**Summary**

- Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings – for example under climate change scenarios.
- We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation–extrapolation.
- We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues.
- We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables.
- The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions.