Determinism as a statistical metric for ecologically important recurrent behaviors with trapline foraging as a case study

Patterns of discrete behaviors tied together in specific sequences are essential for the formation of complex behavioral phenomena. Such behavioral sequences can be of critical ecological importance, for example relating to resource acquisition, predator evasion, and sexual selection. The role of sequential behaviors in ecology, however, is understudied, in substantial part due to the difficulty of quantifying complex sequences. Here, we present a modified version of determinism (DET) from recurrence quantification analysis (RQA) as a standard metric for quantifying sequential behaviors. We focus on a case study of trapline foraging, a taxonomically widespread behavioral strategy in which animals repeatedly visit spatially fixed resources in a predictable order. Using a bumble bee movement dataset, we demonstrate how to calculate DET and create and interpret recurrence plots, which visually demonstrate patterns in foraging sequences. We show a new method for statistical comparisons of DET scores and assess the sensitivity of DET to resource density using simulated foraging sequences. We find that DET complements and offers distinct advantages over previously available methods for many questions and datasets since it does not depend on any particular resource arrangement or experimental setup and is relatively insensitive to resource density. These features make DET a powerful tool for comparing sequential behaviors between differing environments in a range of ecologically important contexts.