How to estimate complementarity and selection effects from an incomplete sample of species

1. Declines in global biodiversity have inspired a generation of studies that seek to characterize relationships between biodiversity and ecosystem functioning. The metrics for complementarity and selection effects derived by Loreau and Hector in 2001 remain some of the most influential and widely used statistics for studying these relationships. These metrics quantify the degree to which the effect of biodiversity on a given ecosystem function depends on only a few species that perform well in monoculture and in mixture (the selection effect) or if the effect of biodiversity on a given ecosystem function is independent of monoculture performance (the complementarity effect). This distinction may be useful in determining the consequences of the loss of rare versus common or dominant species in natural systems. However, because these metrics require observations of all species in a community in monoculture, applications in natural systems have been limited. 2. Here, we derive a statistical augmentation of the original partition, which can be applied to incomplete random samples of species drawn from a larger pool. This augmentation controls for the bias introduced by using only a subsample of species in monocultures rather than having monocultures of all species. 3. Using simulated and empirical examples, we demonstrate the robustness of these metrics, and provide source code for calculating them. We find that these augmentations provide a reliable estimate of complementarity and selection effects as long as approximately 50% of the species present in mixture are present in monoculture and these species represent a random subset of the mixture. 4. We foresee two primary applications for this method: (a) estimating complementarity and selection effects for experimentally assembled communities where monoculture data are lacking for some species, and (b) extrapolating results from biodiversity experiments to diverse natural systems.