Sampling scales define occupancy and underlying occupancy-abundance relationships in animals.

Occupancy-abundance (OA) relationships are a foundational ecological phenomenon and field of study, and occupancy models are increasingly used to track population trends and understand ecological interactions. However, these two fields of ecological inquiry remain largely isolated, despite growing appreciation of the importance of integration. For example, using occupancy models to infer trends in abundance is predicated on positive OA relationships. Many occupancy studies collect data that violate geographical closure assumptions due to the choice of sampling scales and application to mobile organisms, which may change how occupancy and abundance are related. Little research, however, has explored how different occupancy sampling designs affect OA relationships. We develop a conceptual framework for understanding how sampling scales affect the definition of occupancy for mobile organisms, which drives OA relationships. We explore how spatial and temporal sampling scales, and the choice of sampling unit (areal vs. point sampling), affect OA relationships. We develop predictions using simulations, and test them using empirical occupancy data from remote cameras on 11 medium-large mammals. Surprisingly, our simulations demonstrate that when using point sampling, OA relationships are unaffected by spatial sampling grain (i.e., cell size). In contrast, when using areal sampling (e.g., species atlas data), OA relationships are affected by spatial grain. Furthermore, OA relationships are also affected by temporal sampling scales, where the curvature of the OA relationship increases with temporal sampling duration. Our empirical results support these predictions, showing that at any given abundance, the spatial grain of point sampling does not affect occupancy estimates, but longer surveys do increase occupancy estimates. For rare species (low occupancy), estimates of occupancy will quickly increase with longer surveys, even while abundance remains constant. Our results also clearly demonstrate that occupancy for mobile species without geographical closure is not true occupancy. The independence of occupancy estimates from spatial sampling grain depends on the sampling unit. Point-sampling surveys can, however, provide unbiased estimates of occupancy for multiple species simultaneously, irrespective of home-range size. The use of occupancy for trend monitoring needs to explicitly articulate how the chosen sampling scales define occupancy and affect the occupancy-abundance relationship.