A comparative review of statistical methods for discovering differentially expressed genes in replicated microarray experiments

MOTIVATION: A common task in analyzing microarray data is to determine which genes are differentially expressed across two kinds of tissue samples or samples obtained under two experimental conditions. Recently several statistical methods have been proposed to accomplish this goal when there are replicated samples under each condition. However, it may not be clear how these methods compare with each other. Our main goal here is to compare three methods, the t-test, a regression modeling approach (Thomas et al., Genome Res., 11, 1227-1236, 2001) and a mixture model approach (Pan et al., http://www.biostat.umn.edu/cgi-bin/rrs?print+2001,2001a,b) with particular attention to their different modeling assumptions. RESULTS: It is pointed out that all the three methods are based on using the two-sample t-statistic or its minor variation, but they differ in how to associate a statistical significance level to the corresponding statistic, leading to possibly large difference in the resulting significance levels and the numbers of genes detected. In particular, we give an explicit formula for the test statistic used in the regression approach. Using the leukemia data of Golub et al. (Science, 285, 531-537, 1999), we illustrate these points. We also briefly compare the results with those of several other methods, including the empirical Bayesian method of Efron et al. (J. Am. Stat. Assoc., to appear, 2001) and the Significance Analysis of Microarray (SAM) method of Tusher et al. (PROC: Natl Acad. Sci. USA, 98, 5116-5121, 2001).     

Enzymatic methyl esterification of synthetic tripeptides: structural requirements of the peptide substrate. Detection of the reaction products by fast-atom-bombardment mass spectrometry

Eukaryotic protein carboxyl methyltransferase catalyzes a two-substrates reaction in which the methyl group of S-adenosylmethionine is transferred to the free carboxyl group of D-aspartyl and L-isoaspartyl-containing peptide or protein substrates. It has been previously shown that at least three binding sites are required for the interaction of adenosylmethionine with the enzyme and/or the protein substrate [Oliva A., Galletti P., Zappia V., Paik W. K. & Kim S. (1980) Eur. J. Biochem. 104, 595-602], while very little is known concerning the structural requirements of the protein substrate. In this study several synthetic tripeptides were selected in order to elucidate the structural requirements of the methyl-accepting substrates. The results obtained with this series of peptides suggested that: (1) three residues appear to be the minimal length, so far identified, required for a productive enzyme-substrate interaction, several dipeptides being ineffective as substrates [McFadden P. N. & Clarke S. (1986) J. Biol. Chem. 261, 11,503-11,511]; (2) the isoaspartyl residue is not recognized unless its alpha-amino group is involved in a carboamide bond; (3) an hydrogen atom on the amide linkage following the isoaspartyl residue is essential for both recognition and catalysis; (4) oligopeptides containing both D-aspartyl and D-isoaspartyl residues are not recognized by this methyltransferase. On the basis of these results, interaction sites between the peptide substrate and the enzyme molecule have been proposed. This paper also reports the first application of fast-atom-bombardment mass spectrometry to the detection of the products of the enzymatic methyl esterification reaction. By this soft ionization technique, the methyl-esterified peptides as well as the corresponding cyclic imides generated during the spontaneous demethylation process have been identified.     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death III: diffusion pulse death zones

This is the third of three papers in which we study a mathematical model of cytoskeleton-induced neuron death. In the first two papers of this suite [Lomasko, T., Clarke, G., Lumsden, C., 2007a. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death I: cell fate arrival times. J. Theor. Biol. 249, 1-17, doi:10.1016/j.jtbi.2007.05.031; Lomasko, T., Clarke, G., Lumsden, C., 2007b. One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability. J. Theor. Biol. 249, 18-28, doi:10.1016/j.jtbi.2007.05.032], we established that the mean-field limit of our model relates the known patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction by diffusible death factors. In the mean-field limit, the spatially variable concentration of diffusing death factor is replaced by a constant average value. Recent empirical advances now permit the actual diffusion of such factors to be followed in intact neuropil. In this paper we therefore extend the model beyond the mean-field limit, to include the diffusion dynamics of death factor bursts released from dying neurons. A range of novel tissue degeneration patterns is observed, for which we confirm and extend the mean-field prediction that sigmoidal patterns of neuron population decay are a principal hallmark of cell death in the presence of death factor release.     

Beneficence, determinism and justice: an engagement with the argument for the genetic selection of intelligence

In 2001, Julian Savulescu wrote an article entitled 'Procreative Beneficence: Why We Should Select the Best Children', in which he argued for the genetic selection of intelligence in children. That article contributes to a debate on whether genetic research on intelligence should be undertaken at all and, if so, should intelligence selection be available to potential parents. As such, the question of intelligence selection relates to wider issues concerning the genetic determinism of behavioural traits, i.e. alcoholism. This article is designed as an engagement in the intelligence selection debate using an analysis of Savulescu's arguments to raise a series of problematic issues in relation to the ethics of parental selection of intelligence. These problematic issues relate to wider assumptions that are made in order to put forward intelligence selection as a viable ethical option. Such assumptions are more generic in character, but still relate to Savulescu's article, concerning issues of genetic determinism, private allocation and inequality, and, finally, individual versus aggregate justice. The conclusion focuses on what the implications are for the question of agency, especially if intelligence selection is allowed.     

Nestling coloration is adjusted to parent visual performance in altricial birds irrespective of assumptions on vision system for Laniidae and owls,a reply to Renoult et al.

We have recently published support to the hypothesis that visual systems of parents could affect nestling detectability and, consequently, influences the evolution of nestling colour designs in altricial birds. We provided comparative evidence of an adjustment of nestling colour designs to the visual system of parents that we have found in a comparative study on 22 altricial bird species. In this issue, however, Renoult et al. ( J. Evol. Biol., 2009 ) question some of the assumptions and statistical approaches in our study. Their argumentation relied on two major points: (1) an incorrect assignment of vision system to four out of 22 sampled species in our study; and (2) the use of an incorrect approach for phylogenetic correction of the predicted associations. Here, we discuss in detail re‐assignation of vision systems in that study and propose alternative interpretation for current knowledge on spectrophotometric data of avian pigments. We reanalysed the data by using phylogenetic generalized least squares analyses that account for the alluded limitations of phylogenetically independent contrasts and, in accordance with the hypothesis, confirmed a significant influence of parental visual system on gape coloration. Our results proved to be robust to the assumptions on visual system evolution for Laniidae and nocturnal owls that Renoult et al. ( J. Evol. Biol., 2009 ) study suggested may have flawed our early findings. Thus, the hypothesis that selection has resulted in increased detectability of nestling by adjusting gape coloration to parental visual systems is currently supported by our comparative data.     

Comparing different ODE modelling approaches for gene regulatory networks

A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [Casey, R., de Jong, H., Gouz, J.-L., 2006. Piecewise-linear models of genetic regulatory networks: equilibria and their stability. J. Math. Biol. 52 (1), 27-56]. A further modelling approach is the use of discrete-time maps [Coutinho, R., Fernandez, B., Lima, R., Meyroneinc, A., 2006. Discrete time piecewise affine models of genetic regulatory networks. J. Math. Biol. 52, 524-570] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.     

Navigating the unknown: model selection in phylogeography. Models of population structure: tools for thinkers

Despite the widespread use and obvious strengths of model-based methods for phylogeographic study, a persistent concern for such analyses is related to the definition of the model itself. The study by Peter et al. (2010) in this issue of Molecular Ecology demonstrates an approach for overcoming such hurdles. The authors were motivated by a deceptively simple goal; they sought to infer whether a population has remained at a low and stable size or has undergone a decline, and certainly there is no shortage of software packages for such a task (e.g., see list of programs in Excoffier & Heckel 2006). However, each of these software packages makes basic assumptions about the underling population (e.g., is the population subdivided or panmictic); these assumptions are explicit to any model-based approach but can bias parameter estimates and produce misleading inferences if the model does not approximate the actual demographic history in a reasonable manner. Rather than guessing which model might be best for analyzing the data (microsatellite data from samples of chimpanzees), Peter et al. (2010) quantify the relative fit of competing models for estimating the population genetic parameters of interest. Complemented by a revealing simulation study, the authors highlight the peril inherent to model-based inferences that lack a statistical evaluation of the fit of a model to the data, while also demonstrating an approach for model selection with broad applicability to phylogeographic analysis.     

The large sample bounds on the principal strata effect with application to a prostate cancer prevention trial

Issues of post-randomization selection bias and truncation-by-death can arise in randomized clinical trials; for example, in a cancer prevention trial, an outcome such as cancer severity is undefined for individuals who do not develop cancer. Restricting analysis to a subpopulation selected after randomization can give rise to biased outcome comparisons. One approach to deal with such issues is to consider the principal strata effect (PSE, or equally, the survivor average causal effect). PSE is defined as the effect of treatment on the outcome among the subpopulation that would have been selected under either treatment arm. Unfortunately, the PSE cannot generally be estimated without the identifying assumptions; however, the bounds can be derived using a deterministic causal model. In this paper, we propose a number of assumptions for deriving the bounds with narrow width. The assumptions and bounds, which differ from those introduced by Zhang and Rubin (2003), are illustrated using data from a randomized prostate cancer prevention trial.     

A critical review of the statisticalist debate

Over the past decade philosophers of biology have discussed whether evolutionary theory is a causal theory or a phenomenological study of evolution based solely on the statistical features of a population. This article reviews this controversy from three aspects, respectively concerning the assumptions, applications, and explanations of evolutionary theory, with a view to arriving at a definite conclusion in each contention. In so doing I also argue that an implicit methodological assumption shared by both sides of the debate, namely the overconfidence in conceptual analysis as a tool to understand the scientific theory, is the real culprit that has both generated the problem and precluded its solution for such a long time.     

REGRESSION ANALYSIS OF NATURAL SELECTION: STATISTICAL INFERENCE AND BIOLOGICAL INTERPRETATION

Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.     

Modeling and E-M estimation of haplotype-specific relative risks from genotype data for a case-control study of unrelated individuals

The US National Cancer Institute has recently sponsored the formation of a Cohort Consortium (http://2002.cancer.gov/scpgenes.htm) to facilitate the pooling of data on very large numbers of people, concerning the effects of genes and environment on cancer incidence. One likely goal of these efforts will be generate a large population-based case-control series for which a number of candidate genes will be investigated using SNP haplotype as well as genotype analysis. The goal of this paper is to outline the issues involved in choosing a method of estimating haplotype-specific risk estimates for such data that is technically appropriate and yet attractive to epidemiologists who are already comfortable with odds ratios and logistic regression. Our interest is to develop and evaluate extensions of methods, based on haplotype imputation, that have been recently described (Schaid et al., Am J Hum Genet, 2002, and Zaykin et al., Hum Hered, 2002) as providing score tests of the null hypothesis of no effect of SNP haplotypes upon risk, which may be used for more complex tasks, such as providing confidence intervals, and tests of equivalence of haplotype-specific risks in two or more separate populations. In order to do so we (1) develop a cohort approach towards odds ratio analysis by expanding the E-M algorithm to provide maximum likelihood estimates of haplotype-specific odds ratios as well as genotype frequencies; (2) show how to correct the cohort approach, to give essentially unbiased estimates for population-based or nested case-control studies by incorporating the probability of selection as a case or control into the likelihood, based on a simplified model of case and control selection, and (3) finally, in an example data set (CYP17 and breast cancer, from the Multiethnic Cohort Study) we compare likelihood-based confidence interval estimates from the two methods with each other, and with the use of the single-imputation approach of Zaykin et al. applied under both null and alternative hypotheses. We conclude that so long as haplotypes are well predicted by SNP genotypes (we use the Rh2 criteria of Stram et al. [1]) the differences between the three methods are very small and in particular that the single imputation method may be expected to work extremely well.     

Dependence among sites in RNA evolution

Although probabilistic models of genotype (e.g., DNA sequence) evolution have been greatly elaborated, less attention has been paid to the effect of phenotype on the evolution of the genotype. Here we propose an evolutionary model and a Bayesian inference procedure that are aimed at filling this gap. In the model, RNA secondary structure links genotype and phenotype by treating the approximate free energy of a sequence folded into a secondary structure as a surrogate for fitness. The underlying idea is that a nucleotide substitution resulting in a more stable secondary structure should have a higher rate than a substitution that yields a less stable secondary structure. This free energy approach incorporates evolutionary dependencies among sequence positions beyond those that are reflected simply by jointly modeling change at paired positions in an RNA helix. Although there is not a formal requirement with this approach that secondary structure be known and nearly invariant over evolutionary time, computational considerations make these assumptions attractive and they have been adopted in a software program that permits statistical analysis of multiple homologous sequences that are related via a known phylogenetic tree topology. Analyses of 5S ribosomal RNA sequences are presented to illustrate and quantify the strong impact that RNA secondary structure has on substitution rates. Analyses on simulated sequences show that the new inference procedure has reasonable statistical properties. Potential applications of this procedure, including improved ancestral sequence inference and location of functionally interesting sites, are discussed.     

Statistical and mechanistic approaches to understanding the gas-phase fragmentation behavior of methionine sulfoxide containing peptides

Recently, we carried out a statistical analysis of a 'tryptic' peptide tandem mass spectrometry database in order to identify sequence-dependent patterns for the gas-phase fragmentation behavior of protonated peptide ions, and to improve the models for peptide fragmentation currently incorporated into peptide sequencing and database search algorithms [Kapp, E. A., Schutz, F., Reid, G. E., Eddes, J. S., Moritz, R. L., O'Hair, R. A. J., Speed, T. P. and Simpson, R. J. Anal. Chem. 2003, 75, 6251-6264.]. Here, we have reexamined this database in order to determine the effect of a common post-translational or process induced modification, methionine oxidation, on the appearance and relative abundances of the product ions formed by low energy collision induced dissociation of peptide ions containing this modification. The results from this study indicate that the structurally diagnostic neutral loss of methane sulfenic acid (CH3SOH, 64Da) from the side chain of methionine sulfoxide residues is the dominant fragmentation process for methionine sulfoxide containing peptide ions under conditions of low proton mobility, i.e., when ionizing proton(s) are sequestered at strongly basic amino acids such as arginine, lysine or histidine. The product ion abundances resulting from this neutral loss were found to be approximately 2-fold greater than those resulting from the cleavage C-terminal to aspartic acid, which has previously been shown to be enhanced under the same conditions. In close agreement with these statistical trends, experimental and theoretical studies, employing synthetic "tryptic" peptides and model methionine sulfoxide containing peptide ions, have determined that the mechanism for enhanced methionine sulfoxide side chain cleavage proceeds primarily via a 'charge remote' process. However, the mechanism for dissociation of the side chain for these ions was observed to change as a function of proton mobility. Finally, the transition state barrier for the charge remote side chain cleavage mechanism is predicted to be energetically more favorable than that for charge remote cleavage C-terminal to aspartic acid.     

Phylogenetic comparative methods: Harnessing the power of species diversity to investigate welfare issues in captive wild animals

This paper reviews a way of investigating health and welfare problems in captive wild animals (e.g., those in zoos, aviaries, aquaria, or aquaculture systems) that has great potential, but to date has been little used: systematically comparing species with few or no health and welfare issues to those more prone to problems. Doing so empirically pinpoints species‐typical welfare risk and protective factors (such as aspects of their natural behavioral biology): information which can then be used to help prevent or remedy problems by suggesting new ways to improve housing and husbandry, and by identifying species intrinsically best suited to captivity. We provide a detailed, step‐by‐step “how to” guide for researchers interested in using these techniques, including guidance on how to statistically control for the inherent similarities shared by related species: an important concern because simple, cross‐species comparisons that do not do this may well fail to meet statistical assumptions of non‐independence. The few relevant studies that have investigated captive wild animals’ welfare problems using this method are described. Overall, such approaches reap value from the great number and diversity of species held in captivity (e.g., the many thousands of species held in zoos); can yield new insights from existing data and published results; render previously intractable welfare questions (such as “do birds need to fly?” or “do Carnivora need to hunt?”) amenable to study; and generate evidence‐based principles for integrating animal welfare into collection planning.     

Stochastic identification of bioreactor process exhibiting input multiplicity

Bioreactor systems involve complex biochemical reactions, which make the systems highly non-linear in nature. Developing model based controllers for such processes require mathematical representations, which are simple, yet capable of capturing the non-linear process characteristics. Continuous bioreactor falls under the class of non-linear systems that exhibit input multiplicity in the optimal operating region, i.e., the operating region where identical outputs are obtained for multiple inputs. Linear modeling techniques are not useful for the referred class of systems for obvious reasons. Even for non-linear modeling techniques, the real bottleneck is to capture the bell-shaped parabolic structure of steady state characteristics exhibited by these systems. The stochastic approach of modeling, which is based on process input/output time-series data, is very useful for this purpose. The aim of this paper is to address the stochastic modeling issues related to bioreactor processes. In this work, three efficient modeling techniques have been studied, viz. block oriented NARMAX structure (Pearson and Pottmann in J Process Control 10:301-315, 2000), Bootstrap structure detection for NARMAX model (Kukreja et al. in Int J Control 77(2):132-143, 2004) and Wavelet-NARMAX model (Billings and Wei in Int J Syst Sci 36(3):137-152, 2005).     

Rethinking the evolution of extant sub‐Saharan African suids (Suidae,Artiodactyla)

Gongora, J., Cuddahee, R. E., do Nascimento, F. F., Palgrave, C. J., Lowden, S., Ho, S. Y. W., Simond, D., Damayanti, C. S., White, D. J., Tay, W. T., Randi, E., Klingel, H., Rodrigues‐Zarate, C. J., Allen, K., Moran, C. & Larson, G. (2011). Rethinking the evolution of extant sub‐Saharan African suids (Suidae, Artiodactyla). —Zoologica Scripta, 40, 327–335. Although African suids have been of scientific interest for over two centuries, their origin, evolution, phylogeography and phylogenetic relationships remain contentious. There has been a long‐running debate concerning the evolution of pigs and hogs (Suidae), particularly regarding the phylogenetic relationships among extant Eurasian and African species of the subfamily Suinae. To investigate these issues, we analysed the mitochondrial and nuclear DNA sequences of extant genera of Suidae from Eurasia and Africa. Molecular phylogenetic analyses revealed that all extant sub‐Saharan African genera form a monophyletic clade separate from Eurasian suid genera, contradicting previous attempts to resolve the Suidae phylogeny. Two major sub‐Saharan African clades were identified, with Hylochoerus and Phacochoerus grouping together as a sister clade to Potamochoerus. In addition, we find that the ancestors of extant African suids may have evolved separately from the ancestors of modern day Sus and Porcula in Eurasia before they colonised Africa. Our results provide a revision of the intergeneric relationships within the family Suidae.     

History of fern systematics at The New York Botanical Garden

The New York Botanical Garden has had only two fern curators: L. M. Underwood (1896–1907) and J. T. Mickel (1969-present). Both curators published milestone manuals on the North American ferns and conducted research on tropical American pteridophytes. After Underwood’s death. J. K. Small, though not a fern curator, published manuals on the ferns of New York and the southeastern United States. The current fern program is a broad one, involving the herbarium, horticulture, and outside support groups.