Methods for studying allometry in geometric morphometrics: a comparison of performance

Allometry and phylogenetic divergence: Correspondence or incongruence?

The potential connection between trends of within species variation, such as those of allometric change in morphology, and phylogenetic divergence has been a central topic in evolutionary biology for more than a century, including in the context of human evolution. In this study, I focus on size-related shape change in craniofacial proportions using a sample of more than 3200 adult Old World monkeys belonging to 78 species, of which 2942 specimens of 51 species are selected for the analysis. Using geometric morphometrics, I assess whether the divergence in the direction of static allometries increases in relation to phyletic differences. Because both small samples and taxonomic sampling may bias the results, I explore the sensitivity of the main analyses to the inclusion of more or less taxa depending on the choice of a threshold for the minimum sample size of a species. To better understand the impact of sampling error, I also use randomized subsampling experiments in the largest species samples. The study shows that static allometries vary broadly in directions without any evident phylogenetic signal. This variation is much larger than previously found in ontogenetic trajectories of Old World monkeys, but the conclusion of no congruence with phylogenetic divergence is the same. Yet, the effect of sampling error clearly contributes to inaccuracies and tends to magnify the differences in allometric change. Thus, morphometric research at the boundary between micro- and macro-evolution in primates, and more generally in mammals, critically needs very large and representative samples. Besides sampling error, I suggest other non-mutually exclusive explanations for the lack of correspondence between allometric and phylogenetic divergence in Old World monkeys, and also discuss why directions might be more variable in static compared to ontogenetic trajectories. Even if allometric variation may be a poor source of information in relation to phylogeny, the evolution of allometry is a fascinating subject and the study of size-related shape changes remains a fundamental piece of the puzzle to understand morphological variation within and between species in primates and other animals.

Exploring motion using geometric morphometrics in microscopic aquatic invertebrates: 'modes' and movement patterns during feeding in a bdelloid rotifer model species

BACKGROUND

Movement is a defining aspect of animals, but it is rarely studied using quantitative methods in microscopic invertebrates. Bdelloid rotifers are a cosmopolitan class of aquatic invertebrates of great scientific interest because of their ability to survive in very harsh environment and also because they represent a rare example of an ancient lineage that only includes asexually reproducing species. In this class, Adineta ricciae has become a model species as it is unusually easy to culture. Yet, relatively little is known of its ethology and almost nothing on how it behaves during feeding.

METHODS

To explore feeding behaviour in A. ricciae, as well as to provide an example of application of computational ethology in a microscopic invertebrate, we apply Procrustes motion analysis in combination with ordination and clustering methods to a laboratory bred sample of individuals recorded during feeding.

RESULTS

We demonstrate that movement during feeding can be accurately described in a simple two-dimensional shape space with three main 'modes' of motion. Foot telescoping, with the body kept straight, is the most frequent 'mode', but it is accompanied by periodic rotations of the foot together with bending while the foot is mostly retracted.

CONCLUSIONS

Procrustes motion analysis is a relatively simple but effective tool for describing motion during feeding in A. ricciae. The application of this method generates quantitative data that could be analysed in relation to genetic and ecological differences in a variety of experimental settings. The study provides an example that is easy to replicate in other invertebrates, including other microscopic animals whose behavioural ecology is often poorly known.

Utilizing geometric morphometrics to investigate gene function during organ growth: Insights through the study of beetle horn shape allometry

Static allometry is a major component of morphological variation. Much of the literature on the development of allometry investigates how functional perturbations of diverse pathways affect the relationship between trait size and body size. Often, this is done with the explicit objective to identify developmental mechanisms that enable the sensing of organ size and the regulation of relative growth. However, changes in relative trait size can also be brought about by a range of other distinctly different developmental processes, such as changes in patterning or tissue folding, yet standard univariate biometric approaches are usually unable to distinguish among alternative explanations. Here, we utilize geometric morphometrics to investigate the degree to which functional genetic manipulations known to affect the size of dung beetle horns also recapitulate the effect of horn shape allometry. We reasoned that the knockdown phenotypes of pathways governing relative growth should closely resemble shape variation induced by natural allometric variation. In contrast, we predicted that if genes primarily affect alternative developmental processes, knockdown effects should align poorly with shape allometry. We find that the knockdown effects of several genes (e.g., doublesex, Foxo) indeed closely aligned with shape allometry, indicating that their corresponding pathways may indeed function primarily in the regulation of relative trait growth. In contrast, other knockdown effects (e.g., Distal-less, dachs) failed to align with allometry, implicating these pathways in potentially scaling-independent processes. Our findings moderate the interpretation of studies focusing on trait length and highlight the usefulness of multivariate approaches to study allometry and phenotypic plasticity.

Integrative species delimitation in the common ophiuroid Ophiothrix angulata (Echinodermata: Ophiuroidea): insights from COI, ITS2, arm coloration, and geometric morphometrics

Ophiothrix angulata (Say, 1825) is one of the most common and well-known ophiuroids in the Western Atlantic, with a wide geographic and bathymetric range. The taxonomy of this species has been controversial for a century because of its high morphological variability. Here we integrate information from DNA sequence data, color patterns, and geometric morphometrics to assess species delimitation and geographic differentiation in O. angulata. We found three deeply divergent mtDNA-COI clades (K2P 17.0-27.9%). ITS2 nuclear gene and geometric morphometrics of dorsal and ventral arm plates differentiate one of these lineages, as do integrative species delineation analyses, making this a confirmed candidate species.

Complexities of recapitulating polygenic effects in natural populations: replication of genetic effects on wing shape in artificially selected and wild-caught populations of Drosophila melanogaster

Identifying the genetic architecture of complex traits is important to many geneticists, including those interested in human disease, plant and animal breeding, and evolutionary genetics. Advances in sequencing technology and statistical methods for genome-wide association studies have allowed for the identification of more variants with smaller effect sizes, however, many of these identified polymorphisms fail to be replicated in subsequent studies. In addition to sampling variation, this failure to replicate reflects the complexities introduced by factors including environmental variation, genetic background, and differences in allele frequencies among populations. Using Drosophila melanogaster wing shape, we ask if we can replicate allelic effects of polymorphisms first identified in a genome-wide association studies in three genes: dachsous, extra-macrochaete, and neuralized, using artificial selection in the lab, and bulk segregant mapping in natural populations. We demonstrate that multivariate wing shape changes associated with these genes are aligned with major axes of phenotypic and genetic variation in natural populations. Following seven generations of artificial selection along the dachsous shape change vector, we observe genetic differentiation of variants in dachsous and genomic regions containing other genes in the hippo signaling pathway. This suggests a shared direction of effects within a developmental network. We also performed artificial selection with the extra-macrochaete shape change vector, which is not a part of the hippo signaling network, but showed a largely shared direction of effects. The response to selection along the emc vector was similar to that of dachsous, suggesting that the available genetic diversity of a population, summarized by the genetic (co)variance matrix (G), influenced alleles captured by selection. Despite the success with artificial selection, bulk segregant analysis using natural populations did not detect these same variants, likely due to the contribution of environmental variation and low minor allele frequencies, coupled with small effect sizes of the contributing variants.

Dimensions of Morphological Integration

Over several generations of evolutionary and developmental biologists, ever since Olson and Miller’s pioneering work of the 1950’s, the concept of “morphological integration” as applied to Gaussian representations $$N(\mu ,\Sigma )$$ N ( μ , Σ ) of morphometric data has been a focus equally of methodological innovation and methodological perplexity. Reanalysis of a century-old example from Sewall Wright shows how some fallacies of distance analysis by correlations can be avoided by careful matching of the distance rosters involved to a different multivariate approach, factor analysis. I reinterpret his example by restoring the information (means and variances) ignored by the correlation matrix, while confirming what Wright called “special size factors” by a different technique, inspection of the concentration matrix $$\Sigma ^{-1}.$$ Σ - 1 . In geometric morphometrics (GMM), data accrue instead as Cartesian coordinates of labelled points; nevertheless, just as in the Wright example, statistical manipulations do better when they reconsider the normalizations that went into the generation of those coordinates. Here information about both $$\mu $$ μ and $$\Sigma ,$$ Σ , the means and the variances/covariances, can be preserved via the Boas coordinates (Procrustes shape coordinates without the size adjustment) that protect the role of size per se as an essential explanatory factor while permitting the analyst to acknowledge the realities of animal anatomy and its trajectories over time or size in the course of an analysis. A descriptive quantity for this purpose is suggested, the correlation of vectorized $$\mu $$ μ against the first eigenvector of $$\Sigma $$ Σ for the Boas coordinates. The paper reanalyzes two GMM data sets from this point of view. In one, the classic Vilmann rodent neurocranial growth data, a description of integration can be aligned with the purposes of evolutionary and developmental biology by a graphical exegesis based mainly in the loadings of the first Boas principal component. There results a multiplicity of morphometric patterns, some homogeneous and others characterized by gradients. In the other, a Vienna data set comprising human midsagittal skull sections mostly sampled along curves, a further integrated feature emerges, thickening of the calvaria, that requires a reparametrization and a modified thin plate spline graphic distinct from the digitized configurations per se. This new GMM protocol fulfills the original thrust of Olson & Miller’s (Evolution 5:325–338, 1951) “$$\rho $$ ρ F-groups,” the alignment of statistical and biological explanatory guidance, while respecting the enormously greater range of morphological descriptors afforded by well-designed landmark/semilandmark configurations.