A common effect size metric used to quantify the outcome of experiments for ecological meta-analysis is the response ratio (RR): the log proportional change in the means of a treatment and control ...group. Estimates of the variance of RR are also important for meta-analysis because they serve as weights when effect sizes are averaged and compared. The variance of an effect size is typically a function of sampling error; however, it can also be influenced by study design. Here, I derive new variances and covariances for RR for several often-encountered experimental designs: when the treatment and control means are correlated; when multiple treatments have a common control; when means are based on repeated measures; and when the study has a correlated factorial design, or is multivariate. These developments are useful for improving the quality of data extracted from studies for meta-analysis and help address some of the common challenges meta-analysts face when quantifying a diversity of experimental designs with the response ratio.
The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic ...traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.
Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors exist in both the transfer function matrix and the response vector, which have a great influence on ...the accuracy of the identification, especially at the low frequency and high noise. Although the Total Least Squares (TLS) method can consider the errors in the transfer function matrix and the response vector, the problem of unequal precision between them has not been properly solved. In this article, the Weighted Total Least Squares (WTLS) method for load identification is presented. First, the variance–covariance matrices are constructed using stochastic information, which can consider the unequal precision of the data and make the solution less biased and more precise. Then, Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition of the transfer function matrix. To validate the performance of the WTLS method under different noise levels, a load identification simulation with four excitation loads on a plate and a load identification experiment with three excitation loads on a steel plate were studied. The results show that when the noise levels of the transfer function and the response are different, the accuracy of the TLS solution is poor. Especially when the noise levels are high, the identification deviations are large. The WTLS method considers the unequal noise levels using the weight matrices, which provides more stable load estimates at different noise levels. And the identification deviations are greatly reduced compared to the TLS method.
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•A Weighted Total Least Squares method for load identification is proposed.•Unequal precision of transfer function and response is considered.•Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition.•Research on low frequency load identification method under high noise level.
The aim of this study is the determination of the best fit ellipsoid to given points by quaternions. The problem of the fitting ellipsoid is frequently encountered in image processing, computer ...games, medicine, engineering and science applications, geodesy, etc. The ellipsoid fitting problem is the process of determining the ellipsoid that best fits a given set of points in 3D. In the fitting process, it is generally done over two models. The first of these is the algebraic method and the second one is orthogonal (geometric) method. In this study, we tried to solve the problem of algebraic and orthogonal ellipsoid fitting based on Euler angles for the first time over quaternions. The superiority of quaternions over Euler rotation angles is well known. In addition, the variance-covariance matrix of the parameters of the fitted ellipsoid will also be calculated. Numerical applications show that the proposed method can be used successfully.
Two symmetric matrices underlie our understanding of microevolutionary change. The first is the matrix of nonlinear selection gradients (γ) which describes the individual fitness surface. The second ...is the genetic variance–covariance matrix (G) that influences the multivariate response to selection. A common approach to the empirical analysis of these matrices is the element‐by‐element testing of significance, and subsequent biological interpretation of pattern based on these univariate and bivariate parameters. Here, I show why this approach is likely to misrepresent the genetic basis of quantitative traits, and the selection acting on them in many cases. Diagonalization of square matrices is a fundamental aspect of many of the multivariate statistical techniques used by biologists. Applying this, and other related approaches, to the analysis of the structure of γ and G matrices, gives greater insight into the form and strength of nonlinear selection, and the availability of genetic variance for multiple traits.
Research on behavioural syndromes (consistent individual differences in suites of correlated behaviours) requires formal statistical methods to describe and compare syndrome structures. We detail the ...shortcomings of current methods aimed at describing variation in behavioural syndromes, such as multiple pairwise correlations and principal components analysis (PCA). In their place we propose an alternative statistical framework involving: (1) calculation of trait variance–covariance and correlation matrices within each data set; (2) statistical evaluation of specific hypotheses regarding how behaviours covary within a behavioural syndrome; and (3) statistical comparison of behavioural covariances across data sets using structural equation modelling (SEM). Given their unfamiliarity to most behavioural ecologists, we illustrate these methods using an already published data set for two groups of populations of three-spined stickleback, Gasterosteus aculeatus, living in ponds with and without fish predators. Previous analyses suggested a lack of behavioural syndrome structure for stickleback that lived in the absence of fish predators. However, by evaluating a priori hypotheses of how behaviours might covary using SEM, we were able to demonstrate that the two types of populations differed specifically in covariance patterns for aggression, exploration of novel food sources and altered environments, but not for exploration of novel environments and activity. Such detailed inferences cannot readily be made based on conventional statistical approaches alone, and so the methods we outline here should become standard in studies concerning the evolution of behavioural syndromes within and between populations.
Multivariate meta-analysis (MMA) is a powerful statistical technique that can provide more reliable and informative results than traditional univariate meta-analysis, which allows for comparisons ...across outcomes with increased statistical power. However, implementing appropriate statistical methods for MMA can be challenging due to the requirement of various specific tasks in data preparation. The metavcov package aims for model preparation, data visualization, and missing data solutions to provide tools for different methods that cannot be found in accessible software. It provides sufficient constructs for estimating coefficients from other well-established packages. For model preparation, users can compute both effect sizes of various types and their variance-covariance matrices, including correlation coefficients, standardized mean difference, mean difference, log odds ratio, log risk ratio, and risk difference. The package provides a tool to plot the confidence intervals for the primary studies and the overall estimates. When specific effect sizes are missing, single imputation is available in the model preparation stage; a multiple imputation method is also available for pooling the results in a statistically principled manner from models of users' choice. The package is demonstrated in two real data applications and a simulation study to assess methods for handling missing data.
Many data sets in biology, medicine, and other biostatistical areas deal with matrix‐valued time series. The case of a single univariate time series is very well developed in the literature; and ...single multi‐variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi‐variate time series data. Explicit expressions for a matrix autoregressive model along with its cross‐autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application.
The recent demographic transitions to lower mortality and fertility rates in most human societies have led to changes and even quick reversals in phenotypic selection pressures. This can only result ...in evolutionary change if the affected traits are heritable, but changes in environmental conditions may also lead to subsequent changes in the genetic variance and covariance (the G matrix) of traits. It currently remains unclear if there have been concomitant changes in the G matrix of life-history traits following the demographic transition. Using 300 years of genealogical data from Finland, we found that four key life-history traits were heritable both before and after the demographic transition. The estimated heritabilities allow a quantifiable genetic response to selection during both time periods, thus facilitating continued evolutionary change. Further, the G matrices remained largely stable but revealed a trend for an increased additive genetic variance and thus evolutionary potential of the population after the transition. Our results demonstrate the validity of predictions of evolutionary change in human populations even after the recent dramatic environmental change, and facilitate predictions of how our biology interacts with changing environments, with implications for global public health and demography.
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