That's not the Mona Lisa! How to interpret spatial capture-recapture density surface estimates

Spatial capture-recapture methods are often used to produce density surfaces, and these surfaces are often misinterpreted. In particular, spatial change in density is confused with spatial change in uncertainty about density. We illustrate correct and incorrect inference visually by treating a grayscale image of the Mona Lisa as an activity center intensity or density surface and simulating spatial capture-recapture survey data from it. Inferences can be drawn about the intensity of the point process generating activity centers, and about the likely locations of activity centers associated with the capture histories obtained from a single survey of a single realization of this process. We show that treating probabilistic predictions of activity center locations as estimates of the intensity of the process results in invalid and misleading ecological inferences, and that predictions are highly dependent on where the detectors are placed and how much survey effort is used. Estimates of the activity center density surface should be obtained by estimating the intensity of a point process model for activity centers. Practitioners should state explicitly whether they are estimating the intensity or making predictions of activity center location, and predictions of activity center locations should not be confused with estimates of the intensity.