Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications

Left-right leaf asymmetry in decussate and distichous phyllotactic systems

Leaves in plants with spiral phyllotaxy exhibit directional asymmetries, such that all the leaves originating from a meristem of a particular chirality are similarly asymmetric relative to each other. Models of auxin flux capable of recapitulating spiral phyllotaxis predict handed auxin asymmetries in initiating leaf primordia with empirically verifiable effects on superficially bilaterally symmetric leaves. Here, we extend a similar analysis of leaf asymmetry to decussate and distichous phyllotaxy. We found that our simulation models of these two patterns predicted mirrored asymmetries in auxin distribution in leaf primordia pairs. To empirically verify the morphological consequences of asymmetric auxin distribution, we analysed the morphology of a tomato sister-of-pin-formed1a (sopin1a) mutant, entire-2, in which spiral phyllotaxy consistently transitions to a decussate state. Shifts in the displacement of leaflets on the left and right sides of entire-2 leaf pairs mirror each other, corroborating predicted model results. We then analyse the shape of more than 800 common ivy (Hedera helix) and more than 3000 grapevine (Vitis and Ampelopsis spp.) leaf pairs and find statistical enrichment of predicted mirrored asymmetries. Our results demonstrate that left-right auxin asymmetries in models of decussate and distichous phyllotaxy successfully predict mirrored asymmetric leaf morphologies in superficially symmetric leaves.This article is part of the themed issue 'Provocative questions in left-right asymmetry'.

Multivariate sexual selection on male tegmina in wild populations of sagebrush crickets, Cyphoderris strepitans (Orthoptera: Haglidae)

Although the strength and form of sexual selection on song in male crickets have been studied extensively, few studies have examined selection on the morphological structures that underlie variation in males' song, particularly in wild populations. Geometric morphometric techniques were used to measure sexual selection on the shape, size and symmetry of both top and bottom tegmina in wild populations of sagebrush crickets, a species in which nuptial feeding by females imposes an unambiguous phenotypic marker on males. The size of the tegmina negatively covaried with song dominant frequency and positively covaried with song pulse duration. Sexual selection was more intense on the bottom tegmen, conceivably because it interacts more freely with the subtegminal airspace, which may play a role in song amplification. An expanded coastal/subcostal region was one of the phenotypes strongly favoured by disruptive selection on the bottom tegmen, an adaptation that may form a more effective seal with the thorax to prevent noise cancellation. Directional selection also favoured increased symmetry in tegminal shape. Assuming more symmetrical males are better able to buffer against developmental noise, the song produced by these males may make them more attractive to females. Despite the strong stabilizing selection documented previously on the dominant frequency of the song, stabilizing selection on the resonator that regulates dominant frequency was surprisingly absent. Nonetheless, wing morphology had an important influence on song structure and appears to be subject to significant linear and nonlinear sexual selection through female mate choice.

[Symmetry is beauty - or is it? The rise and fall of fluctuating asymmetry]

Fluctuating asymmetry is the stochastic, minor deviation from perfect symmetry in bilaterally symmetrical organisms. It reflects the limit of developmental precision. Such a precision can be influenced by various factors, both internal (genetic mutations, stochastic variation at every levels of development) and external (environmental influences). Fluctuating asymmetry has receive an extreme attention for the past few decades, that culminated in the 90s: it has been used as an estimator of heterozygosity, fitness, environmental stress, and widely applied to human biology, sociobiology and psychology before being more or less discredited in the early 2000s. The reasons for such an extreme popularity and then disgrace are discussed here. Far from suggesting to abandon the study of fluctuating asymmetry, we indicate some of the most promising research avenues. ‡.

Size, shape, and form: concepts of allometry in geometric morphometrics

Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould-Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley-Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

Size, shape, and form: concepts of allometry in geometric morphometrics

Allometry refers to the size-related changes of morphological traits and remains an essential concept for the study of evolution and development. This review is the first systematic comparison of allometric methods in the context of geometric morphometrics that considers the structure of morphological spaces and their implications for characterizing allometry and performing size correction. The distinction of two main schools of thought is useful for understanding the differences and relationships between alternative methods for studying allometry. The Gould–Mosimann school defines allometry as the covariation of shape with size. This concept of allometry is implemented in geometric morphometrics through the multivariate regression of shape variables on a measure of size. In the Huxley–Jolicoeur school, allometry is the covariation among morphological features that all contain size information. In this framework, allometric trajectories are characterized by the first principal component, which is a line of best fit to the data points. In geometric morphometrics, this concept is implemented in analyses using either Procrustes form space or conformation space (the latter also known as size-and-shape space). Whereas these spaces differ substantially in their global structure, there are also close connections in their localized geometry. For the model of small isotropic variation of landmark positions, they are equivalent up to scaling. The methods differ in their emphasis and thus provide investigators with flexible tools to address specific questions concerning evolution and development, but all frameworks are logically compatible with each other and therefore unlikely to yield contradictory results.

Cranial symmetry in baleen whales (Cetacea, Mysticeti) and the occurrence of cranial asymmetry throughout cetacean evolution

Odontoceti and Mysticeti (toothed and baleen whales) originated from Eocene archaeocetes that had evolved from terrestrial artiodactyls. Cranial asymmetry is known in odontocetes that can hear ultrasound (>20,000 Hz) and has been linked to the split function of the nasal passage in breathing and vocalization. Recent results indicate that archaeocetes also had asymmetric crania. Their asymmetry has been linked to directional hearing in water, although hearing frequencies are still under debate. Mysticetes capable of low-frequency and infrasonic hearing (<20 Hz) are assumed to have symmetric crania. This study aims to resolve whether mysticete crania are indeed symmetric and whether mysticete cranial symmetry is plesiomorphic or secondary. Cranial shape was analyzed applying geometric morphometrics to three-dimensional (3D) cranial models of fossil and modern mysticetes, Eocene archaeocetes, modern artiodactyls, and modern odontocetes. Statistical tests include analysis of variance, principal components analysis, and discriminant function analysis. Results suggest that symmetric shape difference reflects general trends in cetacean evolution. Asymmetry includes significant fluctuating and directional asymmetry, the latter being very small. Mysticete crania are as symmetric as those of terrestrial artiodactyls and archaeocetes, without significant differences within Mysticeti. Odontocete crania are more asymmetric. These results indicate that (1) all mysticetes have symmetric crania, (2) archaeocete cranial asymmetry is not conspicuous in most of the skull but may yet be conspicuous in the rostrum, (3) directional cranial asymmetry is an odontocete specialization, and (4) directional cranial asymmetry is more likely related to echolocation than hearing.