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Abstract Evolutionary biologists characterize macroevolutionary trends of phenotypic change across the tree of life using phylogenetic comparative methods. However, within‐species variation can complicate such investigations. For this reason, procedures for incorporating nonstructured (random) intraspecific variation have been developed.Likewise, evolutionary biologists seek to understand microevolutionary patterns of phenotypic variation within species, such as sex‐specific differences or allometric trends. Additionally, there is a desire to compare such within‐species patterns across taxa, but current analytical approaches cannot be used to interrogate within‐species patterns while simultaneously accounting for phylogenetic non‐independence. Consequently, deciphering how intraspecific trends evolve remains a challenge.Here we introduce an extended phylogenetic generalized least squares (E‐PGLS) procedure which facilitates comparisons of within‐species patterns across species while simultaneously accounting for phylogenetic non‐independence.Our method uses an expanded phylogenetic covariance matrix, a hierarchical linear model, and permutation methods to obtain empirical sampling distributions and effect sizes for model effects that can evaluate differences in intraspecific trends across species for both univariate and multivariate data, while conditioning them on the phylogeny.The method has appropriate statistical properties for both balanced and imbalanced data. Additionally, the procedure obtains evolutionary covariance estimates that reflect those from existing approaches for nonstructured intraspecific variation. Importantly, E‐PGLS can detect differences in structured (i.e. microevolutionary) intraspecific patterns across species when such trends are present. Thus, E‐PGLS extends the reach of phylogenetic comparative methods into the intraspecific comparative realm, by providing the ability to compare within‐species trends across species while simultaneously accounting for shared evolutionary history. 

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.