Quantifying the configurational complexity of biological systems in multivariate 'complexity space'

An increasing number of evolutionary studies seek to quantify the morphological complexity of organisms, particularly those comprising serially homologous elements at different hierarchical levels of organization. Numerous operational frameworks have been proposed for doing this, but most focus on one or multiple conflated aspects of what is really a multidimensional concept. Here, we advocate the use of 'complexity spaces': multidimensional spaces defined by different vectors of complexity. We explore their application to biological systems composed of homologous parts and identify three axes on which those systems differ: part number, part differentiation and the regularity of that differentiation. Such complexity spaces can be constructed for systems at different hierarchical levels of biological organization. To illustrate this, we explore the complexity spaces for trilobite body plans (comprising body segments of varying number and form), and for ant colonies (comprising differentiated worker polymorphisms of varying number and form within a 'superorganism'). Many different complexity spaces are possible, but all seek to distinguish different aspects of complexity within an information-theoretic framework, and thereby to clarify patterns of complexity evolution.