Shifting spaces: Which disparity or dissimilarity measurement best summarize occupancy in multidimensional spaces?

Multidimensional analysis of traits are now common in ecology and evolution and are based on trait spaces in which each dimension summarizes the observed trait combination (a morphospace or an ecospace). Observations of interest will typically occupy a subset of this space, and researchers will calculate one or more measures to quantify how organisms inhabit that space. In macroevolution and ecology, these measures called disparity or dissimilarity metrics are generalized as space occupancy measures. Researchers use these measures to investigate how space occupancy changes through time, in relation to other groups of organisms, or in response to global environmental changes. However, the mathematical and biological meaning of most space occupancy measures is vague with the majority of widely used measures lacking formal description. Here, we propose a broad classification of space occupancy measures into three categories that capture changes in size, density, or position. We study the behavior of 25 measures to changes in trait space size, density, and position on simulated and empirical datasets. We find that no measure describes all of trait space aspects but that some are better at capturing certain aspects. Our results confirm the three broad categories (size, density, and position) and allow us to relate changes in any of these categories to biological phenomena. Because the choice of space occupancy measures is specific to the data and question, we introduced https://tguillerme.shinyapps.io/moms/moms, a tool to both visualize and capture changes in space occupancy for any measurement. https://tguillerme.shinyapps.io/moms/moms is designed to help workers choose the right space occupancy measures, given the properties of their trait space and their biological question. By providing guidelines and common vocabulary for space occupancy analysis, we hope to help bridging the gap in multidimensional research between ecology and evolution.