Sample size considerations for species co-occurrence models

The multi-species occupancy model of Rota et al . (2016) is widely applied for inferences about interactions in the occurrence of different species, but convergence and estimation issues under realistic sample sizes are common. We conducted a simulation study to evaluate the ability to recover co-occurrence estimates using standard and penalised likelihood under varying sample size and interaction scenarios while increasing model complexity in two dimensions: the number of interacting species and the number of covariates. We demonstrate that the ability to quantify interactions in species occupancy using these models is highly sensitive to sample size and interaction strength. Even in the simplest scenario, there is high bias and low coverage in natural parameters (used for inference) for sample sizes below 400 sites. Strong co-occurrence is detected consistently above 400 sites, but weak co-occurrence is never consistently detected even with 3000 sites. We demonstrate that mean predictive ability is less affected by sample size and complexity, with low bias in derived probabilities at 100 sites. We caution the use of these models for inference in small datasets or when co-occurrence is expected to be weak, but show they are suitable to detect strong co-occurrence in larger datasets and generate predictions of site occupancy states.