Rob James Boyd, Marc Botham, Emily Dennis, Richard Fox, Colin Harrower, Ian Middlebrook, David Roy, Oliver L. Pescott 

1. Biodiversity monitoring schemes periodically measure species’ abundances and distributions at a sample of sites to understand how they have changed over time. Often, the aim is to infer change in an average sense across some wider landscape. Inference to the wider landscape is simple if the species’ abundances and distributions are similar at sampled to non-sampled locations. Otherwise, the data are geographically biased, and some form of correction is desirable.
2. We combine causal diagrams with “superpopulation models” to correct time-varying geographic biases in biodiversity monitoring data. For a given time-period, expert-derived causal diagrams are used to deduce the set of variables that explain the geographic bias, and superpopulation models adjust for these variables to produce a corrected estimate of a landscape-wide mean of e.g. abundance or occupancy. Estimating a time trend in the variable of interest is achieved by fitting models for multiple time-periods and, if the drivers of bias are suspect to change over time, by constructing per period causal diagrams. We test the approach using simulated data then apply it to real data from the UK Butterfly Monitoring Scheme (UKBMS).
3. Where the variables that explain the geographic bias are known and measured without error, our method is unbiased. Introducing measurement error reduces the method’s efficacy, but it is still an improvement on using the sample mean. When applied to data from the UKBMS, the approach gives different results to the scheme’s current method, which assumes no geographic bias.
4. Where the goal is to estimate change in some variable of interest at the landscape level (e.g. biodiversity indicators), models that do not adjust for geographic bias implicitly assume it does not exist. Our approach makes the weaker assumption that there is no geographic bias conditional on the adjustment variables, so it should yield more accurate estimates of time trends in many circumstances. The method does require assumptions about the drivers of bias, but these are codified explicitly in the causal diagrams. Operationalising our approach should be less costly than full probability sampling, which would be needed to satisfy the assumptions of conventional approaches.