1. Understanding how animal movements change across space and time is a fundamental question in ecology. While classical analyses of trajectories give insightful descriptors of spatial patterns, a satisfying method for assessing the temporal succession of such patterns is lacking.

2. Network analyses are increasingly used to capture properties of complex animal trajectories in simple graphical metrics. Here, building on this approach, we introduce a method that incorporates time into movement network analyses based on temporal sequences of network motifs.

3. We illustrate our method using four example trajectories (bumblebee, black kite, roe deer, wolf) collected with different technologies (harmonic radar, platform terminal transmitter, global positioning system). First, we transformed each trajectory into a spatial network by defining the animal’s coordinates as nodes and movements in between as edges. Second, we extracted temporal sequences of network motifs from each movement network and compare the resulting behavioural profiles to topological features of the original trajectory. Finally, we compared each sequence of motifs with simulated Brownian and Lévy random motions to statistically determine differences between trajectories and classical movement models.

4. Our analysis of the temporal sequences of network motifs in individual movement networks revealed successions of spatial patterns corresponding to changes in behavioural modes that can be attributed to specific spatio-temporal events of each animal trajectory. Future applications of our method to multi-layered movement and social network analysis yield considerable promises for extending the study of complex movement patterns at the population level.

dataset_S1: location data of a bumblebee tracked with a harmonic radar on 15/04/2018. The dataset is organised in three columns (Latitude, Longitude, ID).

Bumblebee search trajectory

We used a harmonic radar to obtain a search trajectory of a bumblebee worker on 15/04/2018 (1 recording every 3.3s, 364 data points, Fig. S1A). We set up a commercial colony of Bombus terrestris (Biobest NV, Westerlo, Belgium) in a flat dry rice farm land in Sevilla (Spain) (Fig. S2). We trained multiple bumblebees to forage on three artificial flowers (i.e. blue platform with 40% (v/v) sucrose solution, see details in Lihoreau et al., 2012) positioned two meters in front of the nest box. Once a regular forager was identified (bumblebee performing several consecutive foraging bouts), we closed the colony entrance and randomly moved the three artificial flowers away in the field. The focal bumblebee was equipped with a transponder (16 mm vertical dipole) upon leaving the nest box and tracked with the harmonic radar until it returned to the colony (Riley et al., 1996). The radar was placed 350 meters away from the colony nest box (Fig. S3) and returned the 2D coordinates of the tagged bumblebee within a range of 700 m.

dataset_S2: location data of a black kite tracked with GPS from 28/05/2019 to 19/08/2019. The dataset is organised in three columns (Latitude, Longitude, ID).

Black kite long-range migration trajectory

We used GPS to track an adult female black kite (Milvus migrans) moving across Spain from 28/05/2019 to 19/08/2019 (1 recording every 6h, 332 data points, Fig. S1B). The bird was caught after an injury and maintained five weeks in an aviary for rehabilitation. We equipped the bird with a Platform Terminal Transmitter (PTT) back-packed (Xerius Tracking, France) and released it in Toulouse (France), where it first moved within a limited area before migrating on its way to Morocco.

Text_S1: command lines needed to run the analysis and the graph produced in this manuscript. It can be run with dataset S2, and the datasets obtained from the movebank website (Roe deer: Animal Identifier: Sandro (M06), from Cagnacci et al., 2011; Wolf: Animal identifier: Zimzik, from Kaczensky et al., 2006). For dataset S1 few lines to remove missing data are needed (contact cristian.pasquaretta@univ-tlse3 for details).