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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 The evolution of miniaturization can result in dramatic alterations of morphology, physiology, and behavior; however, the effects of miniaturization on sexual dimorphism remain largely unknown. Here we investigate how miniaturization influences patterns of sexual size dimorphism (SSD) in geckos. Measuring 1,875 individuals from 131 species, we characterized patterns of SSD relative to body size across two families. We found that miniaturized species were more female biased than non-miniaturized species. Additionally, one family that contained many miniaturized species (Sphaerodactylidae) displayed allometric patterns in SSD with body size, where larger species were male biased and smaller species were more female biased. Smaller species in this lineage also produced proportionally larger eggs. By contrast, another family containing few miniaturized species (Phyllodactylidae) displayed a more isometric trend. Together, these observations are consistent with the hypothesis that selection for increased reproductive success in small species of Sphaerodactylidae results in female-biased SSD in these taxa, which in turn drives the positive SSD allometry observed in this lineage. Thus, selection for increased miniaturization in the clade may be offset by selection on maintaining a female size in smaller taxa that ensures reproductive success. 

Abstract Sexual dimorphism describes phenotypic differences between the sexes; the most prominent of which is sexual size dimorphism (SSD). Rensch’s rule (RR) is an allometric trend in which SSD increases in male-larger taxa and decreases in female-larger ones. Covariation between a trait and overall size within and across species can both be affected by sexual and natural selection. Thus, intraspecific allometric variation could influence the expression of RR. Here we used computer simulations to dissect how RR emerges under specific allometric patterns of intraspecific sexual differentiation in a trait. We found that sexual differentiation in static allometric slopes is the main determinant of RR. Based on our findings, RR and its converse can manifest in both body size and other traits. As a realistic showcase, we also examined RR and static allometry of different body parts in Mediterranean green lizards to establish whether intraspecific and evolutionary allometry are linked. Here, we identified RR and its converse for different traits, where the amount of sexual differentiation in static allometric slopes within species had a significant contribution to RR. Integrating the simulations and the empirical case we corroborate that sexual differentiation in static allometric slopes is a major parameter affecting evolutionary allometry. 

Abstract Species living in distinct habitats often experience unique ecological selective pressures, which can drive phenotypic divergence. However, how ecophenotypic patterns are affected by allometric trends and trait integration levels is less well understood. Here we evaluate the role of allometry in shaping body size and body form diversity in Pristurus geckos utilizing differing habitats. We found that patterns of allometry and integration in body form were distinct in species with different habitat preferences, with ground-dwelling Pristurus displaying the most divergent allometric trend and high levels of integration. There was also strong concordance between intraspecific allometry across individuals and evolutionary allometry among species, revealing that differences in body form among individuals were predictive of evolutionary changes across the phylogeny at macroevolutionary scales. This suggested that phenotypic evolution occurred along allometric lines of least resistance, with allometric trajectories imposing a strong influence on the magnitude and direction of size and shape changes across the phylogeny. When viewed in phylomorphospace, the largest rock-dwelling species were most similar to the smallest ground-dwelling species, and vice versa. Thus, in Pristurus, phenotypic evolution along the differing habitat-based allometric trajectories resulted in similar body forms at differing body sizes in distinct ecological habitats.