Using the Price equation to understand ecosystem service stability in real-world systems
Hundreds of biodiversity-ecosystem function (BEF) experiments have shown that the stability of ecosystem function increases with the number of function-providing species. However, it is unclear if experimental results can predict the consequences of losing species in larger-scale, real-world systems. Studying BEF relationships at larger scales presents an analytical challenge, because real-world community properties such as species richness, species composition and abundance vary unpredictably across space. The Price equation from evolutionary biology can resolve this problem by comparing function at different sites and partitioning between-site variation into three additive terms that describe the relative importance of random species loss (termed “richness”), non-random species loss (“composition”) and abundance fluctuations of species present at both sites (“abundance”). Here, we present a new partition of the Price equation designed to analyze the temporal variance of an ecosystem service, namely pollen deposition. We applied this derivation to two multi-year, real-world datasets containing information on bee visits to 16 watermelon and blueberry farms (>4,000 individual specimens of 88 species) in New Jersey and Pennsylvania. To translate bee visitation into a meaningful measure of pollen deposition, we used additional data (996 single-visit pollen deposition experiments) on pollen deposition efficiency of different bee species.
In watermelon, site-level differences in the temporal variance of pollen deposition were explained almost entirely by the abundance term. Specifically, the effect size of the abundance term was 32 times larger than the effect sizes of species richness and species composition summed together. In watermelon, the abundance term is large because it is driven by temporal fluctuations in the abundance of the dominant bumblebee Bombus impatiens. In contrast, the richness and composition terms are small because differences in bee species richness across sites were due to the presence and absence of rare species with little contribution to variance. In blueberry, no single dominant bee was present and the relative sizes of abundance and richness were comparable. Therefore, we suggest that the shape of the skewed species abundance distributions found in our systems, as well as almost all real-world systems, mediates the relative importance of richness and abundance. We also discuss how systematic differences between controlled experiments and real-world systems may affect commonly-invoked mechanisms for biodiversity-stability relationships. Finally, we suggest that more BEF studies should be conducted in real-world systems, to further understanding of how ongoing changes in ecological communities will affect the ecosystem services on which humans rely.