Varieties of modules: kinds, levels, origins, and behaviors

This article began as a review of a conference, organized by Gerhard Schlosser, entitled "Modularity in Development and Evolution." The conference was held at, and sponsored by, the Hanse Wissenschaftskolleg in Delmenhorst, Germany in May, 2000. The article subsequently metamorphosed into a literature and concept review as well as an analysis of the differences in current perspectives on modularity. Consequently, I refer to general aspects of the conference but do not review particular presentations. I divide modules into three kinds: structural, developmental, and physiological. Every module fulfills none, one, or multiple functional roles. Two further orthogonal distinctions are important in this context: module-kinds versus module-variants-of-a-kind and reproducer versus nonreproducer modules. I review criteria for individuation of modules and mechanisms for the phylogenetic origin of modularity. I discuss conceptual and methodological differences between developmental and evolutionary biologists, in particular the difference between integration and competition perspectives on individualization and modular behavior. The variety in views regarding modularity presents challenges that require resolution in order to attain a comprehensive, rather than a piecemeal and fragmentary, evolutionary developmental biology. J. Exp. Zool. (Mol. Dev. Evol.) 291:116-129, 2001.     

Functional annotation of hierarchical modularity

In biological networks of molecular interactions in a cell, network motifs that are biologically relevant are also functionally coherent, or form functional modules. These functionally coherent modules combine in a hierarchical manner into larger, less cohesive subsystems, thus revealing one of the essential design principles of system-level cellular organization and function-hierarchical modularity. Arguably, hierarchical modularity has not been explicitly taken into consideration by most, if not all, functional annotation systems. As a result, the existing methods would often fail to assign a statistically significant functional coherence score to biologically relevant molecular machines. We developed a methodology for hierarchical functional annotation. Given the hierarchical taxonomy of functional concepts (e.g., Gene Ontology) and the association of individual genes or proteins with these concepts (e.g., GO terms), our method will assign a Hierarchical Modularity Score (HMS) to each node in the hierarchy of functional modules; the HMS score and its p-value measure functional coherence of each module in the hierarchy. While existing methods annotate each module with a set of "enriched" functional terms in a bag of genes, our complementary method provides the hierarchical functional annotation of the modules and their hierarchically organized components. A hierarchical organization of functional modules often comes as a bi-product of cluster analysis of gene expression data or protein interaction data. Otherwise, our method will automatically build such a hierarchy by directly incorporating the functional taxonomy information into the hierarchy search process and by allowing multi-functional genes to be part of more than one component in the hierarchy. In addition, its underlying HMS scoring metric ensures that functional specificity of the terms across different levels of the hierarchical taxonomy is properly treated. We have evaluated our method using Saccharomyces cerevisiae data from KEGG and MIPS databases and several other computationally derived and curated datasets. The code and additional supplemental files can be obtained from http://code.google.com/p/functional-annotation-of-hierarchical-modularity/ (Accessed 2012 March 13).     

Extracting the abstraction pyramid from complex networks

Background  

At present, the organization of system modules is typically limited to either a multilevel hierarchy that describes the "vertical" relationships between modules at different levels (e.g., module A at level two is included in module B at level one), or a single-level graph that represents the "horizontal" relationships among modules (e.g., genetic interactions between module A and module B). Both types of organizations fail to provide a broader and deeper view of the complex systems that arise from an integration of vertical and horizontal relationships.     

A hierarchical model of plumage: morphology,development, and evolution

Plumage is a complex component of the avian phenotype. The plumage of an individual is composed of numerous hierarchically arranged developmental and morphological modules. We present a hierarchical model of plumage that provides an intellectual framework for understanding the development and evolution of feathers. Independence, covariation, and interaction among plumage modules create numerous opportunities for developmental and evolutionary diversification of feather complexity and function. The hierarchical relationships among plumage modules are characterized by both top-down and bottom-up effects in which properties of modules at one level of the hierarchy determine or influence the properties of modules at lower or higher levels of the hierarchy. Plumage metamodules are created by covariation or interaction among modules at different levels of the hierarchy.     

The Influence of Modularity on Cranial Morphological Disparity in Carnivora and Primates (Mammalia)

Background

Although variation provides the raw material for natural selection and evolution, few empirical data exist about the factors controlling morphological variation. Because developmental constraints on variation are expected to act by influencing trait correlations, studies of modularity offer promising approaches that quantify and summarize patterns of trait relationships. Modules, highly-correlated and semi-autonomous sets of traits, are observed at many levels of biological organization, from genes to colonies. The evolutionary significance of modularity is considerable, with potential effects including constraining the variation of individual traits, circumventing pleiotropy and canalization, and facilitating the transformation of functional structures. Despite these important consequences, there has been little empirical study of how modularity influences morphological evolution on a macroevolutionary scale. Here, we conduct the first morphometric analysis of modularity and disparity in two clades of placental mammals, Primates and Carnivora, and test if trait integration within modules constrains or facilitates morphological evolution.

Principal Findings

We used both randomization methods and direct comparisons of landmark variance to compare disparity in the six cranial modules identified in previous studies. The cranial base, a highly-integrated module, showed significantly low disparity in Primates and low landmark variance in both Primates and Carnivora. The vault, zygomatic-pterygoid and orbit modules, characterized by low trait integration, displayed significantly high disparity within Carnivora. 14 of 24 results from analyses of disparity show no significant relationship between module integration and morphological disparity. Of the ten significant or marginally significant results, eight support the hypothesis that integration within modules constrains morphological evolution in the placental skull. Only the molar module, a highly-integrated and functionally important module, showed significantly high disparity in Carnivora, in support of the facilitation hypothesis.

Conclusions

This analysis of within-module disparity suggested that strong integration of traits had little influence on morphological evolution over large time scales. However, where significant results were found, the primary effect of strong integration of traits was to constrain morphological variation. Thus, within Primates and Carnivora, there was some support for the hypothesis that integration of traits within cranial modules limits morphological evolution, presumably by limiting the variation of individual traits.     

Drosophila wing modularity revisited through a quantitative genetic approach

To predict the response of complex morphological structures to selection it is necessary to know how the covariation among its different parts is organized. Two key features of covariation are modularity and integration. The Drosophila wing is currently considered a fully integrated structure. Here, we study the patterns of integration of the Drosophila wing and test the hypothesis of the wing being divided into two modules along the proximo‐distal axis, as suggested by developmental, biomechanical, and evolutionary evidence. To achieve these goals we perform a multilevel analysis of covariation combining the techniques of geometric morphometrics and quantitative genetics. Our results indicate that the Drosophila wing is indeed organized into two main modules, the wing base and the wing blade. The patterns of integration and modularity were highly concordant at the phenotypic, genetic, environmental, and developmental levels. Besides, we found that modularity at the developmental level was considerably higher than modularity at other levels, suggesting that in the Drosophila wing direct developmental interactions are major contributors to total phenotypic shape variation. We propose that the precise time at which covariance‐generating developmental processes occur and/or the magnitude of variation that they produce favor proximo‐distal, rather than anterior‐posterior, modularity in the Drosophila wing.     

Anatomical Network Analysis Shows Decoupling of Modular Lability and Complexity in the Evolution of the Primate Skull

Modularity and complexity go hand in hand in the evolution of the skull of primates. Because analyses of these two parameters often use different approaches, we do not know yet how modularity evolves within, or as a consequence of, an also-evolving complex organization. Here we use a novel network theory-based approach (Anatomical Network Analysis) to assess how the organization of skull bones constrains the co-evolution of modularity and complexity among primates. We used the pattern of bone contacts modeled as networks to identify connectivity modules and quantify morphological complexity. We analyzed whether modularity and complexity evolved coordinately in the skull of primates. Specifically, we tested Herbert Simon’s general theory of near-decomposability, which states that modularity promotes the evolution of complexity. We found that the skulls of extant primates divide into one conserved cranial module and up to three labile facial modules, whose composition varies among primates. Despite changes in modularity, statistical analyses reject a positive feedback between modularity and complexity. Our results suggest a decoupling of complexity and modularity that translates to varying levels of constraint on the morphological evolvability of the primate skull. This study has methodological and conceptual implications for grasping the constraints that underlie the developmental and functional integration of the skull of humans and other primates.     

Cranial modularity and sequence heterochrony in mammals

Heterochrony, the temporal shifting of developmental events relative to each other, requires a degree of autonomy among those processes or structures. Modularity, the division of larger structures or processes into autonomous sets of internally integrated units, is often discussed in relation to the concept of heterochrony. However, the relationship between the developmental modules derived from studies of heterochrony and evolutionary modules, which should be of adaptive importance and relate to the genotype-phenotype map, has not been explicitly studied. I analyzed a series of sectioned and whole cleared-and-stained embryological and neonatal specimens, supplemented with published ontogenetic data, to test the hypothesis that bones within the same phenotypic modules, as determined by morphometric analysis, are developmentally integrated and will display coordinated heterochronic shifts across taxa. Modularity was analyzed in cranial bone ossification sequences of 12 therian mammals. A dataset of 12-18 developmental events was used to assess if modularity in developmental sequences corresponds to six phenotypic modules, derived from a recent morphometric analysis of cranial modularity in mammals. Kendall's tau was used to measure rank correlations, with randomization tests for significance. If modularity in developmental sequences corresponds to observed phenotypic modules, bones within a single phenotypic module should show integration of developmental timing, maintaining the same timing of ossification relative to each other, despite differences in overall ossification sequences across taxa. Analyses did not find any significant conservation of developmental timing within the six phenotypic modules, meaning that bones that are highly integrated in adult morphology are not significantly integrated in developmental timing.     

Modularity and sense organs in the blind cavefish, Astyanax mexicanus

SUMMARY Mexican tetra (Astyanax mexicanus) exist as two morphs: a sighted (surface) form and a blind (cavefish) form. In the cavefish, some modules are lost, such as the eye and pigment modules, whereas others are expanded, such as the taste bud and cranial neuromast modules. We suggest that modularity can be viewed as being nested in a manner similar to Baupläne so that modules express unique sets of genes, cells, and processes. In terms of evolution, we conclude that natural selection can act on any of these hierarchical levels within modules or on all the sensory modules as a whole. We discuss interactions within and between modules with reference to the blind cavefish from both genetic and developmental perspectives. The cavefish represents an illuminating example of module interaction, uncoupling of modules, and module expansion.     

Revisiting the variation of clustering coefficient of biological networks suggests new modular structure

ABSTRACT: A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary. RESULTS: We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn't show dependence of degree. CONCLUSIONS: Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to "deterministic model" of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.     

Constraint and opportunity: the genetic basis and evolution of modularity in the cichlid mandible

Modular variation, whereby the relative degree of connectivity varies within a system, is thought to evolve through a process of selection that favors the integration of certain traits and the decoupling of others. In this way, modularity may facilitate the pace of evolution and determine evolvability. Alternatively, conserved patterns of modularity may act to constrain the rate and direction of evolution by preventing certain functions from evolving. A comprehensive understanding of the potential interplay between these phenomena will require knowledge of the inheritance and the genetic basis of modularity. Here we explore these ideas in the cichlid mandible by investigating patterns of modularity at the clade and species levels and through the introduction of a new approach, the individual level. Specifically, we assessed patterns of covariation in Lake Malawi cichlid species that employ alternate "biting" and "suction-feeding" modes of feeding and in a hybrid cross between these two ecotypes. Across the suction-feeding clade, patterns of modularity were largely conserved and reflected a functionally based pattern. In contrast, the biting species displayed a pattern of modularity that more closely matched developmental modules. The pattern of modularity present in our F2 population was very similar to the pattern exhibited by the biter, suggesting a role for dominant inheritance. We demonstrate that our individual-level metric of modularity (IMM) is a valid quantitative trait that has a nonlinear relationship with shape. IMMs for each model were used as quantitative characters to map quantitative trait loci (QTL) that underlie modularity. Our QTL analysis offers new insights into the genetic basis of modularity in these fishes that may eventually lead to the discovery of the genetic processes that delineate particular modules. In all, our findings suggest that modularity is both a constraining and an evolvable force in cichlid evolution, as distinct patterns occur between species and variation exists among individuals.     

Homology and the hierarchy of biological systems

Homology is the similarity between organisms due to common ancestry. Introduced by Richard Owen in 1843 in a paper entitled "Lectures on comparative anatomy and physiology of the invertebrate animals", the concept of homology predates Darwin's "Origin of Species" and has been very influential throughout the history of evolutionary biology. Although homology is the central concept of all comparative biology and provides a logical basis for it, the definition of the term and the criteria of its application remain controversial. Here, I will discuss homology in the context of the hierarchy of biological organization. I will provide insights gained from an exemplary case study in evolutionary developmental biology that indicates the uncoupling of homology at different levels of biological organization. I argue that continuity and hierarchy are separate but equally important issues of homology.     

Morphological integration and serial homology: A case study of the cranium and anterior vertebrae in salamanders

Serial homology or the repetition of equivalent developmental units and their derivatives is a phenomenon encountered in a variety of organisms, with the vertebrate axial skeleton as one of the most notable examples. Serially homologous structures can be viewed as an appropriate model system for studying morphological integration and modularity, due to the strong impact of development on their covariation. Here, we explored the pattern of morphological integration of the cranium and the first three serially homologous structures (atlas, first, and second trunk vertebrae) in salamandrid salamanders, using micro-CT scanning and three-dimensional geometric morphometrics. We explored the integration between structures at static and evolutionary levels. Effects of allometry on patterns of modularity were also taken into account. At the static level (within species), we analyzed inter-individual variation in shape to detect functional modules and intra-individual variation to detect developmental modules. Significant integration (based on inter-individual variation) among all structures was detected and allometry is shown to be an important integrating factor. The pattern of intra-individual, asymmetric variation indicates statistically significant developmental integration between the cranium and the atlas and between the first two trunk vertebrae. At the evolutionary level (among species), the cranium, atlas, and trunk vertebrae separate as different modules. Our results show that morphological integration at the evolutionary level coincides with morphological and functional differentiation of the axial skeleton, allowing the more or less independent evolutionary changes of the cranial skeleton and the vertebral column, regardless of the relatively strong integration at the static level. The observed patterns of morphological integration differ across levels, indicating different impacts of developmental and phylogenetic constraints and functional demands.     

Modularity, evolvability, and adaptive radiations: a comparison of the hemi- and holometabolous insects

SUMMARY Despite recent attention given to the concept of modularity and its potential contribution to the evolvability of organisms, there has been little mention of how such a contribution may affect rates of diversification or how this would be assessed. A first key prediction is that lineages with relatively greater degrees of modularity in given traits should exhibit higher rates of diversification. Four general conditions for testing this prediction of the modular evolvability hypothesis are outlined here. The potential role of modularity as a deterministic factor in adaptive radiations is best examined by looking at historic patterns of diversification rather than just levels of extant diversity, the focus of most analyses of key innovations.
Recent developmental evidence supports the notion that phenotypes of juvenile and adult stages of insects with "complete" metamorphosis (Holometabola) are distinct developmental and evolvable modules compared to the highly correlated life stages of insects with "incomplete" metamorphosis (Hemimetabola). Family-level rates of diversification for these two groups were calculated from the fossil record. The Holometabola was found to have a significantly and characteristically higher rate of diversification compared to the less modular Hemimetabola, consistent with the idea that intrinsic differences in modularity can influence the long-term evolvability of organisms.
The modular evolvability hypothesis also makes a second key prediction: that characters in more modular clades will exhibit greater levels of variation due to their independence. This provides an independent, phenotypically based test of the hypothesis. We discuss here how this second prediction may be tested in the case of the Hemi- and Holometabola.     

An exploratory data analysis method to reveal modular latent structures in high-throughput data

Background  

Modular structures are ubiquitous across various types of biological networks. The study of network modularity can help reveal regulatory mechanisms in systems biology, evolutionary biology and developmental biology. Identifying putative modular latent structures from high-throughput data using exploratory analysis can help better interpret the data and generate new hypotheses. Unsupervised learning methods designed for global dimension reduction or clustering fall short of identifying modules with factors acting in linear combinations.     

Mosaic heterochrony and evolutionary modularity: the trilobite genus Zacanthopsis as a case study

Logical connections exist between evolutionary modularity and heterochrony, two unifying and structuring themes in the expanding field of evolutionary developmental biology. The former sees complex phenotypes as being made up of semi-independent units of evolutionary transformation; the latter requires such a modular organization of phenotypes to occur in a localized or mosaic fashion. This conceptual relationship is illustrated here by analyzing the evolutionary changes in the cranidial ontogeny of two related species of Cambrian trilobites. With arguments from comparative developmental genetics and functional morphology, we delineate putative evolutionary modules within the cranidium and examine patterns of evolutionary changes in ontogeny at both global and local scales. Results support a case of mosaic heterochrony, that is, a combination of local heterochronies affecting the different parts individuated in the cranidium, leading to the complex pattern of allometric repatterning observed at the global scale. Through this example, we show that recasting morphological analyses of complex phenotypes with a priori knowledge or hypotheses about their organizational and variational properties can significantly improve our interpretation and understanding of evolutionary changes among related taxa, fossil and extant. Such considerations open avenues to investigate the large-scale dynamics of modularity and its role in phenotypic evolution.     

The road to modularity

A network of interactions is called modular if it is subdivided into relatively autonomous, internally highly connected components. Modularity has emerged as a rallying point for research in developmental and evolutionary biology (and specifically evo-devo), as well as in molecular systems biology. Here we review the evidence for modularity and models about its origin. Although there is an emerging agreement that organisms have a modular organization, the main open problem is the question of whether modules arise through the action of natural selection or because of biased mutational mechanisms.     

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

Mandibles of yellow‐necked mouse (Apodemus flavicollis) were used to explore modularity. We tested a biological hypothesis that two separate modules (alveolar region and ascending ramus) can be recognized within the mandible. As a second research goal, we compared two different morphometric procedures under the assumption that methodological approaches that use either geometric or traditional morphometric techniques should give similar results. Besides confirmation of the predicted hypothesis of modularity, the application of both approaches revealed that: (i) modularity was somewhat more evident when it was analysed on the asymmetric (fluctuating asymmetry, FA) than on the symmetric (individual variation) component of variation; (ii) there is correspondence in the patterns of individual variation and FA, which indicates that integration of mandibular traits among individuals is primarily due to direct developmental interactions; and (iii) allometry does not obscure the hypothesized modularity for individual variation or for FA. In addition, traditional morphometric method allowed us to check whether allometry influenced each module to the same extent and to conclude that the ascending ramus is more heavily influenced by general size than the alveolar region. In studies of modularity, differences in methods can lead to discrepancies in the results, and therefore, some caution is required when comparing findings from different investigations. The substantial agreement between our results provides evidence that, when considering two‐module organization of the mouse mandible, direct comparison among studies that use the methods applied herein is, in great part, reliable.