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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. 

It is undeniable that novel 2D devices and heterostructures will have a lasting impact on the advancement of future technologies. However, the inherent instability of many exfoliated van der Waals (vdW) materials is a well-known hurdle yet to be overcome. Thus, the sustained interest in exfoliated vdW materials underscores the importance of understanding the mechanisms of sample degradation to establish proactive protective measures. Here, the impact of prolonged synchrotron-based X-ray beam exposure on exfoliated flakes of two contemporary vdW materials, ${\mathrm{N}\mathrm{i}\mathrm{P}\mathrm{S}}_3$and $\alpha$- ${\mathrm{R}\mathrm{u}\mathrm{C}\mathrm{l}}_3$, is explored using resonant inelastic X-ray scattering (RIXS) and total fluorescence yield X-ray absorption spectroscopy (XAS). In ${\mathrm{N}\mathrm{i}\mathrm{P}\mathrm{S}}_3$, the resulting RIXS and XAS spectra show a suppression, then vanishing, of NiS₆multiplet excitations coupled with an upward shift of the peak energy of the XAS as a function of X-ray dose. In $\alpha$- ${\mathrm{R}\mathrm{u}\mathrm{C}\mathrm{l}}_3$, the signs of beam damage from the RIXS spectra are less evident. However, the post-experiment characterization of both materials using Raman spectroscopy exhibits signals of an amorphous and disordered system compared to pristine flakes; in addition, energy-dispersive X-ray spectroscopy of ${\mathrm{N}\mathrm{i}\mathrm{P}\mathrm{S}}_3$shows evidence of ligand vacancies. As synchrotron radiation is fast becoming a required probe to study 2D vdW materials, these findings lay the groundwork for the development of future protective measures for synchrotron-based prolonged X-ray beam exposure, as well as for X-ray free electron laser. 

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.