Measuring uncertainty in ecosystem service correlations as a function of sample size

The ecosystem service literature has drastically expanded since the Millennium Ecosystem Assessment, yet the nature of how ecosystem services interact across space is still poorly understood. A key unresolved question is how efforts in sampling (a proxy for data availability) affect the calculation of the interactions or associations among ecosystem services. We contribute to answering this question by estimating a suite of ecosystem services and asking how the values of their interactions – in the form of spatial correlations – change as a function of the sampling rate of the landscape. Specifically, we estimate a set of seven ecosystem services for France (agricultural production potential, biodiversity, carbon storage, livestock grazing potential, net ecosystem productivity, pollination, and soil loss), applying four different measures for biodiversity, seven different methods for carbon storage, and three for pollination. We find that spatial correlations are fairly robust to the sampling rate, supporting the notion that moderate sampling rates across a heterogenous landscape are sufficient to obtain reliable estimates of the average correlation occurring across the landscape. In other words, despite heterogeneity in the spatial distribution of ecosystem services, at sufficient sample sizes we only need to randomly sample ten percent of the landscape to acquire an accurate measure of the correlations between all ecosystem services averaged across the entire landscape. Our results have implications for management, with applications for sampling extent and intensity and the identification of ecosystem service bundles.