An equation to estimate absolute population density from visual census of mobile animals

• Visual counts of animals are dependent on animal mobility and survey procedure.
• We develop a mechanistic equation to standardize results from studies on different animals and from different survey procedures.
• The equation provides a generic tool to convert animal counts into absolute density estimates.

Counting animals, from direct observation or from video or photo records, is one of the most common methods to estimate population density, used for aquatic, terrestrial and flying animals. However, numerous studies caution that the counts derived from visual census may be biased to different degrees depending on animal mobility and survey procedure. This methodological inconsistency hampers the comparison of counts of animals with different mobility or obtained by static and moving observers. In the present work, we provide a generic equation describing the visual census process in relation to animal mobility and survey procedure. Counts are converted into absolute density estimates (as individuals per area) depending on sampling area, animal speed, observer speed, visual sampling field and observation time. The equation offers a mechanistic basis for facilitating the standardization of counts of animals with different levels of mobility or resulting from divergent visual census techniques.