Shifting spaces: which disparity or dissimilarity metrics best summarise occupancy in multidimensional spaces?

Abstract

O_LIMultidimensional analysis of traits are now a common toolkit in ecology and evolution and are based on trait-spaces in which each dimension summarise the observed trait combination (a morphospace or an ecospace). Observations of interest will typically occupy a subset of this trait-space, and researchers will apply one or more metrics to quantify the way in which organisms \"inhabit\" that trait-space. In macroevolution and ecology these metrics are referred to as disparity or dissimilarity metrics and can be generalised as space occupancy metrics. Researchers use these metrics to investigate how space occupancy changes through time, in relation to other groups of organisms, and in response to global environmental changes, such as global warming events or mass extinctions. However, the mathematical and biological meaning of most space occupancy metrics is vague with the majority of widely-used metrics lacking formal description.\nC_LIO_LIHere we propose a broad classification of space occupancy metrics into three categories that capture changes in volume, density, or position. We analyse the behaviour of 25 metrics to study changes in trait-space volume, density and position on a series of simulated and empirical datasets.\nC_LIO_LIWe find no one metric describes all of trait-space but that some metrics are better at capturing certain aspects compared to other approaches and that their performance depends on both the trait-space and the hypothesis analysed. However, our results confirm the three broad categories (volume, density and position) and allow to relate changes in any of these categories to biological phenomena.\nC_LIO_LISince the choice of space occupancy metric should be specific to the data and question at had, we introduced moms, a user-friendly tool based on a graphical interface that allows users to both visualise and measure changes space occupancy for any metric in simulated or imported trait-spaces. Users are also provided with tools to transform their data in space (e.g. contraction, displacement, etc.). This tool is designed to help researchers choose the right space occupancy metrics, given the properties of their trait-space and their biological question.\nC_LI