Reducing the false positive rate in the non-parametric analysis of molecular coevolution

Background  

The strength of selective constraints operating on amino acid sites of proteins has a multifactorial nature. In fact, amino acid sites within proteins coevolve due to their functional and/or structural relationships. Different methods have been developed that attempt to account for the evolutionary dependencies between amino acid sites. Researchers have invested a significant effort to increase the sensitivity of such methods. However, the difficulty in disentangling functional co-dependencies from historical covariation has fuelled the scepticism over their power to detect biologically meaningful results. In addition, the biological parameters connecting linear sequence evolution to structure evolution remain elusive. For these reasons, most of the evolutionary studies aimed at identifying functional dependencies among protein domains have focused on the structural properties of proteins rather than on the information extracted from linear multiple sequence alignments (MSA). Non-parametric methods to detect coevolution have been reported to be especially susceptible to produce false positive results based on the properties of MSAs. However, no formal statistical analysis has been performed to definitively test the differential effects of these properties on the sensitivity of such methods.     

Transition Dependency: A Gene-Gene Interaction Measure for Times Series Microarray Data

Gene-Gene dependency plays a very important role in system biology as it pertains to the crucial understanding of different biological mechanisms. Time-course microarray data provides a new platform useful to reveal the dynamic mechanism of gene-gene dependencies. Existing interaction measures are mostly based on association measures, such as Pearson or Spearman correlations. However, it is well known that such interaction measures can only capture linear or monotonic dependency relationships but not for nonlinear combinatorial dependency relationships. With the invocation of hidden Markov models, we propose a new measure of pairwise dependency based on transition probabilities. The new dynamic interaction measure checks whether or not the joint transition kernel of the bivariate state variables is the product of two marginal transition kernels. This new measure enables us not only to evaluate the strength, but also to infer the details of gene dependencies. It reveals nonlinear combinatorial dependency structure in two aspects: between two genes and across adjacent time points. We conduct a bootstrap-based test for presence/absence of the dependency between every pair of genes. Simulation studies and real biological data analysis demonstrate the application of the proposed method. The software package is available under request.     

Response to technical comment ‘A cautionary note for users of linear diversification dependencies’

The comment by Gamisch (2020) draws the attention of users of the R‐package RPANDA (Methods Ecol. Evol., 7, 2016, 589) on situations when properly interpreting the results of linear diversification dependencies requires caution. Here we provide clarifications to help users interpreting their results when using any type of functional diversification dependencies with time or the environment.     

A New Statistical Method for Mixed Variates Analysis in Epidemiological Research

Epidemiologically oriented research often may not do without observational or only partially controlled studies. In many such situations both qualitative characteristics and quantitative ones are observed. In literature there are different methods of handling such problems. The paper presents a method for analyzing dependencies resp. associations between random variates of any kind. The model concerned fullfills the whole field between analysis of variance, analysis of covariance and contingency table analysis. The method is named MIVA or mixed variates analysis, bases on the class of Conditional Gaussian Distributions of the exponential family and results in a unique system of mixed and unmixed measures of association–of pairwise, partial, multiple and global type. These measures are easy to be estimated and tested on significant deviation from zero. They may be used describing or analyzing dependence structures in many epidemiological studies but also in other fields.     

Incremental mutual information: a new method for characterizing the strength and dynamics of connections in neuronal circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system.     

On Testing an Unspecified Function Through a Linear Mixed Effects Model with Multiple Variance Components

Summary We examine a generalized F ‐test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying‐coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two‐way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F ‐test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome‐wide critical value and p ‐value of a genetic association test in a genome‐wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 10⁸ simulations) and asymptotic approximation may be unreliable and conservative.     

Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.     

Processing multiple non-adjacent dependencies: evidence from sequence learning

Processing non-adjacent dependencies is considered to be one of the hallmarks of human language. Assuming that sequence-learning tasks provide a useful way to tap natural-language-processing mechanisms, we cross-modally combined serial reaction time and artificial-grammar learning paradigms to investigate the processing of multiple nested (A(1)A(2)A(3)B(3)B(2)B(1)) and crossed dependencies (A(1)A(2)A(3)B(1)B(2)B(3)), containing either three or two dependencies. Both reaction times and prediction errors highlighted problems with processing the middle dependency in nested structures (A(1)A(2)A(3)B(3)_B(1)), reminiscent of the 'missing-verb effect' observed in English and French, but not with crossed structures (A(1)A(2)A(3)B(1)_B(3)). Prior linguistic experience did not play a major role: native speakers of German and Dutch-which permit nested and crossed dependencies, respectively-showed a similar pattern of results for sequences with three dependencies. As for sequences with two dependencies, reaction times and prediction errors were similar for both nested and crossed dependencies. The results suggest that constraints on the processing of multiple non-adjacent dependencies are determined by the specific ordering of the non-adjacent dependencies (i.e. nested or crossed), as well as the number of non-adjacent dependencies to be resolved (i.e. two or three). Furthermore, these constraints may not be specific to language but instead derive from limitations on structured sequence learning.     

Electrophysiological measures of regional neural interactive coupling. Linear and non-linear dependence relationships among multiple channel electroencephalographic recordings

Linear spectral coherence (Sklat et al., 1973) measures have been used in the neurosciences to test hypotheses which address the question of whether multiple EEG recording sites are independent or whether they are activated by common sources of neurophysiological activity. This measure is appropriate when regional neural sources interact and thereby electrically activate several recording sites through linear transmission pathways which may or may not be different in their linear transformation properties. However, if the transmission media are non-linear, then interactive dependency is not necessarily revealed by a linear coherence test. Therefore, if common sources are activating EEG recording sites through nonlinear media, evaluating the resulting relationships among the signals recorded from these sites requires a test which reveals the presence of such nonlinear relationships. In neurophysiological applications, a polycoherence cross-spectral measure provides such a test for nonlinear dependency (similar to the linear coherence test) among EEG recording sites. The data requirements and statistical properties of these linear and non-linear measures are described and results of a linear coherence analysis are presented in the context of an EEG pilot study of learning diabled children.     

A Generalization of the GMANOVA-Model

It is shown that in some experimental designs the MANOVA- and the GMANOVA-model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart-distributed estimator for the underlying common covariance matrix is attainable, a test for any s-dimensional linear hypothesis on the model parameters is derived.     

A Novel Segmentation, Mutual Information Network Framework for EEG Analysis of Motor Tasks

Background  

Monitoring the functional connectivity between brain regions is becoming increasingly important in elucidating brain functionality in normal and disease states. Current methods of detecting networks in the recorded electroencephalogram (EEG) such as correlation and coherence are limited by the fact that they assume stationarity of the relationship between channels, and rely on linear dependencies. In contrast to diseases of the brain cortex (e.g. Alzheimer's disease), with motor disorders such as Parkinson's disease (PD) the EEG abnormalities are most apparent during performance of dynamic motor tasks, but this makes the stationarity assumption untenable.     

Technical comment on Condamine et al. (2019): a cautionary note for users of linear diversification dependencies

Condamine et al. (2019; 22: 1900–1912) fitted linear and exponential functions of time‐dependent, diversity‐dependent and temperature‐dependent diversification to investigate diversification dynamics of tetrapod families. Here I highlight potential misinterpretations when using linear diversification dependencies and provide some clarifications.     

Multivariate multiple test procedures based on nonparametric copula estimation

Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high‐dimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. In the present paper, we express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family‐wise error rate (FWER) of multiple test procedures that are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange et al. (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power that can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or ?idák corrections. Finally, we demonstrate an application of the proposed methodology to real‐life data from insurance.     

Common marmosets are sensitive to simple dependencies at variable distances in an artificial grammar

Recognizing that two elements within a sequence of variable length depend on each other is a key ability in understanding the structure of language and music. Perception of such interdependencies has previously been documented in chimpanzees in the visual domain and in human infants and common squirrel monkeys with auditory playback experiments, but it remains unclear whether it typifies primates in general. Here, we investigated the ability of common marmosets (Callithrix jacchus) to recognize and respond to such dependencies. We tested subjects in a familiarization-discrimination playback experiment using stimuli composed of pure tones that either conformed or did not conform to a grammatical rule. After familiarization to sequences with dependencies, marmosets spontaneously discriminated between sequences containing and lacking dependencies (‘consistent’ and ‘inconsistent’, respectively), independent of stimulus length. Marmosets looked more often to the sound source when hearing sequences consistent with the familiarization stimuli, as previously found in human infants. Crucially, looks were coded automatically by computer software, avoiding human bias. Our results support the hypothesis that the ability to perceive dependencies at variable distances was already present in the common ancestor of all anthropoid primates (Simiiformes).     

FR-CAPTCHA: CAPTCHA Based on Recognizing Human Faces

A Completely Automated Public Turing test to tell Computers and Humans Apart (CAPTCHA) is designed to distinguish humans from machines. Most of the existing tests require reading distorted text embedded in a background image. However, many existing CAPTCHAs are either too difficult for humans due to excessive distortions or are trivial for automated algorithms to solve. These CAPTCHAs also suffer from inherent language as well as alphabet dependencies and are not equally convenient for people of different demographics. Therefore, there is a need to devise other Turing tests which can mitigate these challenges. One such test is matching two faces to establish if they belong to the same individual or not. Utilizing face recognition as the Turing test, we propose FR-CAPTCHA based on finding matching pairs of human faces in an image. We observe that, compared to existing implementations, FR-CAPTCHA achieves a human accuracy of 94% and is robust against automated attacks.     

The phenotypic variance within plastic traits under migration-mutation-selection balance

How phenotypic variances of quantitative traits are influenced by the heterogeneity in environment is an important problem in evolutionary biology. In this study, both genetic and environmental variances in a plastic trait under migration-mutation-stabilizing selection are investigated. For this, a linear reaction norm is used to approximate the mapping from genotype to phenotype, and a population of clonal inheritance is assumed to live in a habitat consisting of many patches in which environmental conditions vary among patches and generations. The life cycle is assumed to be selection-reproduction-mutation-migration. Analysis shows that phenotypic plasticity is adaptive if correlations between the optimal phenotype and environment have become established in both space and/or time, and it is thus possible to maintain environmental variance (V(E)) in the plastic trait. Under the special situation of no mutation but maximum migration such that separate patches form an effective single-site habitat, the genotype that maximizes the geometric mean fitness will come to fixation and thus genetic variance (V(G)) cannot be maintained. With mutation and/or restricted migration, V(G) can be maintained and it increases with mutation rate but decreases with migration rate; whereas VE is little affected by them. Temporal variation in environmental quality increases V(G) while its spatial variance decreases V(G). Variation in environmental conditions may decrease the environmental variance in the plastic trait.     

An adjusted coefficient of determination (R2) for generalized linear mixed models in one go

The coefficient of determination (R²) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.     

Multiple trait model combining random regressions for daily feed intake with single measured performance traits of growing pigs

A random regression model for daily feed intake and a conventional multiple trait animal model for the four traits average daily gain on test (ADG), feed conversion ratio (FCR), carcass lean content and meat quality index were combined to analyse data from 1 449 castrated male Large White pigs performance tested in two French central testing stations in 1997. Group housed pigs fed ad libitum with electronic feed dispensers were tested from 35 to 100 kg live body weight. A quadratic polynomial in days on test was used as a regression function for weekly means of daily feed intake and to escribe its residual variance. The same fixed (batch) and random (additive genetic, pen and individual permanent environmental) effects were used for regression coefficients of feed intake and single measured traits. Variance components were estimated by means of a Bayesian analysis using Gibbs sampling. Four Gibbs chains were run for 550 000 rounds each, from which 50 000 rounds were discarded from the burn-in period. Estimates of posterior means of covariance matrices were calculated from the remaining two million samples. Low heritabilities of linear and quadratic regression coefficients and their unfavourable genetic correlations with other performance traits reveal that altering the shape of the feed intake curve by direct or indirect selection is difficult.     

Linear dichroism characteristics of ethidium-and proflavine-supercoiled DNA complexes

A flow linear dichroism technique is utilized to study the unwinding of supercoiled DNA induced by the binding of ethidium bromide (EB) and proflavine (PF) at different ratios r (drug added/DNA base). In the case of either EB or PF bound to linear calf thymus DNA, the reduced linear dichroism signals LD/A (LD: linear dichroism; A: absorbance, both measured at the same wavelength), determined at 258, and 520 or 462 nm (corresponding to contributions predominantly from the partially oriented DNA bases, intercalated EB, or PF, respectively) are nearly independent of drug concentration. In the case of supercoiled DNA, the magnitude of LD/A at 258 nm first increases to a maximum value near r = 0.04-0.05, and then decreases as r is increased further, mimicking the behavior of the sedimentation coefficients, viscosities, and gel electrophoresis patterns measured by other workers at similar values of r. However, LD/A at 520 nm, which is due to DNA-bound EB molecules, is constant within the range of r values of 0.02-0.06 in which the magnitude of LD/A determined at 258 nm due to the DNA bases exhibits a pronounced maximum. In contrast, in the case of PF, the magnitudes of LD/A determined at 258 or 462 nm are characterized by similar dependencies on r, both exhibiting pronounced maxima at r = 0.05; this parallel behavior is expected according to a simple intercalation model in which the DNA bases and drug molecules are stacked on top of one another, and in which both are oriented to similar extents in the flow gradient. The unexpected differences in the dependencies of (LD/A)258 and (LD/A)520 on r in the case of EB bound to supercoiled DNA, are attributed to differences in the net overall alignment of the EB molecules and DNA bases in the flow gradient. The magnitude of the LD signal at 258 nm reflects the overall degree of orientation of the supercoiled DNA molecules that, in turn, depends on their hydrodynamic shapes and sizes; the LD signals characterizing the bound EB molecules may reflect this orientation also, as well as the partial alignment of individual DNA segments containing bound EB molecules.(ABSTRACT TRUNCATED AT 400 WORDS)