A Combined Invariant Test for a Null Variance Ratio

This paper investigates the properties of a test that combines the Wald and LMPI (locally most powerful invariant) tests of variance components in unbalanced mixed models. The combined test statistic is easily computed and its null distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the degree of imbalance of the design. Numerical methods are used to show that the approximation is accurate over a wide range of conditions and that the efficiency of the combined test, relative to the power envelope, is satisfactorily high overall.     

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.     

fullfact: an R package for the analysis of genetic and maternal variance components from full factorial mating designs

Full factorial breeding designs are useful for quantifying the amount of additive genetic, nonadditive genetic, and maternal variance that explain phenotypic traits. Such variance estimates are important for examining evolutionary potential. Traditionally, full factorial mating designs have been analyzed using a two‐way analysis of variance, which may produce negative variance values and is not suited for unbalanced designs. Mixed‐effects models do not produce negative variance values and are suited for unbalanced designs. However, extracting the variance components, calculating significance values, and estimating confidence intervals and/or power values for the components are not straightforward using traditional analytic methods. We introduce fullfact – an R package that addresses these issues and facilitates the analysis of full factorial mating designs with mixed‐effects models. Here, we summarize the functions of the fullfact package. The observed data functions extract the variance explained by random and fixed effects and provide their significance. We then calculate the additive genetic, nonadditive genetic, and maternal variance components explaining the phenotype. In particular, we integrate nonnormal error structures for estimating these components for nonnormal data types. The resampled data functions are used to produce bootstrap‐t confidence intervals, which can then be plotted using a simple function. We explore the fullfact package through a worked example. This package will facilitate the analyses of full factorial mating designs in R, especially for the analysis of binary, proportion, and/or count data types and for the ability to incorporate additional random and fixed effects and power analyses.     

The Method of Unweighted Means in Unbalanced Analysis of Variance

For factorial experiments with unbalanced data the method of unweighted means is an alternate method of analysis which is computationally simpler than likelihood ratio based F-tests. The quality of the null approximation to the F-distribution of the statistic for the method of unweighted means and the power of this test relative to the likelihood ratio test are discussed. Recommendations are made of when in the course of data analysis the superior operating characteristics of the likelihood ratio test may not outweigh the computational simplicity of the method of unweighted means test.     

QST–FST comparisons with unbalanced half‐sib designs

Q_ST, a measure of quantitative genetic differentiation among populations, is an index that can suggest local adaptation if Q_ST for a trait is sufficiently larger than the mean F_ST of neutral genetic markers. A previous method by Whitlock and Guillaume derived a simulation resampling approach to statistically test for a difference between Q_ST and F_ST, but that method is limited to balanced data sets with offspring related as half‐sibs through shared fathers. We extend this approach (i) to allow for a model more suitable for some plant populations or breeding designs in which offspring are related through mothers (assuming independent fathers for each offspring; half‐sibs by dam); and (ii) by explicitly allowing for unbalanced data sets. The resulting approach is made available through the R package QstFstComp.     

Simulation‐based evaluation of the performance of the F test in a linear multilevel model setting with sparseness at the level of the primary unit

In a linear multilevel model, significance of all fixed effects can be determined using F tests under maximum likelihood (ML) or restricted maximum likelihood (REML). In this paper, we demonstrate that in the presence of primary unit sparseness, the performance of the F test under both REML and ML is rather poor. Using simulations based on the structure of a data example on ceftriaxone consumption in hospitalized children, we studied variability, type I error rate and power in scenarios with a varying number of secondary units within the primary units. In general, the variability in the estimates for the effect of the primary unit decreased as the number of secondary units increased. In the presence of singletons (i.e., only one secondary unit within a primary unit), REML consistently outperformed ML, although even under REML the performance of the F test was found inadequate. When modeling the primary unit as a random effect, the power was lower while the type I error rate was unstable. The options of dropping, regrouping, or splitting the singletons could solve either the problem of a high type I error rate or a low power, while worsening the other. The permutation test appeared to be a valid alternative as it outperformed the F test, especially under REML. We conclude that in the presence of singletons, one should be careful in using the F test to determine the significance of the fixed effects, and propose the permutation test (under REML) as an alternative.     

Efficacy of DEET and non‐DEET‐based insect repellents against bites of Simulium damnosum vectors of onchocerciasis

Coping strategies including smoke screens are used against nuisance bites of Simulium damnosum Theobald (Diptera:Simuliidae) in onchocerciasis endemic communities. To find more effective alternatives, the efficacy of commercially available N,N‐diethyl‐3‐methylbenzamide (DEET) products with active concentrations of 9.5, 13, 25, 50 and 98.1–100% and ‘NO MAS,’ (active component: para‐menthane‐3,8‐diol and lemon grass oil) were tested at Bui‐Agblekame, Ghana. A Latin square study design was implemented using eight groups of two vector collectors each, who used repellents (treatment), mineral oil or nothing each day until the end of the study. Flies were caught and their numbers each hour recorded using the standard methods for onchocerciasis transmission studies. T‐tests were used to compare the mean duration of protection and a one‐way analysis of variance controlling for catchers and repellents was performed. Tukey's test was used to compare protection by repellents and mineral oil. The highest percentage protection was 80.8% by NO MAS and the least 42.5% by the 13% DEET product. The period of absolute protection was 5 h by NO MAS and 1 h by 50% DEET product. No significant increase in protection was offered beyond 25% active DEET products and no significance was observed in terms of catcher × repellent effect (F = 1.731, d.f. = 48, P = 0.209).     

Pattern‐oriented modelling of population genetic structure

Although several statistical approaches can be used to describe patterns of genetic variation and infer stochastic differentiation, selective responses, or interruptions of gene flow due to physical or environmental barriers, it is worthwhile to note that similar processes, controlled by several parameters in theoretical models, frequently give rise to similar patterns. Here, we develop a Pattern‐Oriented Modelling (POM) approach that allows us to determine how a complex set of parameters potentially driving empirical genetic differentiation among populations generate alternative scenarios that can be fitted to observed data. We generated 10 000 random combinations of parameters related to population size, gene flow and response to gradients (both driven by dispersal and selection) in a spatially explicit model, and analysed simulated patterns with F_ST statistics and mean correlograms using Moran's I spatial autocorrelation coefficients. These statistics were compared with observed patterns for a tree species endemic to the Brazilian Cerrado. For a best match with observed F_ST (equal to 0.182), the important parameters driving simulated scenario are mainly related to population structure, including low population size with closed populations (low N_m), strong distance decay of gene flow, in addition to a strong effect of the initial variance of allele frequencies. These scenarios present a low autocorrelation of allele frequencies. Best matching of correlograms, on the other hand, appears in simulations with a large population size, high N_m and low population differentiation and F_ST (as well as more gene flow). Thus, targeting the two statistics (correlograms and F_ST) shows that best matches with empirical data with two distinct sets of parameters in the simulations, because observed patterns involve both a relatively high F_ST and significant autocorrelation. This conflict can be resolved by assuming that initial variance in allele frequencies can be interpreted as reflecting deep‐time historical variation and evolutionary dynamics of allele frequencies, creating a relatively high level of population differentiation, whereas current patterns in gene flow creates spatial autocorrelation. This make sense in terms of the previous knowledge on population differentiation in D. alata, especially if patterns are explained by a combination of isolation‐by‐distance and allelic surfing due to range expansion after the last glacial maximum. This reveals the potential for more complex applications of POM in population genetics. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1152–1161.     

Order‐restricted Scores Test for the Evaluation of Population‐based Case–control Studies when the Genetic Model is Unknown

The Cochran–Armitage (CA) linear trend test for proportions is often used for genotype‐based analysis of candidate gene association. Depending on the underlying genetic mode of inheritance, the use of model‐specific scores maximises the power. Commonly, the underlying genetic model, i.e. additive, dominant or recessive mode of inheritance, is a priori unknown. Association studies are commonly analysed using permutation tests, where both inference and identification of the underlying mode of inheritance are important. Especially interesting are tests for case–control studies, defined by a maximum over a series of standardised CA tests, because such a procedure has power under all three genetic models. We reformulate the test problem and propose a conditional maximum test of scores‐specific linear‐by‐linear association tests. For maximum‐type, sum and quadratic test statistics the asymptotic expectation and covariance can be derived in a closed form and the limiting distribution is known. Both the limiting distribution and approximations of the exact conditional distribution can easily be computed using standard software packages. In addition to these technical advances, we extend the area of application to stratified designs, studies involving more than two groups and the simultaneous analysis of multiple loci by means of multiplicity‐adjusted p‐values for the underlying multiple CA trend tests. The new test is applied to reanalyse a study investigating genetic components of different subtypes of psoriasis. A new and flexible inference tool for association studies is available both theoretically as well as practically since already available software packages can be easily used to implement the suggested test procedures.     

Genome‐wide selection components analysis in a fish with male pregnancy

A major goal of evolutionary biology is to identify the genome‐level targets of natural and sexual selection. With the advent of next‐generation sequencing, whole‐genome selection components analysis provides a promising avenue in the search for loci affected by selection in nature. Here, we implement a genome‐wide selection components analysis in the sex role reversed Gulf pipefish, Syngnathus scovelli. Our approach involves a double‐digest restriction‐site associated DNA sequencing (ddRAD‐seq) technique, applied to adult females, nonpregnant males, pregnant males, and their offspring. An F_ST comparison of allele frequencies among these groups reveals 47 genomic regions putatively experiencing sexual selection, as well as 468 regions showing a signature of differential viability selection between males and females. A complementary likelihood ratio test identifies similar patterns in the data as the F_ST analysis. Sexual selection and viability selection both tend to favor the rare alleles in the population. Ultimately, we conclude that genome‐wide selection components analysis can be a useful tool to complement other approaches in the effort to pinpoint genome‐level targets of selection in the wild.     

NPQ(T): a chlorophyll fluorescence parameter for rapid estimation and imaging of non‐photochemical quenching of excitons in photosystem‐II‐associated antenna complexes

In photosynthesis, light energy is absorbed by light‐harvesting complexes and used to drive photochemistry. However, a fraction of absorbed light is lost to non‐photochemical quenching (NPQ) that reflects several important photosynthetic processes to dissipate excess energy. Currently, estimates of NPQ and its individual components (q_E, q_I, q_Z and q_T) are measured from pulse‐amplitude‐modulation (PAM) measurements of chlorophyll fluorescence yield and require measurements of the maximal yield of fluorescence in fully dark‐adapted material (F_m), when NPQ is assumed to be negligible. Unfortunately, this approach requires extensive dark acclimation, often precluding widespread or high‐throughput use, particularly under field conditions or in imaging applications, while introducing artefacts when F_m is measured in the presence of residual photodamaged centres. To address these limitations, we derived and characterized a new set of parameters, NPQ_(T), and its components that can be (1) measured in a few seconds, allowing for high‐throughput and field applications; (2) does not require full relaxation of quenching processes and thus can be applied to photoinhibited materials; (3) can distinguish between NPQ and chloroplast movements; and (4) can be used to image NPQ in plants with large leaf movements. We discuss the applications benefits and caveats of both approaches.     

On Distance‐Based Permutation Tests for Between‐Group Comparisons

Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.     

gener: a server‐based analysis of pollen pool structure

The server‐based program gener performs the two‐generation analysis of pollen flow for data consisting of mother/offspring arrays using genetic markers. The gener program decomposes the genetic variance sampled by maternal individuals within and among pollen pool components of genetic variance and is accessible from http://dyerlab.bio.vcu.edu . These estimates are used to construct the test statistic, Φ_ft , whose significance is tested via permutation. The Φ_ft statistic can subsequently be used to quantify genetic effective pollen donor population size (N_ep), effective mating area and dispersal distance. Furthermore, the gener program can calculate Φ_ft values for all pairs of substrata within the data set.     

Predicting the distribution of non‐vagile taxa: a response to McNyset and Blackburn (2006) and re‐evaluation of Stockman et al. (2006)

This paper addresses the issues raised by McNyset and Blackburn (2006 ) in their response to Stockman et al. (2006 ). Re‐evaluation of our published GARP analyses by McNyset and Blackburn showed that a much improved ecological niche model is obtained for predicting the distribution of the trapdoor spider genus Promyrmekiaphila in central/northern California. The improved niche model results in a substantially reduced omission error rate and a predictive model comparable to models obtained using other methods (GLM and BIOCLIM). However, the improved GARP models have a high commission error rate (> 0.75); consequently, the inferences regarding difficulties in modelling non‐vagile taxa drawn by Stockman et al. remain valid. Finally, we discuss other relatively minor criticisms of our study raised by McNyset and Blackburn and issues related to the peer review of our original paper.     

Nonparametric All‐Pairs Multiple Comparisons

Nonparametric all‐pairs multiple comparisons based on pairwise rankings can be performed in the one‐way design with the Steel‐Dwass procedure. To apply this test, Wilcoxon's rank sum statistic is calculated for all pairs of groups; the maximum of the rank sums is the test statistic. We provide exact calculations of the asymptotic critical values (and P‐values, respectively) even for unbalanced designs. We recommend this asymptotic method whenever large sample sizes are present. For small sample sizes we recommend the use of the new statistic according to Baumgartner , Weiss , and Schindler (1998, Biometrics 54 , 1129–1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant procedure can be less conservative and, according to simulation results, more powerful than the original Steel‐Dwass procedure. We illustrate the methods with a practical data set.     

Anion Doping: A New Strategy for Developing High‐Performance Perovskite‐Type Cathode Materials of Solid Oxide Fuel Cells

Overcoming the sluggish activity of cathode materials is critical to realizing the wide‐spread application of intermediate‐temperature solid oxide fuel cells. Herein, a new way is reported to tune the performance of perovskite‐type materials as oxygen reduction electrodes by embedding anions (F^?) in oxygen sites. The obtained perovskite oxyfluorides SrFeO_{3?σ ?δ} F_σ and SrFe_0.9Ti_0.1O_{3?σ ?δ} F_σ (σ = 0.05 and 0.10) show improved electrocatalytic activity compared to their parent oxides, achieving area specific resistance values of 0.875, 0.393, and 0.491 Ω cm² for SrFeO_3?δ , SrFeO_2.95?δ F_0.05, and SrFeO_2.90?δ F_0.10, respectively, at 600 °C in air. Such improved performance is a result of the improved bulk diffusion and surface exchange properties due to anion doping. Moreover, favorable stability in performance is also demonstrated for the F^? anion‐doped perovskites as oxygen reduction electrodes at 650 °C for a test period of ≈200 h. A combination of anion doping and cation doping may provide a highly attractive strategy for the future development of cathode materials.     

genodive version 3.0: Easy‐to‐use software for the analysis of genetic data of diploids and polyploids

genodive version 3.0 is a user‐friendly program for the analysis of population genetic data. This version presents a major update from the previous version and now offers a wide spectrum of different types of analyses. genodive has an intuitive graphical user interface that allows direct manipulation of the data through transformation, imputation of missing data, and exclusion and inclusion of individuals, population and/or loci. Furthermore, genodive seamlessly supports 15 different file formats for importing or exporting data from or to other programs. One major feature of genodive is that it supports both diploid and polyploid data, up to octaploidy (2n = 8x) for some analyses, but up to hexadecaploidy (2n = 16x) for other analyses. The different types of analyses offered by genodive include multiple statistics for estimating population differentiation (φ_ST, F_ST, F?_ST, G_ST, G?_ST, G??_ST, D_est, R_ST, ρ), analysis of molecular variance‐based K‐means clustering, Hardy–Weinberg equilibrium, hybrid index, population assignment, clone assignment, Mantel test, Spatial Autocorrelation, 23 ways of calculating genetic distances, and both principal components and principal coordinates analyses. A unique feature of genodive is that it can also open data sets with nongenetic variables, for example environmental data or geographical coordinates that can be included in the analysis. In addition, genodive makes it possible to run several external programs (lfmm , structure , instruct and vegan ) directly from its own user interface, avoiding the need for data reformatting and use of the command line. genodive is available for computers running Mac OS X 10.7 or higher and can be downloaded freely from: http://www.patrickmeirmans.com/software .     

An Extended ANOVA F‐Test with Applications to the Heterogeneity Problem in Meta‐Analysis

The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly for balanced homoscedastic models. By simulation, the tests are shown to attain acceptable significance levels and high power even in data that do not follow the usual ANOVA model. An important application of the tests is given by the heterogeneity questions concerning the treatment effects across studies in meta‐analysis.     

Enhanced Photovoltaic Performance of Amorphous Donor–Acceptor Copolymers Based on Fluorine‐Substituted Benzodioxocyclohexene‐Annelated Thiophene

Donor–acceptor (D‐A) type π‐conjugated copolymers with crystalline behavior have been extensively investigated as donor semiconductors in organic photovoltaics (OPVs). On the other hand, the development of high‐performance amorphous donor materials is still behind. The amorphous donor copolymer DTS‐C₀(F₂) consisting of dithieno[3,2‐b:2′,3′‐d]silole ( DTS ) donor unit and the recently developed fluorine‐substituted naphtho[2,3‐c]thiophene‐4,9‐dione ( C₀(F₂) ) acceptor unit shows moderate photovoltaic performance upon blending with PC₇₁BM. In this work, to enhance the hole‐transporting characteristics, a 3‐hexylthiophene ( HT ) spacer unit is integrated into the conjugated backbone, resulting in a new amorphous copolymer DTS‐HT‐C₀(F₂) . The strong electron‐accepting nature of C₀(F₂) allows the introduction of the HT spacer without affecting the frontier orbital energies and thus the D‐A character. Without using solvent additives and thermal annealing, OPVs based on DTS‐HT‐C₀(F₂) and [6,6]‐phenyl‐C71‐butyric acid methyl ester PC₇₁BM show an improved power conversion efficiency of 9.12%. Investigation of the device physics unambiguously reveals that the hole mobility of the copolymer in the blend is increased by an order of magnitude by the introduction of HT , while keeping an amorphous film nature, leading to higher short‐circuit current density and fill factor. These results demonstrate the realization of high‐performance OPVs based on amorphous active layers.