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Abstract Due to the hierarchical structure of the tree of life, closely related species often resemble each other more than distantly related species; a pattern termed phylogenetic signal. Numerous univariate statistics have been proposed as measures of phylogenetic signal for single phenotypic traits, but the study of phylogenetic signal for multivariate data, as is common in modern biology, remains challenging. Here, we introduce a new method to explore phylogenetic signal in multivariate phenotypes. Our approach decomposes the data into linear combinations with maximal (or minimal) phylogenetic signal, as measured by Blomberg’s K. The loading vectors of these phylogenetic components or K-components can be biologically interpreted, and scatterplots of the scores can be used as a low-dimensional ordination of the data that maximally (or minimally) preserves phylogenetic signal. We present algebraic and statistical properties, along with 2 new summary statistics, KA and KG, of phylogenetic signal in multivariate data. Simulation studies showed that KA and KG have higher statistical power than the previously suggested statistic Km⁢u⁢l⁢t, especially if phylogenetic signal is low or concentrated in a few trait dimensions. In 2 empirical applications to vertebrate cranial shape (crocodyliforms and papionins), we found statistically significant phylogenetic signal concentrated in a few trait dimensions. The finding that phylogenetic signal can be highly variable across the dimensions of multivariate phenotypes has important implications for current maximum likelihood approaches to phylogenetic signal in multivariate data. 

Abstract Evolutionary biology has long striven to understand why some lineages diversify exceptionally while others do not. Most studies have focused on how extrinsic factors can promote differences in diversification dynamics, but a clade’s intrinsic modularity and integration can also catalyze or restrict its evolution. Here, we integrate geometric morphometrics, phylogenetic comparative methods and visualizations of covariance to infer the presence of distinct modules in the body plan of Characiformes, an ecomorphologically diverse fish radiation. Strong covariances reveal a cranial module, and more subtle patterns support a statistically significant subdivision of the postcranium into anterior (precaudal) and posterior (caudal) modules. We uncover substantial covariation among cranial and postcranial landmarks, indicating body-wide evolutionary integration as lineages transition between compressiform and fusiform body shapes. A novel method of matrix subdivision reveals that within- and among-module covariation contributes substantially to the overall eigenstructure of characiform morphospace, and that both phenomena led to biologically important divergence among characiform lineages. Functional integration between the cranium and post-cranial skeleton appears to have allowed lineages to optimize the aspect ratio of their bodies for locomotion, while the capacity for independent change in the head, body and tail likely eased adaptation to diverse dietary and hydrological regimes. These results reinforce a growing consensus that modularity and integration synergize to promote diversification. 

Abstract Geometric morphometric (GM) tools are essential for meaningfully quantifying and understanding patterns of variation in complex traits like shape. In this field, the breadth of answerable questions has grown dramatically in recent years through the development of new analyses and increased computational efficiency.In this note, we describe the ways in whichgeomorph, a widely usedRpackage for quantifying and analysing GM data, has grown with the field.We presentgeomorph v4.0and describe the ways in which this version has dramatically improved upon previous versions. We also present a new graphical user interface for easy implementation,gmShiny.These contributions positiongeomorphto be the primary tool for GM analyses, particularly those employing a phylogenetic comparative approach. 

Abstract It has become common in evolutionary biology to characterize phenotypes multivariately. However, visualizing macroevolutionary trends in multivariate datasets requires appropriate ordination methods.In this paper we describe phylogenetically aligned component analysis (PACA): a new ordination approach that aligns phenotypic data with phylogenetic signal. Unlike phylogenetic principal component analysis (Phy‐PCA), which finds an alignment of a principal eigenvector that is independent of phylogenetic signal, PACA maximizes variation in directions that describe phylogenetic signal, while simultaneously preserving the Euclidean distances among observations in the data space.We demonstrate with simulated and empirical examples that with PACA, it is possible to visualize the trend in phylogenetic signal in multivariate data spaces, irrespective of other signals in the data. In conjunction with Phy‐PCA, one can visualize both phylogenetic signal and trends in data independent of phylogenetic signal.Phylogenetically aligned component analysis can distinguish between weak phylogenetic signals and strong signals concentrated in only a portion of all data dimensions. We provide empirical examples that emphasize the difference. Use of PACA in studies focused on phylogenetic signal should enable much more precise description of the phylogenetic signal, as a result.Overall, PACA will return a projection that shows the most phylogenetic signal in the first few components, irrespective of other signals in the data. By comparing Phy‐PCA and PACA results, one may glean the relative importance of phylogenetic and other (ecological) signals in the data.