Methods for Studying Morphological Integration and Modularity

Abstract

Morphological integration and modularity are closely related concepts about how different traits of an organism are correlated. Integration is the overall pattern of intercorrelation; modularity is the partitioning of integration into evolutionarily or developmentally independent blocks of traits. Modularity and integration are usually studied using quantitative phenotypic data, which can be obtained either from extant or fossil organisms. Many methods are now available to study integration and modularity, all of which involve the analysis of patterns found in trait correlation or covariance matrices. We review matrix correlation, random skewers, fluctuating asymmetry, cluster analysis, Euclidean distance matrix analysis (EDMA), graphical modelling, two-block partial least squares, RV coefficients, and theoretical matrix modelling and discuss their similarities and differences. We also review different coefficients that are used to measure correlations. We apply all the methods to cranial landmark data from and ontogenetic series of Japanese macaques,Macaca fuscatato illustrate the methods and their individual strengths and weaknesses. We conclude that the exploratory approaches (cluster analyses of various sorts) were less informative and less consistent with one another than were the results of model testing or comparative approaches. Nevertheless, we found that competing models of modularity and integration are often similar enough that they are not statistically distinguishable; we expect, therefore, that several models will often be significantly correlated with observed data.

Two‐module organization of the mandible in the yellow‐necked mouse: a comparison between two different morphometric approaches

“…Goswami & Polly () summarized the majority of exploratory and confirmatory methods for studying morphological integration and modularity. By applying some of the methods, they tested three different models of cranial modularity in Japanese macaques to discuss similarities and differences in the results obtained and to illustrate strengths and weaknesses of the procedures used.…”

Spandrels and trait delimitation: No such thing as “architectural constraint”

“…There are countless approaches for delimiting organismal subsets, based on morphological data from traditional linear measurements to geometric morphometrics (Goswami & Polly, 2010a;Magwene, 2001). There are countless approaches for delimiting organismal subsets, based on morphological data from traditional linear measurements to geometric morphometrics (Goswami & Polly, 2010a;Magwene, 2001).…”

“…Much of quantitative genetics is directed at identifying patterns of dependence and independence between traits, and many other techniques are deployed under the rubrics of modularity and phenotypic integration FIGURE 3 The gastropod umbilicus. However, when the statistical thresholds are varied or different statistical approaches used, then the resulting inference of how many "parts" or modules are present varies accordingly (Goswami & Polly, 2010a;Montes-Cartas et al, 2017;Perez, de Aguiar, Guimarães, & dos Reis, 2009). A "spandrel" is understood as a "leftover" empty space amid real architectural elements.…”

“…The hollow space, known as the umbilicus, in the coils of some snails, as in this Polygyra from tropical Mexico, is often mentioned as representing a biological "spandrel." Drake & Klingenberg (2010) recovered a two module model, Cheverud (1995) a six module model and Goswami and Polly (2010a) a different six module model (see Table 1 in Goswami & Polly 2010a) for the same biological structure. The umbilicus has been coopted in some snail species as a brood chamber, but this does not mean that it is a "part," a trait than can respond quasi-independently from the rest of the shell to selection.…”

Developmental covariation of human vault and base throughout postnatal ontogeny

“…This tendency to produce coordinated variation among different traits is known as morphological integration (Olson and Miller, 1958;Hallgrímsson et al, 2009). In the context of modern morphometrics, morphological integration is expressed by covariances of landmarks that describe anatomical structures (Klingenberg, 2009;Goswami and Polly, 2010).…”