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Abstract Parallel laser photogrammetry (PLP), which consists of attaching two or three parallel laser beams at a known inter‐beam distance to a camera, can be used to collect morphological measurements of organisms noninvasively. The lasers project onto the photo being taken, and because the inter‐beam distance is known, they act as a scale for image analysis programs like ImageJ. Traditionally, this method has been used to measure larger morphological traits (e.g., limb length, crown‐rump length) to serve as proxies for overall body size, whereas applications to smaller anatomical features remain limited. To that end, we used PLP to measure the testes of 18 free‐living mantled howler monkeys (Alouatta palliata)at La Selva Biological Station, Costa Rica. We tested whether this method could reliably measure this relatively small and globular morphology, and whether it could detect differences among individuals. We tested reliability in three ways: within‐photo (coefficient of variation [CV] = 4.7%), between‐photo (CV = 5.5%), and interobserver (intraclass correlation = 0.92). We found an average volume of 36.2 cm³and a range of 16.4–54.4 cm³, indicating variation in testes size between individuals. Furthermore, these sizes are consistent with a previous study that collected measurements by hand, suggesting that PLP is a useful method for making noninvasive measurements of testes. 

We are in a modern biodiversity crisis that will restructure community compositions and ecological functions globally. Large mammals, important contributors to ecosystem function, have been affected directly by purposeful extermination and indirectly by climate and land-use changes, yet functional turnover is rarely assessed on a global scale using metrics based on functional traits. Using ecometrics, the study of functional trait distributions and functional turnover, we examine the relationship between vegetation cover and locomotor traits for artiodactyl and carnivoran communities. We show that the ability to detect a functional relationship is strengthened when locomotor traits of both primary consumers (artiodactyls, n = 157 species) and secondary consumers (carnivorans, n = 138 species) are combined into one trophically integrated ecometric model. Overall, locomotor traits of 81% of communities accurately estimate vegetation cover, establishing the advantage of trophically integrated ecometric models over single-group models (58 to 65% correct). We develop an innovative approach within the ecometrics framework, using ecometric anomalies to evaluate mismatches in model estimates and observed values and provide more nuance for understanding relationships between functional traits and vegetation cover. We apply our integrated model to five paleontological sites to illustrate mismatches in the past and today and to demonstrate the utility of the model for paleovegetation interpretations. Observed changes in community traits and their associated vegetations across space and over time demonstrate the strong, rapid effect of environmental filtering on community traits. Ultimately, our trophically integrated ecometric model captures the cascading interactions between taxa, traits, and changing environments. 

Abstract This article investigates a form of rank deficiency in phenotypic covariance matrices derived from geometric morphometric data, and its impact on measures of phenotypic integration. We first define a type of rank deficiency based on information theory then demonstrate that this deficiency impairs the performance of phenotypic integration metrics in a model system. Lastly, we propose methods to treat for this information rank deficiency. Our first goal is to establish how the rank of a typical geometric morphometric covariance matrix relates to the information entropy of its eigenvalue spectrum. This requires clear definitions of matrix rank, of which we define three: the full matrix rank (equal to the number of input variables), the mathematical rank (the number of nonzero eigenvalues), and the information rank or “effective rank” (equal to the number of nonredundant eigenvalues). We demonstrate that effective rank deficiency arises from a combination of methodological factors—Generalized Procrustes analysis, use of the correlation matrix, and insufficient sample size—as well as phenotypic covariance. Secondly, we use dire wolf jaws to document how differences in effective rank deficiency bias two metrics used to measure phenotypic integration. The eigenvalue variance characterizes the integration change incorrectly, and the standardized generalized variance lacks the sensitivity needed to detect subtle changes in integration. Both metrics are impacted by the inclusion of many small, but nonzero, eigenvalues arising from a lack of information in the covariance matrix, a problem that usually becomes more pronounced as the number of landmarks increases. We propose a new metric for phenotypic integration that combines the standardized generalized variance with information entropy. This metric is equivalent to the standardized generalized variance but calculated only from those eigenvalues that carry nonredundant information. It is the standardized generalized variance scaled to the effective rank of the eigenvalue spectrum. We demonstrate that this metric successfully detects the shift of integration in our dire wolf sample. Our third goal is to generalize the new metric to compare data sets with different sample sizes and numbers of variables. We develop a standardization for matrix information based on data permutation then demonstrate that Smilodon jaws are more integrated than dire wolf jaws. Finally, we describe how our information entropy-based measure allows phenotypic integration to be compared in dense semilandmark data sets without bias, allowing characterization of the information content of any given shape, a quantity we term “latent dispersion”. [Canis dirus; Dire wolf; effective dispersion; effective rank; geometric morphometrics; information entropy; latent dispersion; modularity and integration; phenotypic integration; relative dispersion.] 

Abstract The field of comparative morphology has entered a new phase with the rapid generation of high-resolution three-dimensional (3D) data. With freely available 3D data of thousands of species, methods for quantifying morphology that harness this rich phenotypic information are quickly emerging. Among these techniques, high-density geometric morphometric approaches provide a powerful and versatile framework to robustly characterize shape and phenotypic integration, the covariances among morphological traits. These methods are particularly useful for analyses of complex structures and across disparate taxa, which may share few landmarks of unambiguous homology. However, high-density geometric morphometrics also brings challenges, for example, with statistical, but not biological, covariances imposed by placement and sliding of semilandmarks and registration methods such as Procrustes superimposition. Here, we present simulations and case studies of high-density datasets for squamates, birds, and caecilians that exemplify the promise and challenges of high-dimensional analyses of phenotypic integration and modularity. We assess: (1) the relative merits of “big” high-density geometric morphometrics data over traditional shape data; (2) the impact of Procrustes superimposition on analyses of integration and modularity; and (3) differences in patterns of integration between analyses using high-density geometric morphometrics and those using discrete landmarks. We demonstrate that for many skull regions, 20–30 landmarks and/or semilandmarks are needed to accurately characterize their shape variation, and landmark-only analyses do a particularly poor job of capturing shape variation in vault and rostrum bones. Procrustes superimposition can mask modularity, especially when landmarks covary in parallel directions, but this effect decreases with more biologically complex covariance patterns. The directional effect of landmark variation on the position of the centroid affects recovery of covariance patterns more than landmark number does. Landmark-only and landmark-plus-sliding-semilandmark analyses of integration are generally congruent in overall pattern of integration, but landmark-only analyses tend to show higher integration between adjacent bones, especially when landmarks placed on the sutures between bones introduces a boundary bias. Allometry may be a stronger influence on patterns of integration in landmark-only analyses, which show stronger integration prior to removal of allometric effects compared to analyses including semilandmarks. High-density geometric morphometrics has its challenges and drawbacks, but our analyses of simulated and empirical datasets demonstrate that these potential issues are unlikely to obscure genuine biological signal. Rather, high-density geometric morphometric data exceed traditional landmark-based methods in characterization of morphology and allow more nuanced comparisons across disparate taxa. Combined with the rapid increases in 3D data availability, high-density morphometric approaches have immense potential to propel a new class of studies of comparative morphology and phenotypic integration.