A highly conserved ontogenetic limb allometry and its evolutionary significance in the adaptive radiation of Anolis lizards

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing [Formula: see text] matrices

Theory predicts that the additive genetic covariance ([Formula: see text]) matrix determines a population's short-term (in)ability to respond to directional selection-evolvability in the Hansen-Houle sense-which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

No longer in doubt: Discovery of a second specimen corroborates the validity of Anolis incredulus Garrido and Moreno 1998 (Reptilia, Iguania)

The species Anolis incredulus was proposed based on a single, poorly preserved specimen from the Sierra Maestra (mountain range) of southeastern Cuba. As its name suggests, this species was considered likely to raise doubts when it was first proposed, and it has been explicitly treated by some recent authors as a species inquirenda (a species of doubtful identity). Here we report on a second specimen of Anolis incredulus discovered in the amphibian and reptile collection of the National Museum of Natural History (Smithsonian Institution) that was collected more than 100 years before the holotype. We describe this specimen in detail and compare it both with the description of the holotype of A. incredulus and with presumed closely related Cuban species, providing evidence that it matches closely with the former and is distinct from the latter, thus corroborating the status of A. incredulus as a valid species. We also score and measure the specimen for sets of morphological characters to make inferences about its phylogenetic relationships and ecology (structural habitat use). Our results indicate that Anolis incredulus is likely a member of a clade of mostly Cuban twig-anole species and that it is a member of the twig ecomorph category, although its reported green coloration suggests either an erroneous ecomorph assignment or a difference in color from that of most other species of Cuban twig anoles.

Diversification of the ruminant skull along an evolutionary line of least resistance

Clarifying how microevolutionary processes scale to macroevolutionary patterns is a fundamental goal in evolutionary biology, but these analyses, requiring comparative datasets of population-level variation, are limited. By analyzing a previously published dataset of 2859 ruminant crania, we find that variation within and between ruminant species is biased by a highly conserved mammalian-wide allometric pattern, CREA (craniofacial evolutionary allometry), where larger species have proportionally longer faces. Species with higher morphological integration and species more biased toward CREA have diverged farther from their ancestors, and Ruminantia as a clade diversified farther than expected in the direction of CREA. Our analyses indicate that CREA acts as an evolutionary "line of least resistance" and facilitates morphological diversification due to its alignment with the browser-grazer continuum. Together, our results demonstrate that constraints at the population level can produce highly directional patterns of phenotypic evolution at the macroevolutionary scale. Further research is needed to explore how CREA has been exploited in other mammalian clades.

Beyond facial width-to-height ratios: bizygomatic width is highly sexually dimorphic when adjusting for allometry

A large and ever-growing literature implicates male facial width-to-height ratio (bizygomatic width divided by facial height) as a secondary sexual trait linked to numerous physical and psychological perceptions. However, this research is based entirely on the premise that bizygomatic width is sexually dimorphic, which recent research has called into question. Unfortunately, statisticians for the last 125 years have noted that morphological ratio measurements may engender spurious correlations and biased effect-size estimates. In the current study, we find that bizygomatic width is highly sexually dimorphic (equivalent d = 1.39), even after adjusting for 92 allometric measurements, including multiple facial height and other craniofacial measurements (equivalent d = 1.07) in a sample of 6068 men and women. By contrast, facial width-to-height ratio (fWHR) measurements demonstrated a statistical pattern consistent with the age-old argument that morphological ratio measurements may engender spurious correlations and biased effect-size estimates. Thus, when avoiding facial ratio measurements and adjusting for allometry in craniofacial measures, we found strong support for a key premise in the human evolutionary and behavioural sciences that bizygomatic width exhibits male-biased sexual dimorphism.

Detecting (non)parallel evolution in multidimensional spaces: angles, correlations and eigenanalysis

Parallelism between evolutionary trajectories in a trait space is often seen as evidence for repeatability of phenotypic evolution, and angles between trajectories play a pivotal role in the analysis of parallelism. However, properties of angles in multidimensional spaces have not been widely appreciated by biologists. To remedy this situation, this study provides a brief overview on geometric and statistical aspects of angles in multidimensional spaces. Under the null hypothesis that trajectory vectors have no preferred directions (i.e. uniform distribution on hypersphere), the angle between two independent vectors is concentrated around the right angle, with a more pronounced peak in a higher-dimensional space. This probability distribution is closely related to t- and beta distributions, which can be used for testing the null hypothesis concerning a pair of trajectories. A recently proposed method with eigenanalysis of a vector correlation matrix can be connected to the test of no correlation or concentration of multiple vectors, for which simple test procedures are available in the statistical literature. Concentration of vectors can also be examined by tools of directional statistics such as the Rayleigh test. These frameworks provide biologists with baselines to make statistically justified inferences for (non)parallel evolution.

A highly conserved ontogenetic limb allometry and its evolutionary significance in the adaptive radiation of Anolis lizards

Diversifications often proceed along highly conserved, evolutionary trajectories. These patterns of covariation arise in ontogeny, which raises the possibility that adaptive morphologies are biased towards trait covariations that resemble growth trajectories. Here, we test this prediction in the diverse clade of Anolis lizards by investigating the covariation of embryonic growth of 13 fore- and hindlimb bones in 15 species, and compare these to the evolutionary covariation of these limb bones across 267 Anolis species. Our results demonstrate that species differences in relative limb length are established already at hatching, and are resulting from both differential growth and differential sizes of cartilaginous anlagen. Multivariate analysis revealed that Antillean Anolis share a common ontogenetic allometry that is characterized by positive allometric growth of the long bones relative to metapodial and phalangeal bones. This major axis of ontogenetic allometry in limb bones deviated from the major axis of evolutionary allometry of the Antillean Anolis and the two clades of mainland Anolis lizards. These results demonstrate that the remarkable diversification of locomotor specialists in Anolis lizards are accessible through changes that are largely independent from ontogenetic growth trajectories, and therefore likely to be the result of modifications that manifest at the earliest stages of limb development.