Searching for Modular Structure in Complex Phenotypes: Inferences from Network Theory
The notion of modularity has become a unifying principle to understand structural and functional aspects of biological organization at different levels of complexity. Recently, deciphering the modular organization of molecular systems has been greatly aided by network theory. Nevertheless, network theory is completely absent from the investigation of modularity of complex macroscopic phenotypes, a fundamental level of organization at which organisms experience and interact with the environment. Here, we used geometric descriptors of phenotypic variation to derive a network representation of a complex morphological structure, the mammalian mandible, in terms of nodes and links. Then, by integrating the network representation and description with random matrix theory, we uncovered a modular organization for the mammalian mandible, which deviates significantly from an equivalent random network. The modules revealed by the network analysis correspond to the four morphogenetic units recognized for the mammalian mandible on a developmental basis. Furthermore, these modules are known to be affected only by particular genes and are also functionally differentiated. This study shows that the powerful formalism of network theory can be applied to the discovery of modules in complex phenotypes and opens the possibility of an integrated approach to the study of modularity at all levels of organizational complexity.
KeywordsGeometric morphometrics Correlation networks Variational modularity Simulated annealing Mammalian mandible
- Atchley, W. R., & Hall, B. K. (1991). A model for development and evolution of complex morphological structures. Biological Review, 66, 101–157.Google Scholar
- Batagelj, V., & Mrvar, A. (2008). Pajek 1.23 software. http://vlado.fmf.uni-lj.si/pub/networks/pajek/.
- Bookstein, F. L. (1991). Morphometric tools for landmark data: Geometry and biology. London: Cambridge University Press.Google Scholar
- Cheverud, J. M. (2004). Modular pleiotropic effects of quantitative trait loci on morphological traits. In G. Schlosser & G. P. Wagner (Eds.), Modularity in development and evolution (pp. 132–153). Chicago: Chicago University Press.Google Scholar
- Danon, L., Duch, J., Diaz-Guilera, A., Arenas, A. (2005). Comparing community structure identification. Journal of Statistical Mechanics P09008.Google Scholar
- de Aguiar, M. A. M., & Bar-Yam, Y. (2005). Spectral analysis and the dynamic response of complex networks. Physical Review, E71, 6106.Google Scholar
- Ehrich, T. H., Vaughn, T. T., Koreishi, S. F., Linsey, R. B., Pletscher, L. S., & Cheverud, J. M. (2003). Pleiotropic effects on mandibular morphology I. Developmental morphological integration and differential dominance. Journal of Experimental Zoology Molecular and Developmental Evolution, 296B, 58–79.CrossRefGoogle Scholar
- Galewski, T., Mauffrey, J. F., Leite, Y. L. R., Patton, J. L., & Douzery, E. J. P. (2005). Ecomorphological diversification among South American spiny rats (Rodentia: Echimyidae): A phylogenetic and chronological approach. Molecular Phylogenetics and Evolution, 34, 601–615.CrossRefPubMedGoogle Scholar
- Mehta, M. L. (2004). Random matrices. New York: Academic Press.Google Scholar
- Oksanen, J., Kindt, R., Legendre, P., O’Hara, B., Simpson, G. L., Stevens, M. H. H. (2008). Vegan: Community ecology package. R package version 1.11-4. http://cran.r-project.org.
- Perez, S. I., Diniz-Filho, J. A. F., Rohlf, F. J., & dos Reis, S. F. (2009). Morphological diversification among South American spiny rats (Rodentia: Echimyidae): Ecological and phylogenetic factors. Journal of the Linnean Society, 98, 646–660.Google Scholar
- Raff, R. A. (1996). The shape of life: Genes, development, and the evolution of animal form. Chicago: University of Chicago Press.Google Scholar
- Rohlf, F. J. (2007). tps series softwares. http//life.bio.sunysb.edu/morph/.
- Schlosser, G., & Wagner, G. P. (Eds.). (2004). Modularity in development and evolution. Chicago: Chicago University Press.Google Scholar
- Sheets, H. D. (2003). IMP-integrated morphometrics package. Department of Physics, Canisius College, Buffalo, New York.Google Scholar
- Wagner, G. P. (1984). On the eigenvalues of genetic and phenotypic dispersion matrices: Evidence for a nonrandom organization of quantitative character variation. Journal of Mathematical Biology, 21, 77–95.Google Scholar
- Wagner, G. P. (1996). Homologues, natural kinds and the evolution of modularity. American Zoologist, 36, 36–43.Google Scholar