Department of Theoretical Biology, University of Vienna, Vienna, Austria.
Simon M. Huttegger
Department of Logic and Philosophy of Science, University of California, Irvine, Irvine, CA, USA.
Biological Theory. Winter 2009, Vol. 4, No. 1, Pages 54-67
MIT Press Journals - Biological Theory -
Formal spaces have become commonplace conceptual and computational tools in a large array of scientific disciplines, including both the natural and the social sciences. Morphological spaces (morphospaces) are spaces describing and relating organismal phenotypes. They play a central role in morphometrics, the statistical description of biological forms, but also underlie the notion of adaptive landscapes that drives many theoretical considerations in evolutionary biology. We briefly review the topological and geometrical properties of the most common morphospaces in the biological literature. In contemporary geometric morphometrics, the notion of a morphospace is based on the Euclidean tangent space to Kendall's shape space, which is a Riemannian manifold. Many more classical morphospaces, such as Raup's space of coiled shells, lack these metric properties, e.g., due to incommensurably scaled variables, so that these morphospaces typically are affine vector spaces. Other notions of a morphospace, like Thomas and Reif's (1993) skeleton space, may not give rise to a quantitative measure of similarity at all. Such spaces can often be characterized in terms of topological or pretopological spaces.
The typical language of theoretical and evolutionary biology, comprising statements about the “distance” among phenotypes in an according space or about different “directions” of evolution, is not warranted for all types of morphospaces. Graphical visualizations of morphospaces or adaptive landscapes may tempt the reader to apply “Euclidean intuitions” to a morphospace, whatever its actual topology might be. We discuss the limits of metaphors such as the developmental hourglass and adaptive landscapes that ensue from the geometric properties of the underlying morphospace.