N-dimensional hypervolumes in trait-based ecology: Does occupancy rate matter?

Many methods for estimating the functional diversity of biological communities rely on measuring geometrical properties of n-dimensional hypervolumes in a trait space. To date, these properties are calculated from individual hypervolumes or their pairwise combinations. Our capacity to detect functional diversity patterns due to the overlap of multiple hypervolumes is, thus, limited.Here, we propose a new approach for estimating functional diversity from a set of hypervolumes. We rely on the concept of occupancy rate, defined as the mean or absolute number of hypervolumes enclosing a given point in the trait space. Furthermore, we describe a permutation test to identify regions of the trait space in which the occupancy rate of two sets of hypervolumes differs.We illustrate the utility of our approach over existing methods with two examples on aquatic macroinvertebrates. The first example shows how occupancy rate relates to the stability of trait space utilisation due to increased flow intermittency and allows the identification of taxa in regions of the trait space with low occupancy rates. The second example shows how the permutation test based on occupancy rates can detect differences in trait space utilisation due to river morphology variation even with a high degree of overlap among input hypervolumes.Our newly developed approach is particularly suitable in functional diversity analysis when investigating patterns of overlap among multiple hypervolumes. We emphasise the need to consider analyses based on occupancy rate into functional diversity estimation.