A fundamental theory of actual error for species population monitoring

Rob James Boyd, Susan Jarvis, Xiao-Li Meng, Gary D. Powney, Rebecca Spake, Oliver L. Pescott 

Progress towards many national and international targets to halt and reverse declines of species populations (abundances) will be measured against Multispecies Biodiversity Indicators (MSIs). Like any sample-based estimator, MSIs approximate some real-world quantity (the estimand), and the difference between the two is the ‘actual’ or realised statistical error. We propose a general estimator and its corresponding estimand, both of which apply to many high-profile MSIs. Doing so allows us to decompose the error into a within-species component reflecting the impact of missing data for relevant locations and a cross-species component reflecting the impact of non-sampled species. Building on recent developments in sampling theory, we further decompose each of the within- and cross-species errors into three contributing factors: the ‘data defect’ (akin to sampling bias), the ‘data scarcity’ (reflecting the proportion of sites and species sampled) and the ‘problem difficulty’ (variability of abundance across sites and species). Approaches to reducing the error of MSIs can be recast as approaches to minimising one or more of these three quantities: for example, sample weighting reduces the data defect, sampling previously unmonitored species and locations minimises the data scarcity and focusing on functionally similar species may reduce the problem difficulty. Our theoretical framework thus unifies existing approaches to reducing the error of MSIs, reveals alternative approaches that might be considered in future and highlights opportunities for improving the communication of uncertainty.