Truncated Lévy walks are expected beyond the scale of data collection when correlated random walks embody observed movement patterns.

Abstract

Translating observations taken at small spatio-temporal scales into expected patterns at greater scales is a major challenge in spatial ecology because there is typically insufficient relevant information. Here, it is shown that truncated Lévy walks are the most conservative, maximally non-committal description of movement patterns beyond the scale of data collection when correlated random walks characterize observed movements and when there is partial information about landscape and behavioural heterogeneity. This provides a new conceptual basis for Lévy walks that is divorced from optimal searching theory and free from the difficulties with discerning their presence in empirical data.