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Last update: Thursday, 13-Mar-2014 12:31:06 EDT

Modularity and morphological integration from a geometric perspective

Support: National Science Foundation (Doctoral Dissertation Improvement Grant IOS 0407570)

     To understand how variation affects the evolution of phenotypes, we must study patterns of genetic and phenotypic correlations among traits. Morphological integration refers to the extent to which traits that are affected by a common genetic, developmental, or physiological process tend to be correlated. When these processes exert a pleiotropic effect at a local scale, the resulting sub-set of integrated traits is thought of as a variational module, that is, an aspect of phenotypic variation whose variance is partly uncorrelated from other such aspects.
     During my graduate studies, I proposed a conceptual framework that identifies these "aspects of variation" that we refer to as modules as subspaces embedded within the space of phenotypic variation. This geometric definition breaks with and generalizes the view of modules as measurable body parts or sets thereof. It also helps simplify the inclusion of modularity into multivariate quantitative genetic theory, since a module can be described as a subspace of the G matrix. From a mechanistic point of view, this notion downweighs the relevance of matching body parts with specific developmental events, since the effects of these events on phenotypic variance can span multiple and overlapping sets of traits, regardless of how we choose to measure them.
     The complexity of processes that produce and modify variation all but guarantees that detecting embedded subspaces in phenotypic variation will be a difficult problem, one that requires phenome-level data and sophisticated mathematical machinery to be solved. As a first approximation, I have proposed a two-pronged approach consisting, first, on using parametric and model-selection statistics to compare observed covariance structures with those expected under a variety of models of modularity defined as sets of traits that have been shown to be jointly targeted by specific processes or mutations; and second, on heuristic comparisons between subsets of directions of variation and the whole space of phenotypic variation, using a part-vs-whole version of Partial Least Squares (PLS).
     This work has convinced me that an outstanding challenge for multivariate quantitative genetics theory, which remains largely vector-based, is to give full consideration to these pleiotropic subspaces embedded in G as verifiable sources of constraint and evolvability.

Present and Past Projects A dictionary of genetic effects The statistical power of multivariate GWAS A GWAS of wing shape in Drosophila melanogaster Shape as a function Geometric representation of modularity Modularity and integration in the mouse skull Correlated divergence of functionally coupled traits Dimensionality and coevolution of mating traits under antagonistic selection Earlier projects

Márquez, E.J. 2008. A statistical framework for testing modularity in multidimensional data. Evolution 62:2688-2708.  [ PUBMED ][ PDF ]
Márquez, E.J. 2008. Software MINT: Modularity and Integration analysis tool for morphometric data. University of Michigan, Ann Arbor. [ DOWNLOAD Win32 Win64 ]
Márquez, E.J. 2009. A General Framework for Inferring the Developmental Causes of Modularity of Morphological Variation with Applications to the Craniomandibular Complex in Morphological Variation with Applications to the Craniomandibular Complex in Rodents. Ph.D. Dissertation, University of Michigan, Ann Arbor.  [ UMICH ]

© 2003-2014 Eladio J. Márquez