The n-dimensional hypervolume

Aim: The Hutchinsonian hypervolume is the conceptual foundation for many lines of ecological and evolutionary inquiry, including functional morphology, comparative biology, community ecology and niche theory. However, extant methods to sample from hypervolumes or measure their geometry perform poorly on high-dimensional or holey datasets. Innovation: We first highlight the conceptual and computational issues that have prevented a more direct approach to measuring hypervolumes. Next, we present a new multivariate kernel density estimation method that resolves many of these problems in an arbitrary number of dimensions. Main conclusions: We show that our method (implemented as the 'hypervolume' R package) can match several extant methods for hypervolume geometry and species distribution modelling. Tools to quantify high-dimensional ecological hypervolumes will enable a wide range of fundamental descriptive, inferential and comparative questions to be addressed.