Co-occurrence models fail to infer underlying patterns of avoidance and aggregation when closure is violated

Advances in multi-species monitoring have prompted an increase in the use of multi-species occupancy analyses to assess patterns of co-occurrence among species, even when data were collected at scales likely violating the assumption that sites were closed to changes in the occupancy state for the target species. Violating the closure assumption may lead to erroneous conclusions related to patterns of co-occurrence among species. Occurrence for two hypothetical species was simulated under patterns of avoidance, aggregation, or independence, when the closure assumption was either met or not. Simulated populations were sampled at two levels (N = 250 or 100 sites) and two scales of temporal resolution for surveys. Sample data were analyzed with conditional two-species occupancy models, and performance was assessed based on the proportion of simulations recovering the true pattern of co-occurrence. Estimates of occupancy were unbiased when closure was met, but biased when closure violations occurred; bias increased when sample size was small and encounter histories were collapsed to a large-scale temporal resolution. When closure was met and patterns of avoidance and aggregation were simulated, conditional two-species models tended to correctly find support for non-independence, and estimated species interaction factors (SIF) aligned with predicted values. By contrast, when closure was violated, models tended to incorrectly infer a pattern of independence and power to detect simulated patterns of avoidance or aggregation that decreased with smaller sample size. Results suggest that when the closure assumption is violated, co-occurrence models often fail to detect underlying patterns of avoidance or aggregation, and incorrectly identify a pattern of independence among species, which could have negative consequences for our understanding of species interactions and conservation efforts. Thus, when closure is violated, inferred patterns of independence from multi-species occupancy should be interpreted cautiously, and evidence of avoidance or aggregation is likely a conservative estimate of true pattern or interaction.