Modelling the distribution of rare invertebrates by correcting class imbalance and spatial bias

Aim: Soil arthropods are important decomposers and nutrient cyclers, but are poorly represented on national and international conservation Red Lists. Opportunistic biological records for soil invertebrates are sparse, and contain few observations of rare species but a relatively large number of non-detection observations (a problem known as class imbalance). Robinson et al. (Diversity and Distributions, 24, 460) proposed a method for under-sampling non-detection data using a spatial grid to improve class balance and spatial bias in bird data. For taxa that are less intensively sampled, datasets are smaller, which poses a challenge because under-sampling data removes information. We tested whether spatially stratified under-sampling improved prediction performance of species distribution models for millipedes, for which large datasets are not available. We also tested whether using environmental predictor variables provided additional information beyond what is captured by spatial position for predicting species distributions. Location: Island of Ireland. Methods: We tested the spatially stratified under-sampling method of Robinson et al. (Diversity and Distributions, 24, 460) by using biological records to train species distribution models of rare millipedes. Results: Using spatially stratified under-sampled data improved species distribution model sensitivity (true positive rate) but decreased model specificity (true negative rate). The spatial pattern of under-sampling affected model performance. Training data that was under-sampled in a spatially stratified way sometimes produced worse models than did data that was under-sampled in an unstratified way. Geographic coordinates were as good as or better than environmental variables for predicting distributions of one out of six species. Main Conclusions: Spatially stratified under-sampling improved prediction performance of species distribution models for rare millipedes. Spatially stratified under-sampling was most effective for rarer species, although unstratified under-sampling was sometimes more effective. The good prediction performance of models using geographic coordinates is promising for modelling distributions of poorly studied species for which little is known about ecological or physiological determinants of occurrence