Sample size considerations for species co-occurrence models

Multispecies occupancy models are widely applied to infer 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 of a recently developed model to recover co-occurrence estimates under varying sample size and interaction scenarios while increasing model complexity in two dimensions: the number of interacting species and the number of covariates. Using both standard and penalized likelihood, we demonstrate that the ability to quantify interactions in species occupancy using this model is highly sensitive to sample size, detection probability, and interaction strength. In the simplest scenario, there is high bias in the interaction parameter (used for co-occurrence inference) with less than 100 sites at high detection, and 400-1000 sites at low detection, depending on interaction strength. Strong co-occurrence is detected consistently above 200 sites with high detection probabilities, but weak co-occurrence is never consistently detected even with 2980 sites. We demonstrate that the mean predictive ability of the co-occurrence model is less affected by sample size, with low bias in derived probabilities at 50 sites. Our results highlight that while occupancy patterns are often robust to sample size limitations, reliable inference about co-occurrence demands substantially larger datasets than many studies currently achieve. We caution the interpretation of model output in small datasets or when co-occurrence is expected to be weak, but show methods are suitable to quantify strong co-occurrence in larger datasets and generate predictions of site occupancy states.