Aim
Integrated species distribution modelling has emerged as a useful tool for ecologists to exploit the range of information available on where species occur. In particular, the ability to combine large numbers of ad hoc or presence‐only (PO) records with more structured presence–absence (PA) data can allow ecologists to account for biases in PO data which often confound modelling efforts. A range of modelling techniques have been suggested to implement integrated species distribution models (IDMs) including joint likelihood models, including one dataset as a covariate or informative prior, and fitting a correlation structure between datasets. We aim to investigate the performance of different types of integrated models under realistic ecological data scenarios.

Innovation
We use a virtual ecologist approach to investigate which integrated model is most advantageous under varying levels of spatial bias in PO data, sample size of PA data and spatial overlap between datasets.

Main conclusions
Joint likelihood models were the best performing models when spatial bias in PO data was low, or could be modelled, but gave poor estimates when there were unknown biases in the data. Correlation models provided good model estimates even when there were unknown biases and when good quality PA data were spatially limited. Including PO data via an informative prior provided little improvement over modelling PA data alone and was inferior to using either the joint likelihood or correlation approach. Our results suggest that correlation models provide a robust alternative to joint likelihood models when covariates related to effort or detection in PO data are not available. Ecologists should be aware of the limitations of each approach and consider how well biases in the data can be modelled when deciding which type of IDM to use.