Rob James Boyd, Diana E. Bowler, Nick J. B. Isaac, Oliver L. Pescott 

Species occupancy is often defined as the proportion of areal units (sites) in a landscape that the focal species occupies, but it is usually estimated from the subset of sites that have been sampled. Assuming no measurement error, we show that three quantities–the degree of sampling bias (in terms of site selection), the proportion of sites that have been sampled and the variability of true occupancy across sites–determine the extent to which a sample-based estimate of occupancy differs from its true value across the wider landscape. That these are the only three quantities (measurement error notwithstanding) to affect the accuracy of estimates of species occupancy is the fundamental insight of the “Meng equation”, an algebraic re-expression of statistical error. We use simulations to show how each of the three quantities vary with the spatial resolution of the analysis and that absolute estimation error is lower at coarser resolutions. Absolute error scales similarly with resolution regardless of the size and clustering of the virtual species’ distribution. Finely resolved estimates of species occupancy have the potential to be more useful than coarse ones, but this potential is only realised if the estimates are at least reasonably accurate. Consequently, wherever there is the potential for sampling bias, there is a trade-off between spatial resolution and accuracy, and the Meng equation provides a theoretical framework in which analysts can consider the balance between the two. An obvious next step is to consider the implications of the Meng equation for estimating a time trend in species occupancy, where it is the confounding of error and true change that is of most interest.