Evolutionary Covariation in Geometric Morphometric Data: Analyzing Integration, Modularity, and Allometry in a Phylogenetic Context

Abstract

Quantifying integration and modularity of evolutionary changes in morphometric traits is crucial for understanding how organismal shapes evolve. For this purpose, comparative studies are necessary, which need to take into account the phylogenetic structure of interspecific data. This study applies several of the standard tools of geometric morphometrics, which mostly have been used in intraspecific studies, in the new context of analyzing integration and modularity based on comparative data. Morphometric methods such as principal component analysis, multivariate regression, partial least squares, and modularity tests can be applied to phylogenetically independent contrasts of shape data. We illustrate this approach in an analysis of cranial evolution in 160 species from all orders of birds. Mapping the shape information onto the phylogeny indicates that there is a significant phylogenetic signal in skull shape. Multivariate regression of independent contrasts of shape on independent contrasts of size reveals clear evolutionary allometry. Regardless of whether or not a correction for allometry is used, evolutionary integration between the face and braincase is strong, and tests reject the hypothesis that the face and braincase are separate evolutionary modules. These analyses can easily be applied to other taxa and can be combined with other morphometric tools to address a wide range of questions about evolutionary patterns and processes.

Studying morphological integration and modularity at multiple levels: concepts and analysis

“…The advantage of this approach is that specific aspects of variation or covariation can be emphasized, depending on the choice of the analyses. For example, in some structures, the main patterns of overall variation, represented by the shape changes associated with first few principal components, strongly resemble the main patterns of covariation between parts, which can be obtained as the shape changes associated with the first few partial leastsquares axes [10,12,13,16,18,85]. This indicates that the patterns of covariation between parts are also the dominant patterns of overall variation in the structure under study, and therefore emphasize the strength of integration.…”

“…For instance, the amount of integration can be quantified using the scaled variance of eigenvalues [44,107], patterns of covariation between parts can be examined with partial least-squares analysis [10,13,18,85] and hypotheses of modularity can be tested by comparing the strength of covariation between hypothesized modules with that in alternative partitions of landmarks [15,18,37,43,52,76]. In addition to these 'standard tools' for analysing morphological integration and modularity, some morphometric methods are specifically designed to compare patterns of integration in different covariance matrices, a task that is especially relevant for comparisons across multiple levels.…”

“…Most empirical studies have focused on integration within populations, investigating how the variation among individuals is structured. This is only one aspect of the problem, however, because the concept of integration also applies at different levels [4], including genetic and environmental integration [8,9], integration of fluctuating asymmetry within individuals [9][10][11][12][13][14][15] and evolutionary integration across taxa in a clade [16][17][18][19][20][21]. Most plants, because of their modular body plans, offer additional opportunities to study integration among structures such as leaves or flowers within and among individuals in a population [22,23].…”

Claw morphometrics in monitor lizards: Variable substrate and habitat use correlate to shape diversity within a predator guild

“…A 10,000 permutations test against the null hypothesis indicated that phylogenetic signal did influence claw shape ( p  =   0.0034), so this relationship was investigated further. MorphoJ generated phylogenetically independent contrasts (PICs) as a way of measuring relative shape change decoupled from relatedness (Felsenstein, 1985; Klingenberg & Marugán‐Lobón, 2013). The output was in x‐y coordinates for each branching on the phylogeny.…”

Habitat changes and changing predatory habits in North American fossil canids

“…As we are only interested in quantifying the presence of phylogenetic signal, instead of the strength of the phylogenetic signal, we used the permutation approach developed by Laurin 46 , extended for multivariate analysis by Klingenberg and Gidaszewski 47 , and applied to shape data by other authors (for example, refs [48][49][50][51][52][53][54], to simulate the null hypothesis of complete absence of phylogenetic signal in elbow shape. The mean species shapes are randomly distributed as the tips of the phylogeny in 10,000 permutations, and for each permutation, the tree length was computed.…”