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 often 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. (2018) proposed a method for sub-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 spatial 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 spatial under-sampling method of Robinson et al. (2018) by using biological records to train species distribution models of rare millipedes. Results: Using spatially under-sampled training data improved species distribution model sensitivity (true positive rate) but decreased model specificity (true negative rate). The decrease in specificity was minimal for rarer species and was accompanied by substantial increases in sensitivity. For common species, specificity decreased more, and sensitivity increased less, making spatial under-sampling most useful for rare species. Geographic coordinates were as good as or better than environmental variables for predicting distributions of two out of six species. Main Conclusions: Spatial under-sampling improved prediction performance of species distribution models for rare soil arthropod species. Spatial under-sampling was most effective for rarer species. The good prediction performance of models using geographic coordinates is promising for modeling distributions of poorly studied species for which little is known about ecological or physiological determinants of occurrence.