Oliver L. Pescott , Gary D. Powney, Rob James Boyd

Indicators of biodiversity change across large extents of geographic, temporal and taxonomic space are frequent products of various types of ecological monitoring and other data collection efforts. Unfortunately, many such indicators are based on data that are highly unlikely to be representative of the intended statistical populations. Where there is full control over sampling processes, individual spatial units within a geographical population have known inclusion probabilities, but these are unknown in the absence of any statistical design. This could be due to the voluntary nature of surveys and/or because of dataset aggregation. In these cases some degree of sampling bias is inevitable and, depending on error tolerance relative to some real-world goal, we may need to ameliorate it. One option is poststratification to adjust for uneven surveying of strata assumed to be important for unbiased estimation. We propose that a similar strategy can be used for the prioritisation of future data collection: that is, an adaptive sampling process focused on increasing representativeness defined in terms of inclusion probabilities. This is easily achieved by monitoring the proportional allocation of sampled units in strata relative to that expected under simple random sampling. The allocation of new units is thus that which reduces the departure from randomness (or, equivalently, that equalising unit inclusion probabilities), allowing an estimator to approach that level of error expected under random sampling. We describe the theory supporting this, and demonstrate its application using sample locations from the UK National Plant Monitoring Scheme, a citizen science monitoring programme with uneven uptake, and data on the true distribution of the plant Calluna vulgaris. This in silico example demonstrates how the successful application of the method depends on the extent to which proposed strata capture correlations between inclusion probabilities and the response of interest.