Dean C. Adams

Geometric morphometrics: Ten years of progress following the ‘revolution’

Abstract The analysis of shape is a fundamental part of much biological research. As the field of statistics developed, so have the sophistication of the analysis of these types of data. This lead to multivariate morphometrics in which suites of measurements were analyzed together using canonical variates analysis, principal components analysis, and related methods. In the 1980s, a fundamental change began in the nature of the data gathered and analyzed. This change focused on the coordinates of landmarks and the geometric information about their relative positions. As a by‐product of such an approach, results of multivariate analyses could be visualized as configurations of landmarks back in the original space of the organism rather than only as statistical scatter plots. This new approach, called “geometric morphometrics”;, had benefits that lead Rohlf and Marcus (1993) to proclaim a “revolution”; in morphometrics. In this paper, we briefly update the discussion in that paper and summarize the advances in the ten years since the paper by Rohlf and Marcus. We also speculate on future directions in morphometric analysis.

geomorph: an r package for the collection and analysis of geometric morphometric shape data

Summary 1. Many ecological and evolutionary studies seek to explain patterns of shape variation and its covariation with other variables. Geometric morphometrics is often used for this purpose, where a set of shape variables are obtained from landmark coordinates following a Procrustes superimposition. 2. We introduce geomorph: a software package for performing geometric morphometric shape analysis in the R statistical computing environment. 3. Geomorph provides routines for all stages of landmark-based geometric morphometric analyses in two and three-dimensions. It is an open source package to read, manipulate, and digitize landmark data, generate shape variables via Procrustes analysis for points, curves and surfaces, perform statistical analyses of shape variation and covariation, and to provide graphical depictions of shapes and patterns of shape variation. An important contribution of geomorph is the ability to perform Procrustes superimposition on landmark points, as well as semilandmarks from curves and surfaces. 4. A wide range of statistical methods germane to testing ecological and evolutionary hypotheses of shape variation are provided. These include standard multivariate methods such as principal components analysis, and approaches for multivariate regression and group comparison. Methods for more specialized analyses, such as for assessing shape allometry, comparing shape trajectories, examining morphological integration, and for assessing phylogenetic signal, are also included. 5. Several functions are provided to graphically visualize results, including routines for examining variation in shape space, visualizing allometric trajectories, comparing specific shapes to one another and for plotting phylogenetic changes in morphospace. 6. Finally, geomorph participates to make available advanced geometric morphometric analyses through the R statistical computing platform.

Evolutionary convergence of body shape and trophic morphology in cichlids from Lake Tanganyika

A recent phylogenetic analysis of mitochondrial DNA sequences from eretmodine cichlids from Lake Tanganyika indicated independent origins of strikingly similar trophic specializations, such as dentition characters. Because genetic lineages with similar trophic morphologies were not monophyletic, but instead were grouped with lineages with different trophic phenotypes, raises the question of whether trophic morphology covaries with additional morphological characters. Here, we quantified morphological variation in body shape and trophically associated traits among eretmodine cichlids using linear measurements, meristic counts and landmark‐based geometric morphometrics. A canonical variates analysis (CVA) delineated groups consistent with dentition characters. Multivariate regression and partial least squares analyses indicated that body shape was significantly associated with trophic morphology. When the phylogenetic relationships among taxa were taken into account using comparative methods, the covariation of body shape and trophic morphology persisted, indicating that phylogenetic relationships were not wholly responsible for the observed pattern. We hypothesize that trophic ecology may be a key factor promoting morphological differentiation, and postulate that similar body shape and feeding structures have evolved multiple times in independent lineages, enabling taxa to invade similar adaptive zones.

Are rates of species diversification correlated with rates of morphological evolution

Some major evolutionary theories predict a relationship between rates of proliferation of new species (species diversification) and rates of morphological divergence between them. However, this relationship has not been rigorously tested using phylogeny-based approaches. Here, we test this relationship with morphological and phylogenetic data from 190 species of plethodontid salamanders. Surprisingly, we find that rates of species diversification and morphological evolution are not significantly correlated, such that rapid diversification can occur with little morphological change, and vice versa. We also find that most clades have undergone remarkably similar patterns of morphological evolution (despite extensive sympatry) and that those relatively novel phenotypes are not associated with rapid diversification. Finally, we find a strong relationship between rates of size and shape evolution, which has not been previously tested.

A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data.

Phylogenetic signal is the tendency for closely related species to display similar trait values due to their common ancestry. Several methods have been developed for quantifying phylogenetic signal in univariate traits and for sets of traits treated simultaneously, and the statistical properties of these approaches have been extensively studied. However, methods for assessing phylogenetic signal in high-dimensional multivariate traits like shape are less well developed, and their statistical performance is not well characterized. In this article, I describe a generalization of the K statistic of Blomberg et al. that is useful for quantifying and evaluating phylogenetic signal in highly dimensional multivariate data. The method (K(mult)) is found from the equivalency between statistical methods based on covariance matrices and those based on distance matrices. Using computer simulations based on Brownian motion, I demonstrate that the expected value of K(mult) remains at 1.0 as trait variation among species is increased or decreased, and as the number of trait dimensions is increased. By contrast, estimates of phylogenetic signal found with a squared-change parsimony procedure for multivariate data change with increasing trait variation among species and with increasing numbers of trait dimensions, confounding biological interpretations. I also evaluate the statistical performance of hypothesis testing procedures based on K(mult) and find that the method displays appropriate Type I error and high statistical power for detecting phylogenetic signal in high-dimensional data. Statistical properties of K(mult) were consistent for simulations using bifurcating and random phylogenies, for simulations using different numbers of species, for simulations that varied the number of trait dimensions, and for different underlying models of trait covariance structure. Overall these findings demonstrate that K(mult) provides a useful means of evaluating phylogenetic signal in high-dimensional multivariate traits. Finally, I illustrate the utility of the new approach by evaluating the strength of phylogenetic signal for head shape in a lineage of Plethodon salamanders.

A general framework for the analysis of phenotypic trajectories in evolutionary studies.

Many evolutionary studies require an understanding of phenotypic change. However, while analyses of phenotypic variation across pairs of evolutionary levels (populations or time steps) are well established, methods for testing hypotheses that compare evolutionary sequences across multiple levels are less developed. Here we describe a general analytical procedure for quantifying and comparing patterns of phenotypic evolution. The phenotypic evolution of a lineage is defined as a trajectory across a set of evolutionary levels in a multivariate phenotype space. Attributes of these trajectories (their size, direction, and shape), are quantified, and statistically compared across pairs of taxa, and a summary statistic is used to determine the extent to which patterns of phenotypic evolution are concordant across multiple taxa. This approach provides a direct quantitative description of how patterns of phenotypic evolution differ, as well as a statistical assessment of the degree of repeatability in the evolutionary responses to selection among taxa. We describe how this approach can quantify phenotypic trajectories from many ecological and evolutionary processes, whose data encode multivariate characterizations of the phenotype, including: phenotypic plasticity, ecological selection, ontogeny and growth, local adaptation, and biomechanics. We illustrate the approach by examining the phenotypic evolution of several fossil lineages of Globorotalia.

ANALYSIS OF TWO-STATE MULTIVARIATE PHENOTYPIC CHANGE IN ECOLOGICAL STUDIES

Analyses of two-state phenotypic change are common in ecological research. Some examples include phenotypic changes due to phenotypic plasticity between two environments, changes due to predator/non-predator character shifts, character displacement via competitive interactions, and patterns of sexual dimorphism. However, methods for analyzing phenotypic change for multivariate data have not been rigorously developed. Here we outline a method for testing vectors of phenotypic change in terms of two important attributes: the magnitude of change (vector length) and the direction of change described by trait covariation (angular difference between vectors). We describe a permutation procedure for testing these attributes, which allows non-targeted sources of variation to be held constant. We provide examples that illustrate the importance of considering vector attributes of phenotypic change in biological studies, and we demonstrate how greater inference can be made than by evaluating variance components with MANOVA alone. Finally, we consider how our method may be extended to more complex data.

Natural selection drives patterns of lake–stream divergence in stickleback foraging morphology

To what extent are patterns of biological diversification determined by natural selection? We addressed this question by exploring divergence in foraging morphology of threespine stickleback fish inhabiting lake and stream habitats within eight independent watersheds. We found that lake fish generally displayed more developed gill structures and had more streamlined bodies than did stream fish. Diet analysis revealed that these morphological differences were associated with limnetic vs. benthic foraging modes, and that the extent of morphological divergence within watersheds reflected differences in prey resources utilized by lake and stream fish. We also found that patterns of divergence were unrelated to patterns of phenotypic trait (co)variance within populations (i.e. the ‘line of least resistance’). Instead, phenotypic (co)variances were more likely to have been shaped by adaptation to lake vs. stream habitats. Our study thus implicates natural selection as a strong deterministic force driving morphological diversification in lake–stream stickleback. The strength of this inference was obtained by complementing a standard analysis of parallel divergence in means between discrete habitat categories (lake vs. stream) with quantitative estimates of selective forces and information on trait (co)variances.

Amphibians Do Not Follow Bergmann's Rule

Abstract The tendency for organisms to be larger in cooler climates (Bergmanns rule) is widely observed in endotherms, and has been reputed to apply to some ectotherms including amphibians. However, recent reports provide conflicting support for the pattern, questioning whether Bergmanns clines are generally present in amphibians. In this study, we measured 96,996 adult Plethodon from 3974 populations to test for the presence of Bergmanns clines in these salamanders. Only three Plethodon species exhibited a significant negative correlation between body size and temperature consistent with Bergmanns rule, whereas 37 of 40 species did not display a pattern consistent with this prediction. Further, a phylogenetic comparative analysis found no relationship between body size and temperature among species. A meta-analysis combining our data with the available data for other amphibian species revealed no support for Bergmanns rule at the genus (Plethodon), order (Caudata), or class (Amphibia) levels. Our findings strongly suggest that negative thermal body size clines are not common in amphibians, and we conclude that Bergmanns rule is not generally applicable to these taxa. Thus, evolutionary explanations of Bergmanns clines in other tetrapods need not account for unique life-history attributes of amphibians.

Pattern does not equal process: Exactly when is sex environmentally determined?

Of prime importance in evolutionary biology are the description of pattern and explanations of process. Frequently, however, multiple processes can explain a given pattern. Such cases require experimental protocols or research criteria to distinguish among alternatives so pattern can be critically assigned to process. Noteworthy examples of this approach include evaluating adaptations and identifying character displacement (Gould and Lewontin 1979; Schluter and McPhail 1992). The field of vertebrate sex determination similarly requires such criteria. The sex of organisms is determined by two distinct mechanisms. In genotypic sex determination (GSD), sex is determined at conception by genes usually contained in sex chromosomes. In environmental sex determination (ESD), sex is determined permanently after fertilization by environmental factors (Bull 1983). In ESD (unlike in GSD), there is little if any genetic difference between the sexes (Solari 1994), so sex cannot be predicted by zygotic genotype (Bull 1983). In many ESD vertebrates, sex is determined after fertilization by incubation temperature (TSD). Though ESD’s biological significance seems clear for various taxa (Bull 1983; Conover 1984; Michaud et al. 1999), TSD evolution in vertebrates remains unexplained (Shine 1999). To complicate matters, temperature can influence sex ratios in a multitude of ways other than TSD.