Abstract
Form is a rich concept that agglutinates information about the proportions and topological arrangement of body parts. Modularity is readily measurable in both features, the variation of proportions (variational modules) and the organization of topology (organizational modules). The study of variational modularity and of organizational modularity faces similar challenges regarding the identification of meaningful modules and the validation of generative processes; however, most studies in morphology focus solely on variational modularity, while organizational modularity is much less understood. A possible cause for this bias is the successful development in the last twenty years of morphometrics, and specially geometric morphometrics, to study patters of variation. This contrasts with the lack of a similar mathematical framework to deal with patterns of organization. Recently, a new mathematical framework has been proposed to study the organization of gross anatomy using tools from Network Theory, so-called Anatomical Network Analysis (AnNA). In this essay, I explore the potential use of this new framework-and the challenges it faces in identifying and validating biologically meaningful modules in morphological systems-by providing working examples of a complete analysis of modularity of the human skull and upper limb. Finally, I suggest further directions of research that may bridge the gap between variational and organizational modularity studies, and discuss how alternative modeling strategies of morphological systems using networks can benefit from each other.
Highlights
Modularity is a widespread concept in modern science that emerged from the need to parcellate large, complex systems into smaller, hierarchically nested components (Simon, 1962)
In this essay we used variational modularity to refer to shape-variational modules as derived from morphometric analyses
Anatomical Network Modeling An anatomical network formalizes the way in which body parts are topological related, and, as such, it is a model of the organization of a morphological structure
Summary
Modularity is a widespread concept in modern science that emerged from the need to parcellate large, complex systems into smaller, hierarchically nested components (Simon, 1962). Under the network-based approach, testing the fit of organizational modules to a priori hypotheses of modularity rely on measuring the similarity between two alternative partitions These methods include measures based on pair counting, cluster matching, and information theory (Fortunato, 2010; Fortunato and Hric, 2016), all of which estimate to what extent the partition identified on a topological basis resembles a previously known partition based on metadata (e.g., genetic, developmental, and/or functional modules) or another algorithm. It is not well-known whether, and how, variation and organization work together in structuring and shaping the form of organisms (but see, e.g., Perez et al, 2009; Esteve-Altava et al, 2013; Suzuki, 2013), the hope is that by bridging the gap between them we will have a better understanding of morphological modularity, and possibly help to tackle challenges on both sides
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