markov model.

BACKGROUND: Certain protein families are highly conserved across distantly related organisms and belong to large and functionally diverse superfamilies. The patterns of conservation present in these protein sequences presumably are due to selective constraints maintaining important but unknown structural mechanisms with some constraints specific to each family and others shared by a larger subset or by the entire superfamily. To exploit these patterns as a source of functional information, we recently devised a statistically based approach called contrast hierarchical alignment and interaction network (CHAIN) analysis, which infers the strengths of various categories of selective constraints from co-conserved patterns in a multiple alignment. The power of this approach strongly depends on the quality of the multiple alignments, which thus motivated development of theoretical concepts and strategies to improve alignment of conserved motifs within large sets of distantly related sequences. RESULTS: Here we describe a hidden Markov model (HMM), an algebraic system, and Markov chain Monte Carlo (MCMC) sampling strategies for alignment of multiple sequence motifs. The MCMC sampling strategies are useful both for alignment optimization and for adjusting position specific background amino acid frequencies for alignment uncertainties. Associated statistical formulations provide an objective measure of alignment quality as well as automatic gap penalty optimization. Improved alignments obtained in this way are compared with PSI-BLAST based alignments within the context of CHAIN analysis of three protein families: Gialpha subunits, prolyl oligopeptidases, and transitional endoplasmic reticulum (p97) AAA+ ATPases. CONCLUSION: While not entirely replacing PSI-BLAST based alignments, which likewise may be optimized for CHAIN analysis using this approach, these motif-based methods often more accurately align very distantly related sequences and thus can provide a better measure of selective constraints. In some instances, these new approaches also provide a better understanding of family-specific constraints, as we illustrate for p97 ATPases. Programs implementing these procedures and supplementary information are available from the authors.

Amino Acid Motifs↗

Tests of applicability of several substitution models for DNA sequence data.

Using linear invariants for various models of nucleotide substitution, we developed test statistics for examining the applicability of a specific model to a given dataset in phylogenetic inference. The models examined are those developed by Jukes and Cantor (1969), Kimura (1980), Tajima and Nei (1984), Hasegawa et al. (1985), Tamura (1992), Tamura and Nei (1993), and a new model called the eight-parameter model. The first six models are special cases of the last model. The test statistics developed are independent of evolutionary time and phylogeny, although the variances of the statistics contain phylogenetic information. Therefore, these statistics can be used before a phylogenetic tree is estimated. Our objective is to find the simplest model that is applicable to a given dataset, keeping in mind that a simple model usually gives an estimate of evolutionary distance (number of nucleotide substitutions per site) with a smaller variance than a complicated model when the simple model is correct. We have also developed a statistical test of the homogeneity of nucleotide frequencies of a sample of several sequences that takes into account possible phylogenetic correlations. This test is used to examine the stationarity in time of the base frequencies in the sample. For Hasegawa et al.'s and the eight-parameter models, analytical formulas for estimating evolutionary distances are presented. Application of the above tests to several sets of real data has shown that the assumption of stationarity of base composition is usually acceptable when the sequences studied are closely related but otherwise it is rejected. Similarly, the simple models of nucleotide substitution are almost always rejected when actual genes are distantly related and/or the total number of nucleotides examined is large.

Base Sequence↗