Holey hypervolumes! The multivariate geometry of adaptive radiation.

When the environment changes, organisms must adapt (or go extinct). This is as true for spatial change, when organisms colonise new locations, as it is for temporal change. Environmental changes are often assumed to be more or less continuous, as are the phenotypic changes that permit adaption, but environmental (and phenotypic) variables are also commonly intercorrelated: as one changes, so do others. With such multidimensional variation (‘hypervolumes’), it can be difficult to know whether variation is continuous, and all possible combinations of variables occur. Discontinuities (‘holes’) in environmental or phenotypic hypervolumes could have important consequences for our understanding of environmental change and organisms’ abilities to respond to it. Structure in multivariate environmental variation (including holes) could arise from fundamental physicochemical constraints or from ecological interactions, and holes in phenotypic hypervolumes could be a response to this.

Until very recently the detection of holes has not been possible, but Ben Blonder, at the University of Oxford and a project collaborator, has recently developed a method to do so (2016, American Naturalist). This project will use his method, and others, to develop novel mathematical analyses of existing data describing multivariate variation in fish and their environments, as they adapt to those environments during adaptive radiations (the differentiation of an ancestral species into divergent new populations or species). We aim to address three simple, but completely novel questions, and to then develop further analyses:
(a) Are there holes in multivariate phenotypic distributions? Their existence would suggest contraints on the filling of phenotypic space.
(b) What constraints might be responsible for phenotypic holes? They might coincide with environmental or genetic discontinuities.
(c) Do holes represent phylogenetic constraints or opportunities? Holes could represent ‘the road not taken’ in a taxon’s evolutionary history, but could also represent evolutionary opportunity in the taxon’s future.