Combinatorics

Sociology

Niche

Population

Mathematics

Species richness

Kernel (algebra)

Biology

Trait

Biodiversity

Demography

Species evenness

Set (abstract data type)

Ecology

Programming language

Computer science

Theoretical ecology

Niche differentiation

Methods in Ecology and Evolution

The use of n ‐dimensional hypervolumes in trait‐based ecology is rapidly increasing. By representing the functional space of a species or community as a Hutchinsonian niche, the abstract Euclidean space defined by a set of independent axes corresponding to individuals or species traits, these multidimensional techniques show great potential for the advance of functional ecology theory. In the panorama of existing methods for delineating multidimensional spaces, the r package hypervolume ( Global Ecology and Biogeography , 23, 2014, 595–609) is currently the most used. However, functions for calculating the standard set of functional diversity (FD) indices—richness, divergence and regularity—have not been developed within the hypervolume framework yet. This gap is delaying its full exploitation in functional ecology, meanwhile preventing the possibility to compare its performance with that of other methods. We develop a set of functions to calculate FD indices based on n ‐dimensional hypervolumes, including alpha (richness), beta (and respective components), dispersion, evenness, contribution and originality. Altogether, these indices provide a coherent framework to explore the primary mathematical components of FD within a multidimensional setting. These new functions can work either with hypervolume objects or with raw data (species presence or abundance and their traits) as input data, and are versatile in terms of input parameters and options. These functions are implemented within bat (Biodiversity Assessment Tools), an r package for biodiversity assessments. As a coherent corpus of functional indices based on a common algorithm, it opens the possibility to fully explore the strengths of the Hutchinsonian niche concept in community ecology research.

Functional diversity metrics using kernel density <i>n</i>‐dimensional hypervolumes

Functional diversity metrics using kernel density n‐dimensional hypervolumes