How to reduce sampling error in species population monitoring: from theory to methods

Progress towards national and international targets to halt and reverse declines in species' abundances will be assessed using multispecies indicators (MSIs). A distinction must be drawn between two MSIs. One is the ideal, but unobserved, MSI that would have been measured had all species and sites within the scope of the target been sampled. The other is the empirical MSI estimated from the sample in hand. The discrepancy between the two, the sampling error, determines whether the empirical MSI faithfully reflects progress towards abundance targets. We decompose the sampling error of common sample‐based MSIs algebraically into a geographic component reflecting the effect of non‐sampled sites and a taxonomic component reflecting the effect of non‐sampled species. Building on established results from sampling theory, we further decompose each component into three contributing factors: the data defect (capturing the bias of the sampling process), the data scarcity (capturing the odds that species and sites are not sampled) and the problem difficulty (caused by variation in abundance across sites and species). Having shown that both error components are determined by the same three factors, we review approaches to mitigating them. The approaches can be categorised broadly as obtaining more data, estimating the sample‐based MSI in a different way (e.g. using a model), or redefining the ‘target population'. The target population is effectively the spatial and taxonomic scope of the MSI, so redefining it changes what is being estimated and modifies the problem at hand. Hence, it can be justified only when an accurate answer to a different question (e.g. pertaining to a subset of species from the original population) is preferable to an inaccurate answer to the original one.