Michael L. Collyer

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.

A method for analysis of phenotypic change for phenotypes described by high-dimensional data.

The analysis of phenotypic change is important for several evolutionary biology disciplines, including phenotypic plasticity, evolutionary developmental biology, morphological evolution, physiological evolution, evolutionary ecology and behavioral evolution. It is common for researchers in these disciplines to work with multivariate phenotypic data. When phenotypic variables exceed the number of research subjects—data called ‘high-dimensional data’—researchers are confronted with analytical challenges. Parametric tests that require high observation to variable ratios present a paradox for researchers, as eliminating variables potentially reduces effect sizes for comparative analyses, yet test statistics require more observations than variables. This problem is exacerbated with data that describe ‘multidimensional’ phenotypes, whereby a description of phenotype requires high-dimensional data. For example, landmark-based geometric morphometric data use the Cartesian coordinates of (potentially) many anatomical landmarks to describe organismal shape. Collectively such shape variables describe organism shape, although the analysis of each variable, independently, offers little benefit for addressing biological questions. Here we present a nonparametric method of evaluating effect size that is not constrained by the number of phenotypic variables, and motivate its use with example analyses of phenotypic change using geometric morphometric data. Our examples contrast different characterizations of body shape for a desert fish species, associated with measuring and comparing sexual dimorphism between two populations. We demonstrate that using more phenotypic variables can increase effect sizes, and allow for stronger inferences.

Phenotypic plasticity in two marine snails: constraints superseding life history

In organisms encountering predictable environments, fixed development is expected, whereas in organisms that cannot predict their future environment, phenotypic plasticity would be optimal to increase local adaptation. To test this prediction we experimentally compared phenotypic plasticity in two rocky‐shore snail species; Littorina saxatilis releasing miniature snails on the shore, and Littorina littorea releasing drifting larvae settling on various shores, expecting L. littorea to show more phenotypic plasticity than L. saxatilis. We compared magnitude and direction of vectors of phenotypic difference in juvenile shell traits after 3 months exposure to different stimuli simulating sheltered and crab‐rich shores, or wave‐exposed and crab‐free shores. Both species showed similar direction and magnitude of vectors of phenotypic difference with minor differences only between ecotypes of the nondispersing species, indicating that plasticity is an evolving trait in L. saxatilis. The lack of a strong plastic response in L. littorea might be explained by limits rather than costs to plasticity.

ANALYSIS OF CHARACTER DIVERGENCE ALONG ENVIRONMENTAL GRADIENTS AND OTHER COVARIATES

Abstract Character displacement is typically identified by comparing phenotypic differences in sympatry and allopatry. Recently, however, Goldberg and Lande (2006) pointed out that when phenotypic characters vary along an environmental gradient, the standard approach may fail to identify sympatric character divergence. Here we present a general analytical procedure for identifying sympatric character divergence while accounting for phenotypic changes that covary with environmental variables. Our approach uses residual randomization from a generalized linear model, and allows the statistical comparison of sympatric phenotypic divergence to allopatric phenotypic divergence while accounting for phenotypic variation along a gradient. Through simulation we demonstrate that our approach correctly identifies patterns of sympatric character divergence when they are present, and does not identify such patterns when they are not. Our analytical approach complements and extends the suggestions of Goldberg and Lande (2006), by allowing a full statistical assessment of the varied patterns of character displacement along environmental gradients, or while accounting for other covariates and sources of variation.

PHENOTYPIC PLASTICITY OF NATIVE VS. INVASIVE PURPLE LOOSESTRIFE: A TWO-STATE MULTIVARIATE APPROACH

The differences in phenotypic plasticity between invasive (North American) and native (German) provenances of the invasive plant Lythrum salicaria (purple loosestrife) were examined using a multivariate reaction norm approach testing two important attributes of reaction norms described by multivariate vectors of phenotypic change: the magnitude and direction of mean trait differences between environments. Data were collected for six life history traits from native and invasive plants using a split-plot design with experimentally manipulated water and nutrient levels. We found significant differences between native and invasive plants in multivariate phenotypic plasticity for comparisons between low and high water treatments within low nutrient levels, between low and high nutrient levels within high water treatments, and for comparisons that included both a water and nutrient level change. The significant genotype x environment (G x E) effects support the argument that invasiveness of purple loosestrife is closely associated with the interaction of high levels of soil nutrient and flooding water regime. Our results indicate that native and invasive plants take different strategies for growth and reproduction; native plants flowered earlier and allocated more to flower production, while invasive plants exhibited an extended period of vegetative growth before flowering to increase height and allocation to clonal reproduction, which may contribute to increased fitness and invasiveness in subsequent years.

Morphological Divergence of Native and Recently Established Populations of White Sands Pupfish (Cyprinodon tularosa)

Abstract We used landmark-based geometric morphometric methods to describe patterns of body shape variation and shape covariation with size among populations of the threatened White Sands Pupfish (Cyprinodon tularosa), a species that occurs in dissimilar aquatic habitats. White Sands Pupfish populations include two genetically distinct, native populations that have been historically isolated in Salt Creek, a saline river, and Malpais Spring, a brackish spring. In addition, two populations were established approximately 30 years before this study by translocation of fish from Salt Creek to Lost River (a saline river) and Mound Spring (a brackish spring). We found significant body shape variation among populations and between males and females. Body shapes were more slender for females than for males and more slender for saline river populations than brackish spring populations. Introductions of pupfish to new habitats resulted in significant departures in body shape and shape allometry from the native Salt Creek population. Shape divergence was more pronounced for the Mound Spring population, which is consistent with a greater change in abiotic conditions. Although Mound Spring pupfish, like Malpais Spring pupfish, were more deep-bodied than saline river pupfish, differences in body shape and the level of sexual dimorphism were significant between the two brackish spring populations, indicating that deep-bodied shapes may be achieved from different anatomical configurations. The significant shape divergence of introduced populations warrants consideration for the conservation of this rare species, as creation of refuge populations for native stocks is a current management strategy.

Permutation tests for phylogenetic comparative analyses of high‐dimensional shape data: What you shuffle matters

Evaluating statistical trends in high‐dimensional phenotypes poses challenges for comparative biologists, because the high‐dimensionality of the trait data relative to the number of species can prohibit parametric tests from being computed. Recently, two comparative methods were proposed to circumvent this difficulty. One obtains phylogenetic independent contrasts for all variables, and statistically evaluates the linear model by permuting the phylogenetically independent contrasts (PICs) of the response data. The other uses a distance‐based approach to obtain coefficients for generalized least squares models (D‐PGLS), and subsequently permutes the original data to evaluate the model effects. Here, we show that permuting PICs is not equivalent to permuting the data prior to the analyses as in D‐PGLS. We further explain why PICs are not the correct exchangeable units under the null hypothesis, and demonstrate that this misspecification of permutable units leads to inflated type I error rates of statistical tests. We then show that simply shuffling the original data and recalculating the independent contrasts with each iteration yields significance levels that correspond to those found using D‐PGLS. Thus, while summary statistics from methods based on PICs and PGLS are the same, permuting PICs can lead to strikingly different inferential outcomes with respect to statistical and biological inferences.

Six cryptic species on a single species of host plant: morphometric evidence for possible reproductive character displacement

Abstract 1. Diversification of some highly host‐specific herbivorous insects may occur in allopatry, without shifts in host use. Such allopatric divergence may be accelerated by sexual selection operating on courtship displays. Wing size and shape may affect visual and vibrational courtship displays in tephritid fruit flies. Geometric morphometric methods were used to examine wings of six sympatric cryptic species in the neotropical genus Blepharoneura. All six species feed on flowers of the same species of host (Gurania spinulosa), a neotropical vine in the Cucurbitaceae. Three of the fly species court and mate in close proximity on the host. Thus, courtship behaviours could serve as important reproductive isolating mechanisms. Two sets of hypotheses were tested: (i) species differ in wing shape and wing size; and (ii) species are sexually dimorphic in wing size and wing shape. Wing size differed among a few species, but wing shape differed significantly among all six species. Sexual dimorphism in wing size was found in only one species, but sexual dimorphism in wing shape was found in two of the three species known to court on the same host plant. In the two sexually dimorphic species, wing shape differed among males, but not among females. This suggests that selection for reproductive character displacement might accelerate divergence in wing shape.

On the comparison of the strength of morphological integration across morphometric datasets

Evolutionary morphologists frequently wish to understand the extent to which organisms are integrated, and whether the strength of morphological integration among subsets of phenotypic variables differ among taxa or other groups. However, comparisons of the strength of integration across datasets are difficult, in part because the summary measures that characterize these patterns (RV coefficient and rPLS) are dependent both on sample size and on the number of variables. As a solution to this issue, we propose a standardized test statistic (a z‐score) for measuring the degree of morphological integration between sets of variables. The approach is based on a partial least squares analysis of trait covariation, and its permutation‐based sampling distribution. Under the null hypothesis of a random association of variables, the method displays a constant expected value and confidence intervals for datasets of differing sample sizes and variable number, thereby providing a consistent measure of integration suitable for comparisons across datasets. A two‐sample test is also proposed to statistically determine whether levels of integration differ between datasets, and an empirical example examining cranial shape integration in Mediterranean wall lizards illustrates its use. Some extensions of the procedure are also discussed.