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Abstract

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. 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. 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. 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.
Methods Ecol Evol. 2020;00:1–13. wileyonlinelibrary.com/journal/mee3
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  1© 2020 British Ecological Society
1 | INTRODUCTION
Over the past recent years, the study of animal movements has
experienced a rapid growth thanks to the development of new
technologies to automatically collect long-term individual data
on wild animals (Flack, Nagy, Fiedler, Couzin, & Wikelski, 2018;
Strandburg-Peshkin, Farine, Couzin , & Crofoot, 2015; Tomkiewicz,
Fuller, Kie, & Bates, 2010). Th e acquisition of high resolution
data has also requi red the develo pment of new st atistical tools
to describe and analyse movement s. At the most b asic level , it is
Received: 30 September 2019 
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  Accepted: 24 January 2020
DOI: 10.1111/2041-210X.13364
ANIMAL SOCIAL NETWORKS
Analysis of temporal patterns in animal movement networks
Cristian Pasquaretta1| Thibault Dubois1| Tamara Gomez-Moracho1|
Virginie P. Delepoulle2| Guillaume Le Loc’h3| Philipp Heeb4| Mathieu Lihoreau1
1Research Center on Animal C ognition
(CRCA), C enter for Integrative Biology (CBI),
CNRS, Un iversity Toulouse I II-Paul Sabatier,
Toulouse, Fra nce
2Département de la SARL Xerius,
XeriusTracking, Toulouse, France
3UMR IHAP, ENVT, INRA, Université de
Toulouse, Toulouse, France
4Labor atoire Evol ution et Diversi
Biologique, (EDB UMR 5174) Université de
Toulouse, CNRS, IRD, Toulouse cedex 9,
France
Correspondence
Cristian Pasqu arett a
Email: cristian.pasquarett a@univ-tlse3.fr
Funding informati on
Agence N ationale de la Rech erche, G rant/
Award Number: ANR-16-CE02-0002-01;
Laboratoire d' Excellence (LABEX ) TULIP,
Grant/Award Number: ANR-10-LABX-41
Handling Editor: David Soto
Abstract
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 intro-
duce 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 tra-
jectory 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 compared the resulting be-
havioural 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 be-
havioural 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.
KEYWORDS
animal trajectories, Argos, GPS tracking, harmonic radar, motifs time series, movement
ecology, movement networks, spatial networks
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possible to visualize the sequence of locations visited by the ani-
mal by joining those locations with a line, that is, the animal trajec-
tory. S pee d, step length (dis tance betwe en successive locations),
residency (the time an individ ual remains at a specif ic loc ation
before moving) and turning angle (change of direction between
successive steps) are some of the main param eters that can be
extrac ted from such a traje ctory (Dodge, Weibel, & Lautenschütz,
200 8; Patterson, Thomas, Wilcox, Ovaskainen, & Matthiopoulos,
2008). These parameters tend to be correlated with specific be-
havioural states (Edelhoff, Signer, & Balkenhol, 2016) and can be
grouped into patterns dependent of enviro nmental cons traint s
and spatial variabilit y. So far, however, this approach has y ielded
little information about the temporal dimension of animal trajec-
tories (Jacoby & Freeman, 2016). For many animals, movements
can show dramatic change s with time as a result of motivation,
experience, social interactions or modifications of the environ-
ment (Swingland & Greenwood, 1983). Identif ying these changes
in complex movement dat asets can t hus bring critic al insights into
the fundamental ecology of animals.
Recent at tempts to develop a unified spatio-temporal analytical
framework of movement data have shown the existence of a rela-
tionship between temporal autocorrelations of movement param-
eters (i.e. step length) and spatial distribution of critical resources
(Wittemyer, Polansky, Douglas-Hamilton, & Getz, 2008). Others
have proposed to analyse the sequence of habitats encountered by
an animal to extract behavioural changes in a trajector y (De Groeve
et al., 2016; van Toor, Newman, Takekawa, Wegmann, & Safi, 2016).
Behavioural change point analysis of movement parameters is a pow-
erful tool to estimate the time at which an animal changes it s move-
ment pat terns and how this corresponds to behavioural states such
as resting, foraging or moving (Gurarie, Andrews, & Laidre, 2009;
Teimouri, Indahl, Sickel, & Tveite, 2018). Multiple unsupervised
statistical methods have also been used to reduce complex animal
trajectories into human understandable format such as the circular
standard deviation (Potts et al., 2018), the t-stochastic neighbouring
embedding (t-SNE) algorithm (Bartumeus et al., 2016), the recur-
sive multi-frequency segmentation (Ahearn & Dodge, 2018), or the
Fourier and wavelet analysis (Polansky, Wittemyer, Cross, Tambling,
& Getz, 2010). Despite satisfying the quantitative aspects of spa-
tio-temporal analysis of animal movement data, these methods
often require advanced mathematical knowledge and lack intuitive
tools to help data visualization and interpretation by ecologists.
Network analysis may constitute a simpler, yet powerful, ap-
proach for such analyses (Bastille-Rousseau, Douglas-Hamilton,
Blake, Northrup, & Wittemyer, 2018; Jacoby & Freeman, 2016;
Pasquaretta, Jeanson, Andalo, Chittka, & Lihoreau, 2017; Pasquaretta
et al., 2019). For example, Bastille-Rousseau et al. (2018) transposed
global positioning system (GPS) locations obtained from three differ-
ent species (African elephants, giant Galapagos tortoises, Mule deer)
into networks. In such networks, nodes represent spatial locations
visited by the animals and edges animal movements between these
locations. The analysis of node-level network metrics demonstrated
that locations with high betweenness centrality scores (frequency
at which a node acts as bridge along the shortest paths passing
by two other nodes) was indicative of bridges between migration
areas for tortoises and corridors between foraging sites for ele-
phants (Bastille-Rousseau et al., 2018). Network analysis of spatial
data can thus bring important information for studying associations
of complex behavioural patterns and spatial characteristics. So far,
however, this method relies on a static representation of animal
space use and does not consider the temporal nature of movements
(Bastille-Rousseau et al., 2018; Jacoby & Freeman, 2016).
Here, we built on this approach to analyse temporal patterns in
animal movement networks. Our method consists in transforming tra-
jectories into movement networks and analysing the temporal succes-
sion of motif patterns (i.e. three-node subgraphs, Wasserman & Faust,
1994) in t hese n etwork s. To illustrate the valid ity of the method , we an-
alysed example datasets of insects (bumblebee), birds (black kite) and
mammals (roe deer, wolf) monitored with different technologies and at
different spatio-temporal scales. We argue that this method, easily ac-
cessible to ecologists, can favour comparative analyses and bring new
insights into the movement ecology of a wide range of species.
2 | MATERIALS AND METHODS
2.1 | Movement datasets
We tested our method on animal trajectories obtained from two
original datasets (bumblebee, black kite) provided in Dryad (https ://
doi.org/10.5061/dryad.47d7w m390), and two published datasets
(roe deer, wolf) publicly available on the MoveBank data repositor y
(Wikelski & Kays, 2020). The trajectories were selected to illustrate
how the analysis of spatio-temporal behavioural patterns in move-
ment networks can apply to different types of raw data (harmonic
radar, GPS), to animal species with different locomotion modes (flying,
walking), at different spatial scales (region, across countries) and in
different behavioural contexts (search, migration, roaming).
2.1.1 | Bumblebee search trajectory
We used a harmonic radar to obtain a search trajectory of a bum-
blebee worker on 15 April 2018 (1 recording ever y 3.3 s, 364 data
points, Figure S1a). We set up a commercial colony of Bombus ter-
restris (Biobest NV) in a flat dry rice farm land in Sevilla (Spain; Figure
S2). We trained multiple bumblebees to forage on three artificial
flowers (i.e. blue platform with 40% (v/v) sucrose solution, see de-
tails in Lihoreau et al., 2012) positioned 2 m in front of the nest box.
Once a regular forager was identified (bumblebee performing sev-
eral 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 m away from the colony nest box (Figure S3) and
  
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returned the two-dimensional coordinates of the tagged bumblebee
within a range of 700 m.
2.1.2 | Black kite long-range migration trajectory
We used GPS to track an adult female black kite Milvus migrans mov-
ing across Spain from 28 May 2019 to 19 August 2019 (1 recording
every 6 hr, 332 data points, Figure S1b). The bird was caught after
an injur y and maintained 5 weeks in an aviary for rehabilitation. We
equipped the bird with a platform terminal transmitter (PTT) back-
packed (Xerius Tracking) and released it in Toulouse (France), where
it first moved within a limited area before migrating on its way to
Morocco.
2.1.3 | Roe deer short-range migration trajectory
This dataset was obtained from the EURODEER collaborative pro-
ject (E. Mach Foundation; http://sites.google.com/site/eurod eerpr
oject ; Cagnacci et al., 2011). It consists of one GPS trajector y of an
adult male roe deer Capreolus capreolus collected from 23 October
2005 to 28 October 2006 (1 recording every 4 hr, 1,827 data points;
Figure S1c). The roe deer was tracked in the area of Trentino Alto
Adige (Italy). Behavioural patterns in this trajectory are dominated
by short range migrator y movements representing the yearly leave-
and-back movements between two winter and summer sites. To
compare this trajectory with the other example trajectories, we re-
duced the number of data points to 457 by resampling the trajectory
every 16 hr.
2.1.4 | Wolf roaming trajectory
This dataset was obtained from a study of the Przewalskii horse re-
introduction project of the International Takhi Group (Kaczensky,
Ganbaatar, Enksaikhaan, & Walzer, 2006). It consists of one GPS tra-
jector y of an adult male wolf Canis lupus collected from 05 March
2004 to 18 September 2005 (1 recording every 8 hr, 1,455 data
points in total). The wolf was tracked in the mountains of the Goby
Desert (Mongolia). Behavioural patterns in this trajectory are domi-
nated by territorial movements around the mountains and one main
roaming period (Figure S1d). To compare this trajectory with the
other example trajectories, we reduced the number of data points to
485 by resampling the trajectory each 24 hr.
2.2 | Method overview
We analysed all the trajectories following four major steps . First,
we transformed the raw spatial coordinates into movement net-
work s built using different spatial resolutions (grid sizes). Second,
we extrac ted the temporal sequen ce of network motifs obtained
from these different networks and compared them to define an
optimal grid size for furt her ana lyses. Third, we used the selec ted
temporal sequence of netwo rk motifs to highlight spatio-temporal
locations showing complex behaviours in the original trajec tor y.
Fourth, we extracted the non-random temporal transitions be-
tween consecutive motifs in the experimental datasets and com-
pared them with the non-rando m transitions of simulated dat a
from classical movement models. The complete r code is available
in Dryad (https ://doi.org/10.5061/dryad.47d7w m390) with de-
scription in Text S1.
2.2.1 | Transform spatial coordinates into a
temporal movement network
The first step consisted in transforming the raw movement data into
a format that can be automatically analysed with network metrics.
To do so, we rasterized the animal coordinates on a spatial grid.
Because different grid resolutions affect the topological structure
of the resulting net work (Bastille-Rousseau et al., 2018), we built a
range of net works with different grid resolutions.
Building a movement network from an animal tr ajectory has
the risk of oversimplifying the information depending on grid reso-
lution (Figure 1). Effects vary from large gr id size, where the entire
trajectory can be summarized into movement lo ops starting and
ending at a single location, to small grid size, where each location
of the raw trajectory corresponds to different grid cell. The op-
timal grid resolu tion capturing biologic ally relevant behavioural
patterns is expec ted to lay somewhere in the middle. Previous
studies have used the median of t he step length distribut ion as
grid size, based on the fa ct that this value leads to robust result s
under the assumption of Brownian movements (Bastille-Rousseau
et al., 2018). However, many animal trajectories show more com-
plex patterns. To ad dress t his issue, for each trajectory we tested
nine grid resolutions. Each grid resolution corresponded to one
specific quantile of the step length distribution of the trajectory
(i.e. p = .1, .2, .3, .4, .5, .6, .7, .8, .9). The animal coordinates were
thus t ransformed into nodes and movement s between them into
directed edges (see Figure 1b). We attributed the same node iden-
tity to e ach coordinate falling into the same g rid cell. Empty cells
were considered as non-visited cells at this stage. We then trans-
formed the spatial network into a temporal edge list by associating
a time to each movement of the sequence.
2.2.2 | Extract temporal sequence of network
motifs from movement networks
Treating animal trajectories as behaviour al sequences provides a
description of topol ogical movement structures and can reve al the
processes by which th ese patterns appear and are maintained in
the sequences (De Groeve et al., 2016). For each trajectory, we
extrac ted temporal sequences of motif patterns between three
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nodes from the edge list of each movement network. In the con-
text of movement network s, th ese sequence s refer to subgraphs
that describ e spatio-temp ora l movements (Pasquarett a et al.,
2017) and can be used to understand non-random successions of
patterns in a complex behavioural sequence (Patel, Keogh, Lin, &
Lonardi, 2002).
Among the 13 possible different motifs between three nodes,
five are irrelevant for movement data (Figure S4, see details in
Wasserman & Faust, 1994). Four of the eight remaining motifs be-
long to the family of ‘loosely connected motifs’, that is, subgraphs
missing one edge between two out of three nodes (Juszczyszyn,
2014; Figure 2a). The four other motifs belong to the family of
‘closely connected motifs’, that is, subgraphs with edges between
all nodes. In the context of movement data, the loosely connected
motif M3 indicates movements across locations without any revisit
to any location. All other motifs indicate more complex movement
patterns charac terized by at least one revisit to a location.
Temporal sequences of network motifs can be extracted by di-
viding the edge list into specific motif windows including at least
three different connected nodes (Paranjape, Benson, & Leskovec,
2017). Here we built sliding windows containing a maximum of three
nodes, allowing us to create a temporal sequence of successive mo-
tifs based on the utilization of three consecutive locations. To do
so, we started from the first node of the network and iteratively
analysed the entire sequence to create subsequences of three nodes.
Each node in this subsequence can be visited only once (e.g. M3) or
several times (e.g. M13). Once the first subsequence was created, we
applied the same iterative algorithm to find all the successive motifs
using the last node of the previous subgraph as starting point for the
next one (Figure 2b).
2.2.3 | Adjustment of grid resolution
We applied the Dynamic Time Warping (DTW) algorithm (Sakoe &
Chiba, 1978) to compare temporal sequences of motifs built with
different grid resolutions and select the most suitable grid resolution
given the data. The DTW compares two, or more, time series and
returns the number of steps needed to transform one reference time
series into another. Each step corresponds to the minimum number
of changes needed to transform one query series into its reference
series (see details in Giorgino, 2009).
We used this approach to create matrices of similarit y bet ween
motif time series. From these data, we finally selected the most
suitable motif time series characterized by: (a) the largest num-
ber of different motifs (abundance) and (b) the most equal pro-
portion of each motif (evenness). To do so, we created a list of
temporal sequences of network motifs obtained from different
FIGURE 1 Transformation of an animal movement data into a temporal movement network: the problem of grid resolution. A
hypothetical trajector y is transformed using three different cell sizes: large, medium and small. (a) Original trajectory embedded in each grid
resolution. Orange dots represent the coordinates of the animal. (b) Resulting movement network built by assigning a single node identity to
each of the coordinates that fall into the same cell. The trajectory is thus transformed into a movement network in which spatial coordinates
are nodes (orange dots) and movements between them are directed edges (light blue arrows). Direc ted edges associated to a specific time
produce a temporal movement net work. Shannon diversity index used to select the optimal grid size given the data (see adjustment of grid
resolution paragraph below)
  
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grid resolutions (i.e. p = . 2, .3, .4, .5, .6, .7, .8, .9) and calculated
a similarity matrix using the DTW distance between them with
the function ‘dist’ of the r package stats (R Core Team, 2018). We
applied the Shannon diversity index (Shannon, 1948), using the r
package vegan (Oksanen et al., 2018), to select the optimal time
series. Specifically, we used as opt imal grid size the step length
corresponding to the highest value of Shannon diversit y index (to
illustrate the robustness of the met hod , result s from the second
highest v alue are presented in Text S2). With this procedure, we
ensured an objec tive way to select t he best grid resolut ion value
returning the time series with t he largest number of motifs whic h
prop ortions were also more equally represented. For each dataset,
we identified the best grid resolution to analyse complex move-
ment patterns using sequences of behavioural pat terns instead
of the trajectory parameters themsel ves (e.g . median s tep length,
mean turning angle). We evaluated whether the proportion of mo-
tifs differed across datasets with a chi-square (χ2) test, applie d to
a table with rows and columns correspo nding to motif counts and
animals, using the ‘chisq.test’ function in r.
2.2.4 | Visualization of temporal
behavioural patterns
To illustrate that our method can be used to identif y spatio-temporal
behavioural patterns from complex animal trajectories, we repre-
sented the evolution of motifs through time. Here, we focused only
on the seven motifs identified as indicative of complex movements:
characterized by at least one revisit to a node. We extracted the geo-
graphic locations involved in the construction of these motifs and
represented them in the network to describe spatio-temporal pat-
terns of complex behaviours. Loops (movements starting and end-
ing at the same location) are structurally removed when analysing
network motifs (Wasserman & Faust, 1994). To account for such be-
havioural patterns, we first extracted the number of loops obser ved
inside each motif and we later applied a generalized linear model
(GLM) for count data (Poisson error distribution) to estimate the re-
lationship between motif complexity and the number of loops per-
formed using the glm function of the r package stats (R Core Team,
2018). We also tested different temporal windows by resampling the
roe deer and wolf dataset (see Text S3).
2.2.5 | Evaluation of temporal motifs with a
null model
The evaluation of motif counts of a static network is typically pre-
sented in terms of difference from a null model (Milo et al., 2002).
The null model is usually a randomized version of the empirical net-
work constrained by some of the network characteristics such as
the degree sequence (node randomization) or the strength of the
relationship between nodes (edge randomization) or both (Farine &
Whitehead, 2015). If the count of a specific motif significantly ex-
ceeds that of the null model, the motif is considered to be structur-
ally significant. However, if the null model is far from having realistic
features, the differences obser ved (even if statistically significant)
do not tell anything insightful about the nature of each motif (Art zy-
Randrup, Fleishman, Ben-Tal, & Stone, 2004).
In temporal directed networks, where a temporal correlation
between successive motifs can be expected, an effective way to
FIGURE 2 Possible three-node motifs in movement networks and extraction of their temporal sequence. (a) Eight out of 13 possible
motifs were retained. These included four loosely connected motifs (M3, M4, M5, M6), that is, subgraphs missing one edge between two
out of three nodes, and four closely connected motifs (M8, M10, M12, M13), that is, subgraphs with at least one edge between each node.
(b) Hypothetical directed movement network (lef t) represented as a node sequence (right). Horizontal red bars refer to the subsequence of
three nodes used to extract each motif
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compare the experimental sequence with a randomized sequence
is by time-shuffling, that is randomly sample motifs in a sequence
and change their temporal position. The focus is then made on the
structure of the motif sequence itself and on the probabilit y of tem-
poral co-occurrence (conditional probability) of specific motif associ-
ations. Here we used the conditional probabilities between each pair
of motif to reveal the existence of non-random transitions between
specific behavioural patterns. We first calculated the probability ma-
trix to move from each motif to the next (8 × 8 matrix) and compared
this matrix with 100 probability matrices obtained from time-shuf-
fled time series. For each pair of temporal patterns, we calculated
the 95% confidence intervals (CIs) and compared the probabilities
from the original motifs time series to the corresponding probabili-
ties obtained from time-shuffled motif time series. We used a one-
tail analysis and consider probabilities falling outside of the upper
95% CI as significant. The obtained resulting binary matrix thus as-
signs 1 to all the positive non-random conditional probabilities and
0 to the others.
2.2.6 | Comparing non-random probabilities with
Brownian motion and Lévy walk
Brownian motion and Lévy walks are two main theoretical ran-
dom m ove ment pattern s used to describe trajector ies obs er ved
in n ature (Tur chin, 1998; Figu re 3). Pure Brownian random walk s
have been in trodu ced to desc ribe ani mal sear ch st rategies when
no information is available. Brownian motions are determined by
successive steps in rand om dir ec tions whose step lengt hs and
tur nin g angles are ran domly drawn from a normal dis tribution
(Bartumeus, Catalan, Fulco, Lyra, & Viswanathan, 2002). Lévy
walks are defined by movement patterns following a power-
law distribution (Reynolds, 2018; Shlesinger & Klafter, 1986;
Viswanathan et al., 1996). To estimate the degree by which the
four original trajectories differed from Brownian and Lévy ran-
dom movements, we compar ed the binar y matri ces of t ransition
between motifs obtained for each of the four animal trajecto-
ries with 100 probabilit y matri ces obtained from both simulated
Brownian an d vy trajec tories by calculating the Jaccard in dex
of similarity using the function birewire.similarity in the r pack-
age ‘Birewire’ (Gobbi, Iorio, Albanese, Jurman, & Saez-Rodriguez,
2017). We thus obtained four distributions of Jaccard indices
(one for each dataset) and compared them using t-stat istic . We
adjusted the α value using the seq uential Bonferro ni correction
(Rice, 1989).
3 | RESULTS
3.1 | Identification of optimal grid size
The crucia l ste p in transfo rm ing a n ani mal t raje ct or y int o a
movement network inv olves the se le ctio n of an o ptimal grid
resolution that is small enough to obtain a suitable number of
nodes to create a network, and large enough to provide insight-
ful details on the anim al m oveme nt pat te rn s. For eac h datase t,
we extracted the step length values of the nine quantiles of
the step length distribution of the trajectory, and removed any
qua ntiles with step length value close to zero (i .e. values lower
than 10–6). We obt aine d seven possi ble quan tile valu es for th e
bla ck kite, and nine quant il e va lu es for the bu mblebee, the ro e
deer and th e wo lf (Tab le S1). We used th es e quan tile values as
cell size to build sp atial gr id s and gener ate move ment net wo rk s.
From these networks, we extrac ted temporal se quences of net-
work motifs and compared them using the DTW distance to se-
lec t th e opt im al gr id reso lu tion gi ven t he data . We then applied
the Shannon diversity index to select the motif time series for
each dataset as candi date se quence for subsequent analys es .
The Shannon diver sity in de x ret ai ne d the moti f tim e serie s 5, 5,
7 and 8, corresp on ding to a cell si ze of ste p l en gt h val ue 11. 20 9
(i. e. qua ntile 0.5) for the bumble be e, 0.0075 (i.e. quantile 0.7)
for the bl ack kit e, 0. 0037 (i.e . quant ile 0 .7) for the ro e deer an d
0.2642 (i.e. quantile 0.8) for t he wolf (Figure 4; see Table S1 for
the values of all quant iles). Th us , th e opti mal gr id size selected
for the temp or al anal ys es of networ k motifs va ried ac ross the
four datasets.
FIGURE 3 Examples of simulated
random movements. Brownian motion is
characterized by a stationary behaviour
throughout the entire trajectory whereas
Lévy walk shows an alternance of local
stationarity and ballistic movements
  
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3.2 | Analysis of behavioural patterns
The propor tion of motifs was different across the four datasets
(χ2 = 56.77, df = 21, p < .001). The dominant motif was the motif M3
(Figure 5) that characterizes unidirectional movements across three
nodes without revisits. This motif has dif ferent biological meanings
depending on the species under consideration. In the black kite and
the roe deer, a succession of M3 motifs is characteristic of migra-
tory movement patterns. In the wolf, however, this temporal pattern
is characteristic of movement s towards familiar locations in a home
range, such as hunting areas. In the bumblebee, the succession of
M3 motif is indicative of search flights.
The seven other motifs characterize bidirectional movements
with at least one revisit to the same node, indicating a temporal re-
use of specific areas. The different proportions of such motifs in the
movements may have different biological meanings in the different
species and, once identified, are open to study.
To fur ther explo re and int erpret the successi on of te mp oral
motifs, we cons tr uc ted simpli fied traj ec torie s highl ighting th e
spatial lo catio ns of the simple (uni direc ti onal) motif an d the more
complex (bidirectional) motifs in the original data. Because motif
analysis does not allow to include loops (self-edges), we also con-
struc te d sim plifi ed traj ec torie s hig hlighting the s patial loc ation s
of each loop (Figure 6). The number of loops on the same location
increased with the complexity of network motifs indicating that
for all four trajectories, more complex behavioural patterns rep-
resent areas of temporal interest in animals (GLM for count data—
bumblebee: estimate = 0.243, SE = 0.058, z = 4.175, p < .001;
black kite: estimate = 0.203, SE = 0.025, z = 8.252, p < .0 01; roe
deer: estimate = 0.122, SE = 0.019, z = 6.296, p < .0 01; wo lf :
estimate = 0.275, SE = 0.014, z = 19.698, p < .001). In the bumble-
bee trajector y, bidi rection al motifs occur re d when the individ ual
was in the nest area and near flowers, indicating an association
bet we en comp lex behaviou ra l patte rns and familiar loc ation s,
FIGURE 4 Motif time series selection.
The Shannon diversity index was applied
to motif time series for each dataset: (a)
bumblebee, (b) black kite, (c) roe deer, (d)
wolf. The highest Shannon diversity index
value, used to select the most suitable
motif time series for each dataset, is
highlighted in red
FIGURE 5 Proportion of network
motifs in each dataset. For each species
(a) bumblebee, (b) black kite, (c) roe deer,
(d) wolf, the proportion of motifs has been
divided into two main categories: a motif
describing a unidirectional movement
(orange) and seven motifs describing more
complex bidirectional patterns (blue)
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while loop s tende d to be concent rated ar ound the nest only, a
beh aviou ral pa tt ern re minis cent of orient ation fligh ts (Os borne
et al., 2013; Figure 6a). In the black kite trajectory, more complex
bidirectional motifs occurred in areas around the release point
and few l oc ations af ter the star t of the mig ration an d th ey a lso
correspond to singl e lo cations of intensive use (loops; Figure 6b).
FIGURE 6 Spatio-temporal sequence of behavioural patterns. Evolution of motifs: temporal sequence of network motifs for each
dataset. Blue: bidirectional motifs (M4, M5, M6, M8, M12, M13). Red: unidirectional motif (M3). Complex motifs: temporal motifs mapped
on original trajec tories. Blue gradient encodes the temporal sequence of the more complex bidirectional motifs. Loops: movements starting
and ending at the same location mapped on original trajectories. Blue gradient encodes the temporal sequence of loops. (a) Bumblebee
data: bidirectional motifs are obser ved around the location of the nest and the artificial flowers (F1–F3) while loops are disproportionally
observed around the nest location. (b) Black kite data: bidirectional motifs are observed before migration and at stopover locations along
the migration route and loop behaviours tend to correspond to those locations. (c) Roe deer data: bidirectional motifs are observed in both
winter and summer territories while loops evidence some specific sub-areas of repeated intensive use. (d) Wolf data: bidirectional motifs are
observed in two territories (main and roaming areas) during specific periods of the year as well as some small area of temporary use sparse
along the animal path. Loops here are observed only for the summer territory of the wolf (Kaczensky et al., 2006)
  
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In th e roe deer tr aj ec tory, co mplex motifs occ urred i ntens ely in
two different areas while loops gathere d a round specifi c smal ler
areas (Figure 6c). In the wolf trajec tory, complex bidirectional
motifs were obs er ved in two spat ially differe ntiated a reas, while
loops were only observed in one of them (Figure 6d).
3.2.1 | Comparison with Brownian and Lévy walks
We studied the degree by which the four experimental datasets dif-
fered from Brownian and Lévy random movements. We calculated
probability matrices of temporal co-occurrence (conditional prob-
ability) of specific motif associations from original trajectories and
from simulated ones. We extracted the Jaccard index of similarity
between each original matrix and 100 Brownian motions and 100
Lévy walks thus obtaining two distributions of 100 values for each
trajectory. We compared the obtained distributions between them
using a t-test with Bonferroni correction. Between each pair of dis-
tributions, the one having higher mean resembles more to the se-
lected theoretical model than the other one. The trajectories of the
bumblebee and the roe deer tend to be equally similar to Brownian
motion and to differ from both the black kite and wolf trajectories
(Table 1, Brownian motion).The bumblebee trajectory resembles
more to a Lévy random walk than the other trajectories (Table 1,
Lévy w alk).
4 | DISCUSSION
Network analyses are power ful tools to statistically describe and
compare the spatial structures of animal movements (Jacoby &
Freeman, 2016). So far, however, these approaches do not take into
account the temporal dimension of movements, which is essential to
interpret complex behavioural patterns and their dynamics (ontog-
eny, repetition, changes). Here we introduced a method to automati-
cally extract motif patterns from animal tracking data and analyse
their succession over time.
Our approach builds on the utilization of movement networks to
analyse patterns of space use by animals (Bastille-Rousseau et al.,
2018; Jacoby & Freeman, 2016; Pasquaretta et al., 2017). Starting
from the proposition of Bastille-Rousseau et al. (2018) to isolate
areas of intensive use from static spatial network representations
of animal movements, we propose to keep trace of temporal infor-
mation and create behavioural time series embedded in space. Our
method is simple to operate and thus expected to be embraced
by a large community of ecologists. First the animal trajectory is
transformed into a spatial movement network in which nodes are
geographic locations and edges are movements bet ween these loca-
tions. Next, the step length distribution of the trajectory is used to
calculate multiple movement networks, extract their motif time se-
ries and compare them to estimate the optimal grid size providing the
most diverse sequence of motifs. This selection is used to objectively
determine the most suitable resolution for the spatio-temporal anal-
ysis of animal trajectories given the data. The temporal exploration of
movement trajectories from four case studies demonstrates that our
approach is functional and insightful. The analysis of movement pat-
terns matched very well with our knowledge of the ecological con-
text in which the data were recorded, allowing us to identify simple
behavioural pat terns associated with search routines and migration
(unidirectional motifs), an d more complex pat terns (bidirec tional mo-
tifs) correlated with the exploitation of familiar areas (migration sites,
home range), revisit s to specific locations (nest, flowers), resting
phases during migrations (stopovers, sparse area of temporary use).
In the bumblebee dataset, complex motifs occurred when the
individual was near to biologically relevant locations (nest and flow-
ers). These results are consistent with the well-described observa-
tions that bumblebees searching for nectar resources often return to
their nest and previously discovered flowers (Lihoreau et al., 2012;
Osborne et al., 2013), possibly to explore new areas from known ref-
erence spatial locations (Lihoreau, Ings, Chittka, & Reynolds, 2016).
Additionally, the loop analysis revealed a strong tendency of the
bumblebee to remain around the nest before flying longer distances.
This finding is in accordance with previous works demonstrating
that bumblebees use learning flights, in the form of loops around
the nest, to learn and memorize the location of the nest in the en-
vironment (Osborne et al., 2013). In the black kite dataset, com-
plex movement patterns and loops overlap almost perfectly, which
likely indicates the existence of stopover sites along the migratory
route of the bird. The spatio-temporal analysis of the roe deer data-
set highlighted the existence of two successive migratory events
during which similar use of spatially distinct home ranges occurs.
Interestingly, loops were concentrated around specific areas which
might correspond to areas of core usage (i.e. 50% of the time is spent
in these specific areas) of the home range of the animal during both
summer and winter seasons. The wolf dataset presents complex bi-
directional motifs across a summer and a winter territory (Kaczensky
TAB LE 1  Student s t-statistics bet ween distributions of 100
Jaccard indices calculated from the comparison of each binary non-
random motif conditional probabilities with 100 simulated matrices
obtained from a Brownian and a Lév y random movement model
Brownian motion Lévy walk
Bumblebee—Black kite
(t = 5.97; p < .001)
Bumblebee—Black kite
(t = 6.68; p < .001)
Bumblebee—Roe deer
(t = 2.59; p = .009) ns
Bumblebee—Roe deer
(t = 8.97; p < .001)
Bumblebee—Wolf
(t = 9.3 1; p < .001)
Bumblebee—Wolf
(t = 5.24; p < .001)
Wolf—Black kite
(t = −2. 58; p = .009) ns
Wolf—Black kite
(t = −1. 14; p = .255) ns
Roe deer—Black kite
(t = 3.75; p < .001)
Roe deer—Black kite
(t = 1.40; p = .162) ns
Roe deer—Wolf
(t = 7.3 2; p < .001)
Roe deer—Wolf (t = 2.55;
p = .010) ns
Note: We applied a Bonferroni correction for six multiple comparisons
(new reference α = 0.008).
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et al., 2006). Sparse areas of temporary use are also revealed along
the trajectory suggesting possible resting areas during the roaming
process. In this case, interestingly, loop behaviours were only ob-
served in the summer territory, suggesting the possible existence of
valuable resources in this area.
Comparing the four trajectories with simulated random move-
ment indicated that some trajec tor ies resemble more to a Brownian
motion or L évy walk than others. The bumblebee trajec tor y, for
example, resembles more to a Lévy walk than the other trajecto-
ries, thus confirming previous studies suggesting the existence of
Lévy flights as optimal search strategy in bumblebees (Lihoreau
et al., 2016; Reynolds, 2008; Reynolds, Smith, Reynolds, Carreck, &
Osbo rne, 20 07). The b lack kite and the wolf t rajectories appeared
differe nt from both Brownian and Lév y motions thus sug gesting
the possibility to study these movements using more complex be-
havioural models. Indeed, Brownian motio n of ten undere sti mate s
long range movements while pur e L évy walk often overest imates
them (Vallaeys, Tyson, Lane, Deleersnijder, & Hanert, 2017). More
realistic motions might also be tes ted in th e future (e.g. correlated
random walks; Bovet & Benhamou, 1988) to compare trajectories
between them and against specific hypothesis.
Future quantitative analyses using multiple trajectories from
more individuals will be essential to develop fruitful research on the
movement ecology of species. Studies of animal movement are gen-
erally based on high resolution data from a few individuals, partly
because obtaining long-term data in the field is not an easy task.
However, with the fast development of automated tracking systems,
analyses of rich movement datasets based on large numbers of tra-
jectories from many individuals are becoming possible (Cagnacci,
Boitani, Powell, & Boyce, 2010). Our automated analysis has the
main advantages of capturing the temporal properties of complex
movement patterns into synthetic and standardized network met-
rics that facilitate comparative analyses. The metrics obtained are
comparable through time for the same individual (e.g. if we are in-
terested in learning and memory) or across individuals (e.g. to assess
inter-individual variability in a population, between populations or
between species). This approach may therefore facilitate the devel-
opment of a truly comparative movement ecology based on statis-
tics on standard network metrics.
Our utilization of network metrics could be adjusted depend-
ing on the t ype of data collected and the question addressed.
Interestingly, it is possible to study motifs with more than three
nodes to compare multiple spatio-temporal level of behavioural
complexity that might not emerge from the study of low order mo-
tifs. For instance, a four-node sequence such as A-B-C-D-A provides
a description of a large area of interest for an animal while the three-
node equivalent A-B-C plus C-D-A only provides description of two
unidirec tional movements between locations without any evidence
of spatio-temporal clusters. Note however, the limitation of compu-
tational capabilities tend to restrict operational motif size for this
type of analysis and debate on how to extract subgraphs with more
than three nodes is still open (Agasse-Duval & Lawford, 2018; Ning,
Liu, Yu, & Xia, 2017; Williams, Wang, Williams, & Yu, 2014).
Importantly, our method enables to compare the spatio-temporal
structure of behavioural patterns to known theoretical move-
ment models. In the future, a functional motif analysis could be
implemented to highlight cluster of functional roles (McDonnell,
Yaveroğlu, Schmerl, Iannella, & Ward, 2014). Functional motifs
could help describe potential changes in behavioural patterns. The
utilization of network motifs to analyse animal movements offers a
detailed representation of behavioural patterns which is certainly
complementary to more classical descriptors of animal movements
(e.g. step length, turning angle) and other methods used to obtain
behavioural modes (e.g. t-SNE). For instance, the t-SNE method is
a procedure to cluster spatial data based on their similarity in var-
ious quantitative traits (e.g. straightness, net displacement, mean
velocity, see Bartumeus et al., 2016). It enables to describe animal
movements as behavioural patterns thus transforming a raw animal
trajectory into smaller spatial segments representing diverse be-
havioural modes. The t-SNE method relies on the interpretation of
these behavioural modes. Our spatio-temporal network method, by
associating motifs to the specific segments obtained from the t-SNE,
could be used to improve their interpretation by the use of direct
visualization. Analysis of large movement dataset s with our method
will also provide the opportunity to develop time series analyses of
network motifs using Markov chains. This approach would be a pow-
erful means to move from describing and comparing to predicting
temporal sequences of animal movements.
As illustrated above, another major advantage of our method is
that it is broadly applicable and can suit different types of move-
ment data collected with dif ferent technologies (GPS, PTT, har-
monic radar), at different spatial scales (local territories, countries)
and temporal scales (minutes, years), on animals with different loco-
motion modes (walking, flying) and in different ecological contexts
(exploration, exploitation, migration). In principle, temporal analyses
of spatial net work can be used to study virtually all types of animal
movement data in which individual animals are regularly re-located.
If trajectories are incomplete, for instance because the signal of
the animal is lost for some period of time, linear interpolation can
be used to fill gaps (Strandburg-Peshkin et al., 2015; Strandburg-
Peshkin, Farine, Crofoot, & Couzin, 2017). For any species, however,
the main limiting factor is the length of the trajectory (i.e. number of
data points). If the trajectory has too few data points, there is a high
risk that simplification into a movement network does not provide
enough motifs to allow for an insight ful exploration of the data.
We have shown that network analyses can be used to investigate
the temporal dimension of animal movements and get insights into
how the animals interact with their ecological environment (exploita-
tion of known resources, migration routes, stopover sites, territo-
ries and roaming areas). Since most animals (including those studied
here) frequently interact with social partners or competitors, a major
challenge for future studies is to analyse the temporal behavioural
movement patterns of interacting animals. Impor tant steps have
been made to develop new methods to extract social network from
animal trajectories and future directions have been pointed towards
using social telemetry data to identify preferred habitats for entire
  
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Methods in Ecology and Evolu!on
PASQUARE TTA ET Al.
groups (Robitaille, Webber, & Vander Wal, 2019). Our method can
help analyse these data by allowing the characterization of complex
behavioural patterns of space use by multiple interacting individuals.
For example, a preliminary analysis of the trajectories of two wolves
(male and female) inhabiting the same area of the Mongolia deser t
shows that the looping behaviours of both animals occur in separate
zones. Specifically, the male repeatedly used locations surrounding
the female's territory and performed the highest density of loops
in an area facing the area where the female exhibited the highest
density of loops (blue locations in Figure 7).
From this type of data, it is possible to cons tru ct tempor al
proximit y matr ices between individuals and apply classic social
network appro aches to study interac tio ns among individuals
(not showed here). The temporal dimension of our networks can
thus inform about non-random associations between behavioural
patterns expressed by the individuals. For instance, specific se-
quences of complex motifs (M8, M10, M12, M13) or loops may
reveal behavioural patterns characteristic of mating, territory for-
mation and mai nten ance or dispersa l following social interactions.
More generally, our work is part of a rapidly growing research
domain aiming at developing multi-layere d network methods to
study social , spatial and temporal dimensions of animal moveme nt
(Finn, Silk, Por ter, & Pinter-Wollman, 2019; Mourier, Ledee, &
Jacoby, 2019; Silk, Finn, Porter, & Pinter-Wollman, 2018). By in-
cluding motifs as an at tribute of each node in each layer, it will be
possible to integrate the temporal, social and spatial dimensions
of movements into a single analytical framework and open new
promising grounds for extending the analysis of complex move-
ment patterns at the population level.
ACKNOWLEDGEMENTS
This work was funded by the CNRS, a grant from the Agence
Nationale de la Recherche to M.L. (ANR-16-CE02-0002-01), and
the Laboratoire d'Excellence (LABEX) TULIP (ANR-10-LABX-41).
We acknowledge Prof. Lars Chittka and Dr. Joe Woodgate for pro-
viding access to the harmonic radar (bumblebee trajectory) and
XeriusTracking for the GPS data (black kite trajectory). We declare
no conflict s of interest. We thank two anonymous reviewers, the as-
sociate editor and Dr. David Jacoby for comments that have helped
improve the manuscript.
AUTHORS' CONTRIBUTIONS
C.P. and M.L . conceived the ideas and designed the methodology.
C.P., T.D., T.G.-M. and M.L. collected the bumblebee data. V.P.D. pro-
vided the black kite data. C.P. analysed the data. C.P. and M.L. led
the writing of the manuscript. All authors contributed critically to
the drafts and gave final approval for publication.
DATA AVAILABILITY STATEMENT
We implemented our method in R. We provide the codes and the
bumblebee and black kite datasets in Dr yad Digital Repository
https://doi.org/10.5061/dryad.47d7wm390 (Pasquaretta et al., 2015).
The roe deer dataset was obtained from MOVEBANK (Wikelski &
Kays, 2020). Animal Identifier: Sandro (M06), from Cagnacci et al.
(2011) (https ://www.moveb ank.org/). The wolf dataset was obtained
from MOVEBANK (Wikelski & Kays, 2020), Animal identifier: Zimzik,
from Kaczensky et al. (2006) (https ://www.moveb ank.org/).
ORCID
Cristian Pasquaretta https://orcid.org/0000-0001-8308-9968
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How to cite this article: Pasquaretta C, Dubois T,
Gomez-Moracho T, et al. Analysis of temporal patterns in
animal movement networks. Methods Ecol Evol. 2020;00:
1–13 . https ://doi.org/10.1111/2041-210X.13364
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