Fine-scale environmental variation in species distribution modelling: regression dilution, latent variables and neighbourly advice

P>1. Developing the next-generation of species distribution modelling (SDM) requires solutions to a number of widely recognised problems. Here, we address the problem of uncertainty in predictor variables arising from fine-scale environmental variation. 2. We explain how this uncertainty may cause scale-dependent 'regression dilution', elsewhere a well-understood statistical issue, and explain its consequences for SDM. We then demonstrate a simple, general correction for regression dilution based on Bayesian methods using latent variables. With this correction in place, unbiased estimates of species occupancy vs. the true environment can be retrieved from data on occupancy vs. measured environment, where measured environment is correlated with the true environment, but subject to substantial measurement error. 3. We then show how applying our correction to multiple co-occurring species simultaneously increases the accuracy of parameter estimates for each species, as well as estimates for the true environment at each survey plot - a phenomenon we call 'neighbourly advice'. With a sufficient number of species, the estimates of the true environment at each plot can become extremely accurate. 4. Our correction for regression dilution could be integrated with models addressing other issues in SDM, e.g. biotic interactions and/or spatial dynamics. We suggest that Bayesian analysis, as employed here to address uncertainty in predictor variables, might offer a flexible toolbox for developing such next-generation species distribution models.