![Trajectory diagram of pike released in a flooded grassland and recaptured when emigrating into an adjacent pond. Arrow represent trajectory path for each pit-tagged individual. Colors correspond to trajectory clusters. Density curves at the periphery of the trajectory diagram represents the distribution of all samples according to δ13C (x) and δ15N (y), and capture (green=release; red=departure).The dashed line separates piscivorous from zooplanktivorous individuals [zooplanktivorous (δ15N < 10 ‰) vs piscivorous (δ15N > 10 ‰)]. Data from Cucherousset et al. (2013).](https://www.researchgate.net/profile/Anthony-Sturbois/publication/357121687/figure/fig5/AS:1119461163712512@1643911748173/Trajectory-diagram-of-pike-released-in-a-flooded-grassland-and-recaptured-when-emigrating_Q320.jpg)
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ARTICLE
Stable Isotope Trajectory Analysis (SITA): A new approach
to quantify and visualize dynamics in stable isotope studies
Anthony Sturbois
1,2,3,4
| Julien Cucherousset
5
| Miquel De C
aceres
6
|
Nicolas Desroy
3
|PascalRiera
7
| Alexandre Carpentier
8
| Nolwenn Quillien
9
|
Jacques Grall
4
| Boris Espinasse
10
| Yves Cherel
11
| Gauthier Schaal
4
1
Vivarmor Nature, Ploufragan, France
2
Réserve naturelle nationale de la Baie de Saint-Brieuc, site de l’étoile, Hillion, France
3
Ifremer, Laboratoire Environnement et Ressources Bretagne nord, Dinard, France
4
Laboratoire des Sciences de l’Environnement Marin (LEMAR), UMR 6539 CNRS/UBO/IRD/IFREMER, Plouzané, France
5
UMR 5174 EDB (Laboratoire
Evolution & Diversité Biologique), CNRS, Université Paul Sabatier, IRD, Toulouse, France
6
CREAF, Cerdanyola del Vallès, Spain
7
Sorbonne Université, CNRS, Station Biologique de Roscoff, UMR7144, Place Georges Teissier, Roscoff Cedex, France
8
Université de Rennes 1, BOREA, Muséum National d’Histoire Naturelle, Sorbonne Université, Université de Caen Normandie, Université des
Antilles, Campus de Beaulieu, Rennes, France
9
France Energies Marines, Plouzané, France
10
Department of Arctic and Marine Biology, UiT The Arctic University of Norway, Tromsø, Norway
11
Centre d’Etudes Biologiques de Chizé, UMR 7372 du CNRS-La Rochelle Université, Villiers-en-Bois, France
Correspondence
Anthony Sturbois
Email: anthony.sturbois@espaces-
naturels.fr
Funding information
Agence de l’eau Loire-Bretagne, Grant/
Award Number: 180212501; European
maritime and fisheries fund, Grant/Award
Number: FEAMP 621-B; Institut Polaire
Français Paul Emile Victor, Grant/Award
Number: IPEV program N109; Ministre de
la Transition Ecologique et Solidaire,
Grant/Award Number: EJ N;2102930123;
Office Français de la Biodiversit, Grant/
Award Number: STABLELAKE SOLAKE;
Région Bretagne, Grant/Award Number:
OSIRIS PFEA621219CR0530023; Spanish
Ministry of Economy, Grant/Award
Number: CGL2017-89149-C2-2-R
Handling Editor: Aimeé T. Classen
Abstract
Ecologists working with stable isotopes have to deal with complex datasets includ-
ingtemporalandspatialreplication,which makes the analysis and the representa-
tion of patterns of change challenging, especially at high resolution. Due to the lack
of a commonly accepted conceptual framework in stable isotope ecology, the analy-
sis and the graphical representation of stable isotope spatial and temporal dynamics
of stable isotope value at the organism or community scale remained in the past
often descriptive and qualitative, impeding the quantitative detection of relevant
functional patterns. The recent community trajectory analysis (CTA) framework
provides more explicit perspectives for the analysis and the visualization of ecologi-
cal trajectories. Building on CTA, we developed the Stable Isotope Trajectory Analy-
sis (SITA) framework, to analyze the geometric properties of stable isotope
trajectories on n-dimensional (n≥2) spaces of analysis defined analogously to the
traditional multivariate spaces (Ω) used in community ecology. This approach pro-
vides new perspectives into the quantitative analysis of spatio-temporal trajectories
in stable isotope spaces (Ω
δ
) and derived structural and functional dynamics
Received: 4 June 2021 Revised: 21 September 2021 Accepted: 29 September 2021
DOI: 10.1002/ecm.1501
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any
medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
© 2021 The Authors. Ecological Monographs published by Wiley Periodicals LLC on behalf of Ecological Society of America.
Ecological Monographs. 2022;92:e1501. https://onlinelibrary.wiley.com/r/ecm 1of26
https://doi.org/10.1002/ecm.1501
(Ω
γ
space). SITA allows the calculation of a set of trajectory metrics, based on either
trajectory distances or directions, and new graphical representation solutions, both
easilyperformableinanRenvironment.Here,weillustratetheuseofourapproach
by reanalyzing previously published datasets from marine, terrestrial, and freshwa-
ter ecosystems. We highlight the insights provided by this new analytic framework
at the individual, population, community, and ecosystems levels, and discuss appli-
cations, limitations, and development potential.
KEYWORDS
changes, composition, dynamics, food web, functioning, spatial, stable isotope, structure,
temporal, trajectories
INTRODUCTION
Stable isotope analysis has emerged as one of the most pop-
ular approaches to assess the trophic ecology of organisms
(Fry, 2008), fluxes of matter and energy within and between
ecosystems (Peterson & Fry, 1987), and animal movements
(Bouillon et al., 2011; Rubenstein & Hobson, 2019). The
quantitative analysis of stable isotope data is based on a
large variety of available analytical tools ranging from quali-
tative inferences using isotopic niche (Newsome et al., 2007)
to complex Bayesian mixing models that can be used to
characterize food web structure and trophic pathways at
multiple levels of biological organization (Layman
et al., 2012). Understanding and quantifying spatial and
temporal changes is an overarching topic in stable isotope
ecology but studies are, to date, largely qualitative, and the
development of quantitative approaches is needed.
The quantitative analysis of stable isotope dynamics in
response to ecological and environmental changes, notably
those induced by human activities, has been explored
through the comparative analysis of temporal trajectories
in a two-dimensional (usually δ
13
Candδ
15
N) isotopic
space (δspace). For instance, Schmidt et al. (2007)and
Wantzen et al. (2002) quantified the direction and magni-
tude of temporal changes in food web structure based on
the geometric properties of trajectories in the δspace.
Schmidt et al. (2007) used specifically circular charts and
statistics to represent and test direction shifts in the δ
space. Turner et al. (2010) characterized attributes of path
trajectories (size, direction, and shape) over data sets con-
taining more than two temporal samples to provide a
quantitative description of how stable isotope composi-
tions change in response to spatial and temporal gradients,
and tested their differences. Despite the fact that these
works have provided substantial new perspectives notably
for statistical and hypothesis testing, some limitations
remain for the explicit quantitative description, analysis,
and representation of the magnitude and the nature of
changes in stable isotope composition.
In community ecology, severalstatisticalframeworks
have been proposed and used to test hypotheses on commu-
nity dynamics (Buckley, Day, Lear, et al., 2021; De C
aceres
et al., 2019). The dynamics of ecological communities has
been traditionally represented on ordination diagrams in
which changes over time are represented by a set of vectors
linking consecutive ecological states (Austin, 1977;
Hudson & Bouwman, 2007; Legendre & Salvat, 2015;
Matthews et al., 2013). The geometric properties of trajecto-
ries, defined in the space of an ordination diagram, are con-
sidered as relevant parameters to quantify the dynamics of
ecological systems. The potential of geometrically based
methods was illustrated by De C
aceres et al. (2019)inthe
communitytrajectoryanalysis(CTA)framework.Compared
with previous approaches based on ordination diagrams, De
C
aceres et al. (2019) considered community dynamics as tra-
jectories in a chosen space of community resemblance, with
no limit in the number of dimensions included. In CTA, tra-
jectories are defined as objects composed of consecutive seg-
ments to be analyzed and compared using distance- and
direction-based metrics in the chosen multivariate space.
Extending the initial framework, Sturbois, De C
aceres, et al.
(2021) developed new CTA metrics and synthetic representa-
tion approaches, such as trajectory roses, and the inclusion of
trajectory metrics in maps or ordination diagram.
By analogy to community ecology, the term and the
concept of trajectory have been informally used in stable
isotope ecology to characterize dynamics and represent
them in spaces of analysis (either δspace, p-space sensu,
Newsome et al., 2007; or spaces based on community-
wide indices, e.g., Rigolet et al., 2015). The analysis and
representation of stable isotope trajectories or contrasted
patterns requires the use of quantitative geometric prop-
erties in 2D δspaces often complemented by vectors in
stable isotope scatter plots and/or circular representation
(Agostinho et al., 2021; Black & Armbruster, 2021;
Cucherousset et al., 2013; Schmidt et al., 2007). However,
scientists are increasingly faced with multivariate
datasets (i.e., >2 dimensions) in stable isotope ecology in
2of26 STURBOIS ET AL.
response to the potential use of (1) other isotopes to com-
plement δ
13
C and δ
15
N (e.g.,
34
S ([Connolly et al., 2004],
δD [Doucett et al., 2007]) and (2) numerous structural
and functional community-wide metrics or indices
(Cucherousset & Villéger, 2015; Layman et al., 2007).
While the availability of long-term, large-scale, and high-
resolution data is one of the most limiting factors to study
temporal patterns in stable isotope ecology, the develop-
ment of methods to analyze, synthesize, and ultimately
represent the dynamics of ecological systems still remains
an essential issue to complete current approaches by
more quantitative and formal explicit frameworks.
Building on CTA, we aim to provide a framework for
the temporal analysis of stable isotope data at different
levels of biological organization, from individuals to eco-
systems to derive structural and functional trajectories in
a new approach referred to as Stable Isotope Trajectory
Analysis (SITA). We (1) provide a general definition of
the trajectory concept applied in stable isotope ecology,
adapted from CTA framework to stable isotope analysis,
(2) present the package ecotraj designed for ecological
trajectory analyses and here used specifically for SITA,
and (3) illustrate potential applications of SITA using
field, experimental or modeled data that include four
main topics in stable isotope ecology: (i) individual and
(ii) population levels, (iii) structural and functional tra-
jectories of entire food webs, and (iv) modeling of stable
isotope dynamics at high spatio-temporal resolutions.
TRAJECTORY CONCEPTS
Trajectory concept in stable isotope ecology
Founding works
Wantzen et al. (2002) and Schmidt et al. (2007) were the
first to study directions and distances in δspaces. Build-
ing on these works and the Adams and Collyer (2009)
approach, Turner et al. (2010) provided a more explicit
use of the concept of trajectory by the definition of trajec-
tory attributes (size, direction, and shape). Despite the
fact that Layman et al. (2012) recommended these geo-
metrically based approaches in conjunction with area
based in bivariate or multivariate isotopic space, to our
knowledge, their use has currently been limited to bivari-
ate spaces (e.g., δ
13
C-δ
15
N biplots).
Conceptual definition
A trajectory in stable isotope ecology can be defined as a
path in a chosen space of analysis, (Ω
δ
or Ω
γ
, depending
whether the space is based on raw stable isotope data, or
on derived indices, respectively), composed of one or dif-
ferent consecutive segments, resulting from repeated
observations of a same sampling unit (individuals,
populations, stations, food web, etc.). Observed temporal
patterns can be characterized by distances and directions
in Ωand used to define the nature (i.e., ecological mean-
ing) and magnitude (i.e., importance) of temporal
changes. The overall trajectory concept in stable isotope
ecology can be adapted to different ecological questions,
as illustrated in Section Applications of SITA.
Characterizing stable isotope trajectories
Formal definition of trajectory in stable isotope
ecology
We follow here the CTA notation used by De C
aceres
et al. (2019) to describe and compare trajectories in a
multidimensional space of community composition.
Given a target sample (individual, population, entire food
web, station) whose dynamics is surveyed, let o
1
,o
2
,…,o
n
be an ordered set of nobservations (n> 1) and t
1
,t
2
,…,t
n
the corresponding set of ordered survey times
(i.e., t
1
<t
2
<…<t
n
). For all iin {1, 2, …,n}, x
i
contains
the coordinates corresponding to o
i
in a multi-
dimensional space Ω. The geometry of the trajectory Tis
formalized using a set of n1 directed segments {s
1
,…,
s
n-1
}, where s
i
={x
i
,x
i+1
} is a segment with endpoints
(community states) x
i
and x
i+1
.
Definition of spaces supporting SITA
As for CTA, SITA requires the definition of Ωdefined by
the resemblance between pairs of observations, measured
using a dissimilarity coefficient d. SITA is based on dis-
similarity values contained in a distance matrix Δ=[d]
(De C
aceres et al., 2019).
The trajectory concept in stable isotope ecology may
be addressed in terms of stable isotope composition or
food web structure and functioning involving similar
attributes (i.e., trajectory metrics) but different data
inputs and space of analysis.
Stable isotope Ω
δ
space
Ω
δ
is defined with stable isotope values of different ele-
ments. Coordinates in this space of analysis correspond
to raw stable isotope data. Despite δ
13
C and δ
15
N being
the most commonly used in a bidimensional context,
other elements that are ecologically meaningful may also
be considered for defining the Ω
δ
space (e.g., hydrogen
δD, sulfur δ
34
S, or oxygen δ
18
O). Coordinates in Ω
δ
are
used to compute the resemblance between ecological
ECOLOGICAL MONOGRAPHS 3of26
states using d, where we suggest the adoption of the
Euclidean distance, as it is commonly used in stable iso-
tope ecology (Ben-David et al., 1997; Kline Jr. et al., 1993;
Schmidt et al., 2007; Turner et al., 2010; Wantzen
et al., 2002; Whitledge & Rabeni, 1997).
Structural and functional Ω
γ
space
Looking for patterns in stable isotope ecology often leads
to the calculation of community-wide metrics or any
structural or functional indices based on raw stable iso-
tope data (Cucherousset & Villéger, 2015; Layman
et al., 2007; Rigolet et al., 2015). Ω
γ
is defined with any
indices derived from raw stable isotope data, used as eco-
logical proxies, such as to characterize food web struc-
ture, and allow a comparison within and among systems.
Trajectory metrics
Metrics detailed in Section Trajectory metrics, here
adapted for a stable isotope purpose in Ω
δ
and Ω
γ
, are
part of the CTA framework (see De C
aceres et al. [2019]
and Sturbois, De C
aceres, et al. [2021] for equations and
more details). Note that additional metrics, not used here,
are defined in these articles.
Distance-based metrics
Segment length (S). The trajectory segment length is the
distance between two consecutive surveys (i.e., measure-
ments). The length of a segment is given by the distance
between its two endpoints. The greater the length of a
trajectory segment, the greater is the distance between
states. This metric is particularly relevant to analyze the
magnitude and the variability of trophic trajectories and
allows the distinction between gradual and abrupt
changes.
Trajectory path length (L(T)). The trajectory path length is
the sum of segment lengths for a given sampling unit.
This metric informs about the overall temporal change.
Net change (NC). The net change is defined as the length
between a pair of states, which includes a chosen base-
line state (i.e., initial or reference state). When calculated
at the scale of an overall study period or at the end level
of a gradient, this metric evaluates the difference between
the initial and the final state, that is, the overall net tra-
jectory change.
Net Change Ratio (NCR). The net change ratio is defined
as the ratio between the overall net trajectory change and
the trajectory path length. A high NCR indicates that a
great part of the trajectory path contributes to net
changes and illustrates a relative consistency in the
drivers of ecological dynamics. Inversely, a low NCR
illustrates the versatility of these drivers and highlights
that a small part of the trajectory path contributes to net
changes.
Recovering or Departing Trajectory (RDT). Let us consider
a triplet of states composed of baseline, intermediate, and
final states. The dynamics with respect to the baseline
state can be defined as recovering (i.e., return to the ini-
tial state) or departing (i.e., increasing distance from the
initial state) by subtracting NC
baseline to intermediate
to
NC
baseline to final
.RDT > 0 indicates a closer position at
final state than intermediate state and consequently
implies a recovering toward the initial state (RIS).
Inversely, RDT < 0 indicates a farther ecological state at
final than intermediate state and consequently implies a
departure from the initial state (DIS).
Direction-based metrics
Angle Ɵ.Ɵis the angle between two consecutive seg-
ments ordered in time measured on the Euclidean plane
that contains the three states. The angle 0<Ɵ<180is
defined as the change of direction in this plane. The tra-
jectory is linear when Ɵ=0.IfƟ=180, the trajectory
is still linear but opposite in sense.
Angle ω.Instead of considering consecutive segments,
angle ωallows the assessment of the linearity of changes
with respect to a chosen reference segment (e.g., first seg-
ment) of an ecological trajectory.
When space Ωis 2D, ω(as well as Ɵ) can be reported
in a 0–360system, if needed.
Angle α.When space Ω
δ
and Ω
γ
is 2D, it becomes also rel-
evant to consider trajectory segment directions with
respect to the interpretation of the axes defining the
space. Angle αis measured considering the second axis of
the 2D diagram as the North (0). αallows the compari-
son of segment direction with respect to the influence of
the variables used to interpret the two axes. When Ωis
an ordination space, users may calculate αif they decide
that the variance is sufficiently explained by the first two
axes of the ordination and can refer to the loadings of
original variables or their degree of correlation with addi-
tional variables. In an Ω
δ
space, αangles are a convenient
way to express dynamics with respect to single isotope
variability.
Directionality (DIR). The overall directionality of trajecto-
ries provides information about the consistency with
which a sample follows the same direction and, therefore,
the stability of ecological drivers that condition the stable
4of26 STURBOIS ET AL.
isotope trajectory. DIR is bounded between 0 and 1 where
the maximum value corresponds to a straight trajectory
(see equation 3 in De C
aceres et al., 2019).
Geometric resemblance between trajectories
De C
aceres et al. (2019) developed a geometrically based
approach to trajectory resemblance that included the
shape, size, direction, and position of trajectories with
respect to the resemblance between all observations
(state) belonging to a same trajectory. The approach
defines resemblance between pairs of segments or overall
trajectories and allows the centering trajectories to
exclude differences in position, while keeping the other
components of trajectory resemblance. Different distance
are proposed and discussed to compute dissimilarity cal-
culation depending of users interests (De C
aceres
et al., 2019).
Representing trajectories in stable isotope
ecology
The representation concepts provided here are valid for
the representation of trajectories in both Ω
δ
and Ω
γ
spaces.
Trajectory diagrams
Temporal dynamics in stable isotope ecology are some-
times represented in 1D or 2D δspace by segment
or arrows between consecutive surveys (Agostinho
et al., 2021; Guzzo et al., 2011). Here, we propose a trajec-
tory diagram (TD) concept to customize ordination dia-
grams by adding notably SITA metrics. Trajectory
segments are normally represented by segments between
surveys to form the trajectory path whose last segment is
ended by an arrow. If one wants to go further in the rep-
resentation of trajectory net changes, (1) net changes
may be represented at each transitional state by the data
point size and (2) the overall net change may be repre-
sented by a dotted line or arrow between the initial and
final state of a time series. We recommend also the gener-
alization of density curves in the periphery of trajectory
diagrams, as is sometimes done to compare different food
webs (Zapata-Hern
andez et al., 2021).
Trajectory rose diagram
Schmidt et al. (2007) first introduced the use of direction
and distance in their arrow diagrams. Building on
this approach, we propose a complementary use of the
trajectory rose (TR) diagrams proposed by Sturbois,
De C
aceres, et al. (2021) to represent stable isotope
dynamics in a circular way. The TR diagram consists of a
circular bar plot of angles ranging from 0to 360. The
barplot structure of TR allows the presence of rep-
resenting factors in different bar sections. Depending on
the aim of the analysis, users can choose to represent the
distribution of Ɵ,ωor αangles. Bars sizes represent the
number of segments concerned by each range of direc-
tion (e.g., 15) and cumulative segment length may be
represented by a point at the head of each bar and col-
ored according to length values (Sturbois et al., 2021). In
δ
13
C/δ
15
NΩ
δ
space, angle αillustrates different stable
isotope (SI) trajectory patterns according to increase
and/or decrease in δ
13
C and δ
15
N values (0–90:+δ
13
C
and +δ
15
N; 90–180:+δ
13
C and δ
15
N; 180–270:δ
13
C
and δ
15
N; 270–360:δ
13
C and +δ
15
N). In Ω
γ
space,
directions distribution refers to structural and functional
indices. Note that the TR diagram may be adapted if one
wants to represent, with similar visually importance,
both direction and distance (segment lengths or net
changes instead of number of trajectory segments). In
this case, the information of the TR becomes more simi-
lar to that of arrow diagrams (Schmidt et al., 2007).
Trajectory heat map
Stable isotope datasets with high temporal resolutions
may require special representations as they can poten-
tially saturate TD or TR diagrams.
Here, we propose the concept of a trajectory heat map
(TH) to represent long-term SI dynamics. The heat map
is a two-dimensional representation of data in which the
changes in the distribution of a chosen trajectory metric
over time are represented using cell colors (see
Section Spatio-temporal variability of δ
13
C and δ
15
N
modeled isoscapes in the northeast Pacific). TH allows the
representation of the distribution of distance- and
direction-based trajectory metrics.
If users aim to favor the representation of directions
in TH, angles Ɵ,ωor αcan be represented in a matrix of
fixed cell size whose colors vary depending of the number
of a given direction range occurring in a given period. As
in the TR, we advise the use of any direction bin size
(e.g., 15) to provide a synthetic representation. The TH
can be completed by peripheric bar plots to represent tra-
jectory lengths involved in each direction range and
period (see Section Spatio-temporal variability of δ
13
C
and δ
15
N modeled isoscapes in the northeast Pacific). In
2D Ω
δ
space, angle αillustrates, for example, different SI
trajectory patterns according to respective increase
and/or decrease of the two SI values (see Section Direc-
tion-based metrics). TH therefore provides a relevant
ECOLOGICAL MONOGRAPHS 5of26
visual summary of complex data sets, highlighting the
magnitude and the nature of SI dynamics (TH cells clus-
tering, barplots). In the TH concept, users can easily
choose to represent the distribution of segment lengths or
any trajectory metrics with respect to time, depending on
ecological questions.
Trajectory maps
Expanding Sturbois, De C
aceres, et al. (2021), we propose
the use of trajectory metrics as trajectory map (TM) input
for the representation of temporal patterns in sampling
units on geographic coordinates. Two examples are
included here to illustrate the potential of the TM
concept.
Trajectory map from initial state
We suggest the adaptation of the TM concept proposed by
Sturbois, De C
aceres, et al. (2021) to represent site scale
dynamics in Ω
δ
or Ω
γ
through geometrical properties of
trajectories in synthetic figures accounting for temporal
variability at the spatial unit scale. The use of a single
map is proposed to represent all at once for each site of a
study area (see Section Biological invasions and trophic
structure dynamics of lake fish communities): (1) net
change between x
1
and x
n-survey
, (2) segment length
(or subtrajectory length) S
i>1
, and S
j>i
, and (3) RIS or DIS
segment or subtrajectory lengths between x
i
and x
n-survey
.
Net changes are represented through a circular symbol
proportional to the length to vector x
1
-x
j>i
. On both sides,
a bottom triangle symbol represents the x
1
-x
i>1
vector and
a top triangle the x
i>1
-x
j>i
vector. For both triangles, the
size is proportional to the length of respective vectors,
while the orientation and color of the top triangle illus-
trate the direction (recovering or departing) of the second
vector with respect to the initial or baseline state.
Isoscape trajectory map
The spatial distribution of SI in environmental materials
can be predicted, using models of isotope-fractionating
processes and data describing environmental condi-
tions, and represented through isotopic landscape,
called isoscapes (Bowen, 2010;Westetal.,2008). We
adapted the TM concept for isoscape datasets charac-
terized by high spatial resolutions and a minimum of
two temporal surveys or modeling. This particular con-
cept of TM is inspired by wind/current map where the
magnitude and the direction of wind/current are repre-
sented through multiple vector covering large areas. In
the isoscape TM (ITM), the direction of arrows repre-
sents angle αin a 2D Ω
δ
space (e.g., δ
13
C/δ
15
N), and
size illustrates trajectory length (see Section Spatio-
temporal variability of δ
13
Candδ
15
N modeled isoscapes
in the northeast Pacific). The representation of trajec-
tory length is improved by a color raster of spatially
interpolated length values.
SOFTWARE AVAILABILITY
In 2019, De C
aceres and colleagues proposed the CTA
framework and functions for the calculation of associated
metrics. These functions were included in package
vegclust. In 2021, Sturbois et al. extended the CTA frame-
work with new metrics and figure concepts. New func-
tions were added in package vegclust. The present article
goes further in the adaptation of CTA, bridging a gap
identified in the consideration of dynamics in SI ecology,
and starting the exploration of trajectory analysis beyond
the sites species matrix. All these recent developments,
and the fact that trajectory analysis can be applied to
different spaces, claimed a new package specifically
devoted to ecological trajectory analysis that would
allow taxonomic, functional or SI trajectory analyses
within the same tool through complementary space of
analysis (Ω).
The package ecotraj (De C
aceres [2019], Sturbois, De
C
aceres, et al. [2021]) assists ecologists in the analysis of
temporal changes of ecosystems, defined as trajectories
on a chosen multivariate space, by providing a set of tra-
jectory metrics and visual representations. It includes
functions to perform trajectory plots and to calculate the
set of distance and direction-based metrics (length,
directionality, angles, etc.) as well as metrics to relate
pairs of trajectories (dissimilarity and convergence).
Currently, Trajectory analysis (SITA as well as CTA)
can be performed using the “ecotraj”functions available
on CRAN and GitHub repositories (https://emf-creaf.
github.io/ecotraj/index.html). R codes to create figures
are also shared to facilitate the use and the customiza-
tion of our trajectory chart concepts (Data S1) and a
new vignette has been added in the documentation of
the package.
APPLICATIONS OF SITA
Six ecological applications (EA) were chosen to illus-
trate the use of SITA metrics and representation con-
cepts for stable isotope dynamics within different
ecological systems and to answer various ecological
questions (Figure 1): stable isotope trajectories at the
(1) individual (EA1 and EA2) and (2) population (EA1,
EA3 and EA4) levels, (3) structural and functional tra-
jectories at the scale of entire food webs (EA4 and EA5),
and (4) stable isotope dynamics at high spatio-temporal
resolutions (EA6).
6of26 STURBOIS ET AL.
Spatial and temporal resource partitioning
in fur seals
Context
Many generalist populations are composed of individual
specialists and individual specializations are increasingly
recognized as an important component of many ecological
and evolutionary processes (Bolnick et al., 2003), making
crucial testing the consistency of individual specialization.
Methods
δ
13
Candδ
15
N values of metabolically inert tissues reflect
diet at the time of their growth, and continuously growing
tissues can be used as time-recorders of the movement and
dietary history of individuals. Fur seals (the Antarctic fur
seal Arctocephalus gazella [AFS] and sub-Antarctic fur seal
A. tropicalis [SAFS]) whisker SI values yielded unique
long-term information on individual behavior that inte-
grated the spatial, trophic, and temporal dimensions of the
ecological niche (Cherel et al., 2009;Kernaléguen
et al., 2012). The foraging strategies of these two species of
sympatric fur seals were examined in the 2001/2002 winter
at Crozet, Amsterdam, and Kerguelen islands (Southern
Indian Ocean) by measuring the SI compositions of serially
sampled whiskers (see Kernaléguen et al., 2012,2015 for SI
preparation and analyses). The method consists of the anal-
ysis of consecutive whisker sections (3-mm long) starting
from the proximal (facial) end, with the most recently syn-
thesized tissue remaining under the skin. Only individuals
(n=47) with whiskers totaling at least 30 sections were
selected, and only those 30 sections were considered here
(Sturbois, Cucherousset, et al., 2021a), from t
1
(more recent
values) to t
30
(oldest values). SITA was performed to track
individual specialization within and among four fur seal
populations. Different metrics (segments lengths, trajectory
ECOLOGICAL
TOPICS
DATA inputs
& SPACE of
analysis
TRAJECTORY
METRICS
ECOLOGICAL
APPLICATIONS REPRESENTATIONS
1. 2. 3. 4. 5.
Structure
& functioning Indices
Individual SI
Population SI
High spatio-temporal
SI raw data
Angle Ɵ
Angle ω
Angle α
Segment length
Trajectory path
Directionnality
Net changes
RDT
Net change ratio
EA 4
EA 5
EA 1
EA 2
EA 3
EA 6
Trajectory
diagram
Trajectory map
Trajectory rose
Isoscape Traj. map
Traj. Heatmap
FIGURE 1 Levels of analysis and ecological questions drive input data used to define the space of analysis supporting SITA. While
structural and functional analysis requires community-wide metrics or indices to define Ω
γ,
raw stable isotope data are used for the
definition of Ω
δ
that supports stable isotope trajectories at different levels from individual to population, or for ecological questions that
involve high stable isotope spatio-temporal resolutions. The SITA adaptability allows the calculation of distance- and direction-based
trajectory metrics in both, Ω
δ
and Ω
γ
, and their visualization in different figures devoted to the representation of dynamics
ECOLOGICAL MONOGRAPHS 7of26
path, net changes, angle α)werecalculatedinthe2DΩ
δ
space (δ
13
C/δ
15
N) for each individual. Dissimilarities
between individual trajectories were calculated (directed
segment path dissimilarity; De C
aceres et al., 2019), and
was used with the resulting symmetric matrix as input in a
hierarchical cluster analysis (ward.D2 clustering method),
to define different groups of similar individual trajectories.
Segment length, trajectory path length, and whisker δ
13
C/
δ
15
N values were summarized to illustrate the trophic vari-
ability for each trajectory cluster. Hermans–Rasson and
Watson–William tests were performed to test the homoge-
neity of angle distribution among trajectory within each
cluster and the difference of segment direction between
clusters. SITA metrics were represented in trajectory dia-
grams and a trophic TR.
Results
SITA revealed contrasted stable isotope dynamics among
species, sexes, and individuals. Hierarchical cluster analy-
sis identified six main trajectory clusters, characterized
by differences in SITA metrics and whisker δ
13
C/δ
15
N
values (Table 1and Figure 2). Clusters 1, 3, and 4 were
exclusively composed of trajectories corresponding to
males, from AFS only (clusters 1 and 4) or from both spe-
cies (cluster 3). These clusters were characterized by the
highest values in distance-based metrics, revealing wider
foraging strategies (Table 1). Clusters 1 and 4 were char-
acterized by lower δ
13
C values contrasting with cluster
3. Cluster 2, characterized by a lower isotopic variability,
grouped all of the 15 AFS females from Crozet and Ker-
guelen and included also one AFS male and three SAFS
females. Individuals in cluster 5 (five females and one
TABLE 1 Characteristics of fur seal trajectory clusters: number of individuals (n), stable isotopes (SI), distance-based metrics, number
of individuals depending of species and genders (female A. gazella [FAFS], male A. gazella [MAFS], female A. tropicalis [FSAFS], male A.
tropicalis [MSAFS]) and breeding sites (Crozet [Cro], Kerguelen [Ker], Amsterdam [Am]). Values are means SE. Data sets from
Kernaléguen et al. (2012)
Clusters n
Whisker SI values Distance-based SITA metrics n/species-genders n/breeding places
δ
13
C‰δ
15
N‰
Trajectory
path
Segment
length
Net
changes FAFS MAFS FSAFS MSAFS Cro Ker Am
1222.29 0.17 9.77 0.20 21.77 6.14 1.50 0.21 3.86 0.51 2 2
219 17.54 0.04 10.52 0.02 14.59 0.99 0.99 0.03 1.79 0.09 15 1 3 13 6
3616.65 0.07 11.93 0.07 19.61 1.01 1.33 0.03 2.70 0.11 2 4 6
4418.96 0.23 11.39 0.14 35.22 3.51 2.36 0.12 6.53 0.24 4 4
5616.57 0.03 10.79 0.03 9.39 0.80 0.64 0.03 1.21 0.09 5 1 6
610 15.42 0.02 13.32 0.04 12.54 0.55 0.84 0.02 1.59 0.06 10 10
Total 47 15 9 18 5 31 6 10
FIGURE 2 Individual fur seal trophic trajectories for males and
females of A. gazella and A. tropicalis. Arrows connect all whiskers
section stable isotope values from t
1
to t
30
(i.e., most recent to oldest
stable isotope values). Colors correspond to trajectory clusters and
shapes to breeding sites. Data from Kernaléguen et al. (2012)
8of26 STURBOIS ET AL.
male SAFS from Crozet) exhibited the lowest isotopic
variability. Cluster 6 was exclusively composed of SAFS
females from Amsterdam, revealing a clear trophic segre-
gation of females breeding there.
Different foraging strategies characterized by some
overlaps, and partly influenced by breeding sites
(Figure 2), were revealed for AFS males (distributed in
four trajectory clusters) and SAFS females (three clusters).
The time series of net changes (Figure 3,Table1) revealed
that each individual exhibited a more or less well defined
trophic cycle whose amplitude and period depended on
trajectory clusters. The distribution of trajectory segment
directions (αangles) was heterogeneous for five of the six
clusters (Herman–Rasson tests, p> 0.05) and some differ-
ences also existed among clusters (Figure 4).
Discussion
The estimated δ
13
C values of the Polar Front and of
the Subtropical Front for fur seal whiskers were
approximately 19 and 16‰, respectively (Cherel
et al., 2009). Accordingly, Kernaléguen et al. (2015,
2012) showed (1) a spatial foraging gradient from south-
ern cold waters to northern and warmer areas for, in the
order, AFS male, AFS female and SAFS male and
female, (2) male benthic feeding strategy near breeding
places, and (3) δ
13
Candδ
15
N oscillation patterns in
most whiskers. Trajectory analysis results were congru-
ent with those conclusions, but we went further show-
ing that individual feeding strategies transcend pre-
established categories such as species, genders, and
breeding places, which was not primarily evident from
analysis at the population level. This application con-
firms that SITA metrics and representations are relevant
to track the shape and the magnitude of stable isotope
trajectories in δspace, at different scales, from individ-
ual to population, and particularly to reveal subtle rele-
vant functional patterns in spatio-temporal resource
partitioning.
Ontogenic stable isotope trajectories of
juvenile fish
Context
Intraspecific variability has strong ecological implications
across levels of biological organization and can modulate
the outcomes of individual life history. This is particu-
larly true for movement along habitats, which is an ubiq-
uitous phenomenon with important consequences on
individuals.
Methods
Cucherousset et al. (2013) released 192 individually
tagged, hatchery-raised, juvenile pike (Esox lucius L.)
with variable body size and initial trophic position (fin
δ
13
C/δ
15
N values). Based on δ
15
N values, individuals
were classified into zooplanktivorous (δ
15
N<10‰) and
piscivorous (δ
15
N>10‰), as cannibalism is commonly
observed in this species. Individuals were released in a
temporarily flooded grassland (FG) where pike eggs usu-
ally hatch in the Brière marsh (France) to identify the
determinants of juvenile natal departure. The release site
was connected through a unique point to an adjacent
pond (AP) used as a nursery habitat. The pond strongly
differs from the FG in many ecological features such as
food availability (zooplankton and fish prey). Fish were
continuously recaptured when migrating from the FG to
the AP. Recaptured individuals (n=29) were anesthe-
tized, checked for tags, measured for fork length,
FIGURE 3 Fur seal individual trophic trajectories. Net change
time series for males and females of both AFS and SAFS. Arrows
connect all whiskers section stable isotope values from t
1
to t
30
(i.e., most recent to oldest stable isotope values). Colors correspond
to trajectory clusters. Data from Kernaléguen et al. (2012)
ECOLOGICAL MONOGRAPHS 9of26
fin-clipped to quantify changes in δ
13
C and δ
15
N values
(Sturbois, Cucherousset, et al., 2021a), and released. Net
changes and angle αwere calculated in Ω
δ
, and followed
by hierarchical clustering of trajectories, as explained for
the previous example.
Results
Overall, released individuals exhibited lower δ
13
C
(2.49 ‰0.82, mean SD) and δ
15
N(1.46 ‰0.89)
when recaptured. The hierarchical cluster analysis
FIGURE 4 Angle αtrajectory roses of fur seals trajectory cluster. Angle αwas calculated in 2D Ω
δ
space (δ
13
C/δ
15
N) and represented
by range (15) of direction. Bar size represents the number of trajectory segments (all individual within each trajectory clusters). Watson–
William (WW) two test and Herman–Rasson (HR) test were used to test the difference between cluster and the uniformity of directions,
respectively. (p-values: >0.05; * <0.05; ** < 0.01; < 0.001). Data from Kernaléguen et al. (2012)
10 of 26 STURBOIS ET AL.
performed on pike trajectory dissimilarities matrix
between release at FG and departure to AP separated four
main trajectory clusters (Figure 5and Table 2). Clusters
1 and 2 grouped mostly zooplanktivorous individuals at
release, characterized by late emigration to the pond
(18.50 0.87 and 18.20 0.86 days, mean SE). Cluster
1 was characterized by higher net changes (3.16 0.63)
and more uniform direction (248.142.17) than cluster
1(1.670.10; 266.578.89). Clusters 3 and 4 grouped
initially piscivorous individuals. High δ
15
N values for most
FIGURE 5 Trajectory diagram of pike released in a flooded grassland and recaptured when emigrating into an adjacent pond. Arrows
represent the trajectory path for each pit-tagged individual. Colors correspond to trajectory clusters. Density curves at the periphery of the
trajectory diagram represent the distribution of all samples according to δ
13
C(x) and δ
15
N(y), and capture (green =release;
red =departure). The dashed line separates piscivorous from zooplanktivorous individuals (zooplanktivorous [δ
15
N<10‰] vs. piscivorous
[δ
15
N>10‰]). Data from Cucherousset et al. (2013)
TABLE 2 Characteristics of pike trajectory clusters: number of individuals (n), residence time in flooded grassland (Res. time), size shift
(mm), growth rate (mm day
1
), SI shift, SITA metrics, trophic status at release (zooplanktivorous [δ
15
N < 10] vs. piscivorous [δ
15
N > 10]).
Values are means SE (SD for total). Data sets from Cucherousset et al. (2013)
Clusters nRes. time Size shift Growth rate
SI shifts SITA metrics Trophic status
δ
13
C‰δ
15
N‰Net changes Angle αZplankt. Pisciv.
14 18.50 0.87 35.25 1.44 1.90 0.38 2.90 0.20 1.24 0.14 3.16 0.63 248.14 2.17 3 1
25 18.20 0.86 34.40 0.71 1.90 0.23 1.58 0.03 0.10 0.11 1.67 0.10 266.57 8.89 5
315 13.67 1.42 26.13 4.78 1.91 0.10 2.90 0.28 2.10 0.19 3.13 0.26 233.92 1.35 15
45 9.60 1.21 18.20 1.71 1.96 0.18 1.86 0.17 1.09 0.15 2.63 0.42 239.12 5.53 5
Total 29 14.41 5.14 27.45 10.06 1.92 0.27 2.49 0.82 1.46 0.89 2.95 1.02 242.41 15.60 8 21
ECOLOGICAL MONOGRAPHS 11 of 26
individuals at emigration suggested either that these indi-
viduals kept feeding at higher trophic levels than individ-
uals from clusters 1 and 2, or a post-release period in the
FG not long enough to reach the isotopic equilibrium. Dif-
ference in residence time (i.e., 13.67 1.4 and 9.60 1.2
for clusters 3 and 4 respectively) was responsible for the
difference in δ
15
N values between these two clusters
(i.e., there was less time for hatchery SI values of
cluster 3 to be diluted in FG stable isotope values). Among
all clusters, the growth rate was very similar (1.92
0.27 mmday
1
).
Discussion
Results obtained using SITA confirm the initial findings
and interpretation in Cucherousset et al. (2013) but also
provided additional information. The cluster analysis of
trajectory dissimilarity allowed an efficient discrimination
of trajectory patterns. Although these patterns were briefly
discussed in the initial study, we were able to define trajec-
tory and SI properties in the four clusters, which clearly
separated different ontogenic strategies among released
individuals. Furthermore, the use of the TD offered a more
complete representation of (1) trajectories properties at the
population level (density curves), and (2) clusters and indi-
viduals levels (individual trajectory paths).
Trophic consequences of experimental
warming on lizards
Context
Climate change is an important facet of ongoing environ-
mental changes induced by human activities. While there
is an increasing knowledge of how species will respond
to climate changes in term of distribution, our ability to
understand and predict changes in biotic interactions,
such as predator–prey dynamics, is limited.
Methods
Bestion et al. (2019a) experimentally quantified the conse-
quences of a 2C warming on the trophic niche of a gener-
alist lizard predator (Zootoca vivipara). Climate was
manipulated in a 10 10 m enclosure with similar natu-
ral vegetation and invertebrate communities, and a wide
variety of thermal microhabitats (dense vegetation, rocks
and logs, ponds; see Bestion et al. [2019a]formore
details). In June 2013, individuals belonging to two life
stages (juveniles and adults) and from both sexes were
allocated at similar density to 10 enclosures: five enclo-
sures with a “present-day climate”and five enclosures
with a “warm climate,”that is, 2C warmer on average.
There was no difference in δ
13
Candδ
15
N values between
treatments at the start of the experiment. In mid-
September 2013, surviving lizards were recaptured and a
tail tip was collected for SI analysis. Because SI values of
trophic resources varied among enclosures, a baseline cor-
rection (δ
13
C
cor
and δ
15
N
cor
) was performed to allow
between-treatment comparisons (Bestion et al., 2019a,
2019b). Enclosures from the two treatments were paired in
five blocks (A–E used as replicates), and used to character-
ize, respectively, the initial (present-day climate) and final
(warmer climate) states of a one-segment trajectory for five
paired lizard populations in response to warming. Because
the analysis focused particularly on shifts rather than
absolute SI values, we favored the representation of net
change and angle α,calculatedinΩ
δ
,inTR.
Results
Some differences in the magnitude of trajectories were
observed among pairs of enclosures (Figure 6). Block C
was characterized by the highest net change (1.63 0.19)
for all individuals (adults and juveniles of both sexes),
whereas shifts in SI values in response to warming
were more limited in other blocks (A: 0.36 0.15;
B: 0.39 0.36; D: 0.55 0.44; E: 0.47 0.21‰). Some
differences were also observed within paired enclosures
where net changes were contrasted between individuals.
For instance, in block D, adult males displayed the
highest response (1.12), whereas juvenile females dis-
played the lowest response (0.12). Differences were also
observed in the direction of the trajectories (Figure 6). In
block C, all individuals displayed similar directional
changes (10.23 3.88) with trajectories mainly implying
increase in δ
15
N
cor
values and limited δ
13
C
cor
shifts.
The other blocks displayed more variable responses to
warming. For example, individuals from block A
exhibited different directions in Ω
δ
, revealing different
patterns of SI changes.
Discussion
Using conventional statistical analyses, Bestion et al.
(2019a) concluded that lizards from warmer conditions had
higher δ
15
N
cor
values, whereas nonsignificant changes in
δ
13
C
cor
values were observed. By pairing enclosures for tra-
jectory analysis, SITA resultswereinaccordancewiththese
findings, but they also highlighted the existence, in some
cases, of other responses to warming, with approximately
12 of 26 STURBOIS ET AL.
25% of all individuals (life stage, sex and blocks) displaying
slight decreases in δ
13
C
cor
and δ
15
N
cor
values. These find-
ings may reveal some additional context dependency in the
response to warming observed at the individual level.
Contrasted trajectories in pristine and
impacted sandy beaches undergoing green
tide events
Context
Excess nutrient inputs is one of the most important
human-induced pressures in freshwater and marine
water bodies. The assessment of the consequences of the
resulting eutrophication on ecosystems functioning is
necessary to identify and describe disturbance pattern,
especially in comparison with unperturbed habitat.
Methods
Quillien et al. (2016) studied changes in sandy beach
(SB) food web structure and functioning in response to
green algae proliferation during green tide (GT) events.
Fieldwork was conducted seasonally in the bay of Doua-
rnenez (Brittany, France) in May, July, September and
November 2012 at two SB: one impacted by GT events and
the other under pristine conditions (No_GT). Sampling and
laboratory steps performed for community and SI analyses
were described in Quillien et al. (2016). Trophic trajectories
inpristineandimpactedSBwereanalyzedbothatthefood
+15Ncor
+13
C
−15Ncor
−
13Ccor
+15Ncor
+13
C
−15Ncor
−
13Ccor
+15Ncor
+13
C
−15Ncor
−
13Ccor
+15Ncor
+13
C
−15Ncor
−
13Ccor
(c) Juvenile female (d) Juvenile male
(a) Adult female (b) Adult male
0
0.5
1
1.5
2
0
0.5
1
1.5
2
Distribution of angle α
Net change
Blocks of
mesocosms
A (n=65)
C (n=55)
D (n=74)
E (n=65)
B (n=68)
cor cor
cor
cor
FIGURE 6 Angle αtrajectory roses for each lizard life stage/sex categories within each block of enclosures (warming between present
day and warm treatments). Angle αwas calculated in 2D Ω
δ
space (δ
13
C
cor
and δ
15
N
cor
). Bar size represents the net change for each
enclosure block (colors) and each life stage/sex (a: adult females; b: adult males; c: juvenile females; d: juvenile males). Data from Bestion
et al. (2019b)
ECOLOGICAL MONOGRAPHS 13 of 26
web (1) and basal source/centroid/population (2) levels. At
the food web level, functional diversity indices (Villéger
et al., 2008) were calculated in the SI space (Sturbois,
Cucherousset, et al., 2021a) as proposed by Cucherousset
and Villéger (2015) and Rigolet et al. (2015): Isotopic func-
tional richness (IFRic), evenness (IFEve) and divergence
(IDFiv). Mean distance to nearest neighbor (MNN) and
centroid (MDC) were also calculated. Patterns of biomass
were assessed by weighting SI values of every species prior
to indices calculations. A principal component analysis
(PCA), followed by SITA was performed on trophic indices
(Ω
γ
) to analyze changes in food webs properties at pristine
and impacted SB over time. Distance (segment length, net
changes) and direction-based metrics (DIR, angle Ɵ)were
calculated. SITA was complementarily performed in Ω
δ
defined with δ
13
Candδ
15
N values (Sturbois, Cucherousset,
et al., 2021a) for basal sources and food web centroids.
Distance-based metrics were calculated and trajectories at
the different levels were represented in trajectory diagrams.
Results: Structural and functional trajectories
The pristine SB was characterized by a lower structural
andfunctionaltemporalvariability (trajectory path =
6.09, mean segment length =2.33 0.48) than
impacted SB (16.13, 5.38 1.46) (Figure 7). Low DIR
indicated non-straightforward trajectories for both sites
(No_GT =0.45 vs. GT =0.33). Considering the first
two Ω
γ
dimensions, responsible for 92% of the total var-
iance, the first trajectory segments (i.e., between May
and July) were quite similar in direction for both sites
(angle α:No_GT=89.06vs. GT =69.07) but differ-
ent in magnitude (S1 length: No_GT =2.29
vs. GT =5.43), therefore highlighting similar trends of
index values, except for IFDiv (Figure 7). For GT SB,
S1 and S2 were followed by a directional rupture in Ω
γ
(Ɵ
1
=107.00;Ɵ
2
=133.14) implying contrasted func-
tional and structural shifts. At No_GT SB, S2 followed
a more straightforward path, whereas S3 was charac-
terized by an important direction change (Ɵ
1
=34.03;
Ɵ
2
=138.90). At the scale of the overall study period,
structural and functional variability was higher in
SB harboring GT (NC =4.74) than in pristine SB
(NC =3.30). Between May and November, pristine SB
was characterized by positive shifts in IFRic, and MDC
and MNN, and negative shifts in IF Eve and IFDiv. At
GT SB, IFDiv and IFRic were characterized by a mod-
erate increase, whereas MNN, IFEve, and MDC
decreased. At the scale of each trajectory segment,
No_GT SB was mainly characterized by shifts in IFRic
values, whereas GT SB was typified by highest magni-
tudes of changes and contrasted shifts. Specifically, the
decrease in MDC and MNN values occurring between
July and September started to recover in November.
Sources/centroid-specific trajectories in the
δ
13
C and δ
15
N space
Basal sources trajectories were longer, therefore
highlighting a high variability in SI values (Figure 8).
Whereas particulate organic matter (POM) in impacted
and pristine beaches exhibited similar trajectory length
(6.67 vs. 5.99), sedimentary organic matter (SOM) was
characterized by a lower variability where GT occurred
(3.66 vs. 6.05). Ulva spp. was characterized by the highest
SI variability (8.56). Specifically, POM trajectories at
both sites were similar in terms of nature, seemingly
cyclic, but different in magnitude. SOM at both sites
depicted more complex trajectories, with similar but not
synchronized SI trends, notably in September and
November (i.e., November SOM No_GT vs. September
SOM GT, and inversely). Trajectories of centroids did
not reflect the magnitude of basal sources dynamics in
GT (trajectory path =1.40, net change =0.76) and
No_GT SB (1.62, 0.53). Trajectories of basal sources and
centroid highlighted a constant enrichment in
13
C,
except for SOM in September, while δ
15
N patterns were
less obvious.
Discussion
Results were congruent with the conclusions of Quillien
et al. (2016) that showed a simplification of food web
structure and functioning in the SB where the GT tide
occurred. The consideration of SI dynamics at basal
sources and centroids levels helps to better understand
structural and functional trajectories at both sites. The
interest in SITA was due to the consideration of both sites
through their own dynamics exhibited at different levels.
Specifically, SITA pointed out (1) low differences and var-
iability of food web centroids at both beaches, and
(2) contrasted structural and functional trajectories
depicting the initiation of two potential food web cycles,
which differed in nature and magnitude.
Biological invasions and trophic structure
dynamics of lake fish communities
Context
Community assembly can strongly impact the dynamics
of biological diversity and the functioning of ecosystems
14 of 26 STURBOIS ET AL.
(Bannar-Martin et al., 2018). Environmental changes
strongly affect the way species interact and how commu-
nities assemble and it is therefore important to assess
how the trophic structure of communities will respond to
these changes.
Methods
This question was investigated by quantifying the tempo-
ral dynamic of the trophic structure of fish communities
in a network of gravel pit lakes displaying varying levels
of biological invasions (Zhao et al., 2019). Fish were sam-
pled in 2014, 2016, and 2018 using a standardized proto-
col (gill netting and electrofishing) in six gravel pit lakes
located along the Garonne river (Figure 9) (Alp
et al., 2016; Evangelista et al., 2017; Zhao et al., 2019).
Fish were identified at the species level, counted, mea-
sured, and fin clips were collected for δ
13
C and δ
15
N
analyses.
The overall data set (all lakes and sampling year
pooled) included 19 species. Five species were present in
more than 75% of all communities (18 lakes years): two
non-native species, namely pumpkinseed (Lepomis
Overall changes
May – Nov.
S1
May - July
S2
July – Sept.
S3
Sept. – Nov.
(a)
(c) (d) (e)
IFDiv IFEve MDC MNN
Indices
IFRic
IFDiv IFEve MDC MNN
Indices
IFRic IFDiv IFEve MDC MNN
Indices
IFRic IFDiv IFEve MDC MNN
Indices
IFRic
Ind_shift
Ind_shift
2
1
0
0
0
0
2
1
1.5
0.5
1
1.5
0.5
-1
-0.5
0.5
-0.5
-1
-1.5
-2
(b)
FIGURE 7 Structural and functional trajectories at impacted (green) and pristine (blue) beaches. (a) Trajectory diagram in Ω
γ
space.
Only two dimensions are shown, representing 92% of the total variance. Solid lines ending with an arrow represent segment lengths and
dotted arrow net changes. (b–e) Bar plots represent the shift in value of five structural and functional indices: isotopic functional richness
(IFRic), evenness (IFEve), divergence (IDFiv), and mean distance to nearest neighbor (MNN), and centroid (MDC). Bar plot panels show
changes in indices values between May and November (b) and for all pairs of consecutives periods (c: May to July, d: July to September, e:
September to November). Data from Quillien et al. (2016)
ECOLOGICAL MONOGRAPHS 15 of 26
gibbosus) and black bullhead (Ameiurus melas)andthree
native species, namely roach (Rutilus rutilus), perch (Perca
fluviatilis) and rudd (Scardinius erythrophthalmus). Rarer
species such as Oncorhynchus mykiss,Gymnocephalus
cernua,Anguilla anguilla, and others were sampled only
for 1 year in one lake. Across all sites and all years, the
most abundant species included two invasive species
mosquitofish (Gambusia affinis)(22.9818.35%) and
black bullhead (17.46 16.37%) followed by the native
roach (15.72 14.55%).
The variability of frequency and relative abundance
among lakes and years illustrated the strong community
dynamics occurring in lakes. A trajectory analysis was
performed to determine if changes in community compo-
sition were associated to changes in the SI structure of
communities over time. Four SI structure indices
(namely isotopic richness, δ
13
C range, δ
15
N range, isoto-
pic evenness following Cucherousset & Villéger, 2015
and Layman et al., 2007) were calculated (Sturbois,
Cucherousset, et al., 2021a) using abundance data and
used in SITA for Ω
γ
. Distance (segment length, net
change, trajectory path, NCR, RDT) and direction-based
(angle Ɵ, directionality) were calculated and are repre-
sented in TD and maps.
FIGURE 8 Trajectory diagram of food web centroids and basal sources at impacted and pristine beaches. Panels represent
specific trajectories for food web centroid, particular organic matter (POM), sedimentary organic matter (SOM), and Ulva spp. Size of
dots corresponds to net changes, arrows to trajectory path, and colors to beach (GT: green, No_GT: blue). Data from Quillien
et al. (2016)
16 of 26 STURBOIS ET AL.
FIGURE 9 Structural trajectories of fish communities in six gravel pit lakes. (a) Trajectory diagram in Ω
γ
space. Only two dimensions are
displayed, representing 80.3% of the total variance. Bar plots represent the shift in the value of four structural indices: isotopic functional richness
(IFRic), evenness (IFEve), and δ
13
Candδ
15
N ranges. (b) Bar plot panels show changes in indices values. (c) Structural trajectory map: net changes
(Nc) are represented with green circles between 2014 and 2018. Bottom triangles represent S1 (2014 to 2016) and top ones S2 (2016 to 2018). The
size of the symbols corresponds to segment lengths. For triangles, colors are used to distinguish recovering (black) from departing trajectories (gray)
ECOLOGICAL MONOGRAPHS 17 of 26
Results
SITA highlighted a high level of variability between
lakes. Lakes Lamartine (trajectory path: 6.70), Lavernose
(4.95) and Bidot (4.45) were characterized by a recovering
pattern (Figure 9a,c) between 2016 and 2018, as indicated
by high angle Ɵ(146.05, 164.09, 172.41), low DIR
(0.19, 0.09, 0.04) and moderate NCR (0.35, 0.48, 0.31)
values, respectively. The efficiency of the recovering pat-
tern contributed to low net changes (2.37, 2.37, 1.38). In
the opposite, lakes Pouvil (TP: 4.54), Birazel (3.94) and
Bois-Vieux (2.90) were characterized by different trajec-
tory patterns characterized by lower angle Ɵ(63.25,
16.22, 100.99), and higher DIR (0.65, 0.91, 0.44) and
NCR (0.88, 0.99, 0.66) values. Differences were also
observed in the nature of the structural trajectories
among lakes (Figure 9a,b). Specifically, the structural tra-
jectory of Lake Bidot was mainly characterized by a
decrease in the δ
13
C range, contrasting with Lake Birazel
trajectories that were mainly characterized by a strong
increase in δ
13
C range and isotopic richness, and a mod-
erate increase in δ
15
N range and isotopic evenness. We
also found that the structural trajectories of Lake Pouvil
were primarily characterized by a strong increase in δ
15
N
range and isotopic richness and a decrease in evenness.
Discussion
SITA approach provided a global and quantitative analy-
sis to compare the magnitude and nature of structural
change over time and across multiple lakes with different
invasion levels. Coupling distance and direction-based
metrics underlined the recovering and departing trajecto-
ries characterized by contrasting changes in isotopic indi-
ces. In some lakes, exhibiting departing trajectories,
direction-based metrics underlined persistent changes
through strong linear trajectories, while potential cyclic
dynamics were suggested for recovering lakes over the
study period. The TM constitutes a synthesis of distance-
based metrics and an efficient way to compare the struc-
tural food web variability of all lakes. The SITA approach
could therefore help to understand the patterns of trophic
structure variability in disturbed ecosystems.
Spatio-temporal variability of δ
13
C and δ
15
N
modeled isoscapes in the northeast Pacific
Context
Isoscapes are increasingly used to assess the relative tro-
phic position of higher trophic levels, to provide
information on the relative productivity of different
regions, and they can also be used to track the migration
of animals. Despite isoscapes providing a wide distribu-
tion of the variations of SI values, this tool is currently
limited for the synthetic analysis of SI dynamics.
Methods
Espinasse et al. (2020) tested the application of isoscapes
modeled from satellite data to the description of second-
ary production in the northeast Pacific. Several key
parameters (sea surface temperature, sea level anomaly,
and chlorophyll a) were used as inputs on a general
additive model. The output model fits in a 0.250.25
spatial grid covering the region spanning from 46 to
62N and from 195 to 235E and supporting δ
13
Cand
δ
15
N isoscapes from 1998 to 2017 (Espinasse, 2020). We
subset modeled δ
13
Candδ
15
N values of a 11spatial
grid from the original modeled dataset. Isoscapes
modeled for 2013, 2015, and 2017 were selected as they
were characterized by high SI dynamics and conse-
quently constituted relevant inputs to test our ITM con-
cept. Modeled SI values for which one of the parameter
was missing were excluded. Mapping trajectory metrics
requires that stations are synchronously surveyed. Con-
sequently, stations where values were missing for one
date within each pair of dates (2013–2015 and 2015–
2017) were also excluded. The subset of stations
supporting SITA was finally composed of 489 and 488 sta-
tions for the periods 2013–2015 and 2015–2017, respec-
tively. Segment lengths (2013–2015 and 2015–2017), and
angle αwere calculated in the modeled 2D Ω
δ
space
(δ
13
C/ δ
15
N) for all stations and periods and used as
input in a modeled ITM. RDT and overall NCR were also
calculated to qualify departing or recovering patterns
between 2015 and 2017 with respect to the δ
13
Cand
δ
15
N values modeled in 2013. Additionally, a long-term
SITA was performed from 1998 to 2017, using directions
and net changes calculated for all pairs of dates (1998–
1999, …, 2016–2017) as input for a TH.
Results
Modeled ITM revealed contrasted dynamics between
2013–2015 and 2015–2017 (Figure 10). While differences
in the nature of changes (i.e., direction) were highlighted
in the ITM, the overall magnitudes of the dynamics were
similar (total segment length =638.90 between 2013 and
2015 vs. 620.41 between 2015 and 2017). A few areas con-
centrated an important part of the overall dynamics,
especially in the southeast part and, to a lesser extent, in
18 of 26 STURBOIS ET AL.
the northern part of the modeled area. The ITMs
suggested an overall recovering pattern between 2015
and 2017 with respect to the model defined in 2013,
which was confirmed by an RDT < 0 for 76% of stations
and a low overall mean of NCR values (0.21).
The TH (Figure 11) revealed that angle αranging from
0to 90and 180to 270was the most frequent from
1998 to 2017. While SI trajectories characterized by
increases in δ
13
Candδ
15
N values alternated with patterns
of decrease in both isotope values and exhibited the major
part of the overall changes, some fine scales patterns were
also revealed at the beginning of the modeled period.
Discussion
The ITM provides a relevant visual synthesis of
(1) spatio-temporal dynamics complementary to
(2) modeled isoscapes. (1) ITM, including trajectories of
two SI, highlight areas of high variability associated
with eddies that enhanced local production in the open
ocean (Espinasse et al., 2020). It also allowed the easy
identification of areas with SI values that were stable
over time, which is useful for animal tracking studies
(Trueman & St John Glew, 2019). (2) Modeled isoscapes
also illustrate this pattern beyond the decrease in δ
13
C
and δ
15
N values from the coast to offshore (Espinasse
et al., 2020). One solution to identify this second pattern
in the ITM may exist in the addition of trajectory clus-
ters (color of vectors) from a trajectory similarity
analysis. In such cases, users should be careful with the
figure readability. The main advantage of this concept
of TM lies in its ability to synthesize spatio-temporal
dynamics from four isoscapes, which is a major
challenge when dealing with massive amounts of
spatialized data.
FIGURE 10 Isoscape trajectory maps in the northeast Pacific for the periods 2013–2015 and 2015–2017. SITA metrics were mapped to
illustrate stable isotope spatio-temporal dynamics. Direction of arrows (angle α) illustrates direction in the modeled 2D Ω
δ
space according to
increase and/or decrease in δ
13
C and δ
15
N values (0–90:+δ
13
C and +δ
15
N; 90–180:+δ
13
C and δ
15
N; 180–270:δ
13
C and δ
15
N; 270–
360:δ
13
C and +δ
15
N). Length of arrows and colored background rasters illustrate modeled trajectory segment length at each station. Data
from Espinasse et al. (2020)
ECOLOGICAL MONOGRAPHS 19 of 26
The TH provides an effective synthesis of high tempo-
ral resolution SI dynamics for a 20 years period, highlight-
ing cyclic patterns of enrichment and depletion in
13
Cand
15
N isotopes. Coupled with quantitative SITA metrics, ITM
and TH appear as promising tools for isoscapes space–time
analyses. These innovative figure concepts allow the illus-
tration of differences in the magnitude and nature of
spatio-temporal SI dynamics, and they can be easily
coupled with statistics to track accurately significant pat-
terns in high resolutions data sets.
DISCUSSION
Building on previous works dealing with ecological
dynamics in SI ecology, we adapted CTA to provide a
FIGURE 11 Trajectory heatmap. Heatmap panel: Angle αin the modeled 2D Ω
δ
space exhibited by all stations within all pairs of dates
(1998–1999, …, 2016–2017) are represented by the range of direction (15) according to period. Color gradient from dark blue to yellow
indicates the number of stations exhibited by a given range of direction within a given period. Xbarplot: Sum of segment lengths across
stations and times, exhibiting the chosen angle. The blue gradient indicates the net change magnitude. Ybarplot: Overall net changes
according to range of directions (angle α). Bars are colored according to increase and/or decrease in δ
13
C and δ
15
N values (Pink: 0–90:
+δ
13
C and +δ
15
N; Blue: 90–180:+δ
13
C and δ
15
N; Red: 180–270:δ
13
C and δ
15
N; Green: 270–360:δ
13
C and +δ
15
N). Data from
Espinasse et al. (2020)
20 of 26 STURBOIS ET AL.
formal and explicit framework for the analyses and repre-
sentations of spatial and temporal trajectories in SI ecol-
ogy. The different examples used here, sourced from
marine, terrestrial, and freshwater ecosystems, illustrate
the insights provided by this new analytic framework.
SITA originates from the CTA framework, and we believe
that the representation solutions proposed here
(e.g., trajectory diagrams, TH) are also easily transferable
to many different fields of ecology, including community
ecology.
Tracking stable isotope dynamics with
SITA metrics
Distance- and direction-based metrics provide quantita-
tive synthetic information and allow effective compari-
sons at the individual, population, community, and
ecosystem scales, all being relevant scales that are widely
explored in ecology (Layman et al., 2012). Our approach
was complementary to original analyses in the different
application data sets. Coupled with the calculation of
distance- and direction-based metrics, the analysis of tra-
jectory similarity helped to highlight contrasted individ-
ual strategies that were not revealed from analysis at the
population level, because they did not systematically fol-
low species, age, or gender a priori classifications (EA1
and 3). When applied at the individual to the population
levels, SITA allows the study of the shape and the magni-
tude of stable isotope trajectories to track for resource
partitioning (EA1), adaptation to a changing environ-
ment (EA2, EA3 and EA4), or animal migrations (EA1).
The SITA framework allows the measurement of changes
in terms of both stable isotope composition (Ω
δ
), and
structure and functioning (Ω
γ
), which is useful and rele-
vant for understanding contrasted food web dynamics in
response to environmental or anthropic pressures (EA4).
The definition of recovering and departing patterns with
respect to initial states highlights different dynamics
through the distinction of sites characterized by long-
term changes from those characterized by ecological
periodicity (EA5), or unexplained, seemingly chaotic, var-
iability. SITA can also identify shifts and cycles in the
composition of sources (EA4, EA6). While not illustrated
here, using mixing models to define Ω(see p-spaces
defined in Newsome et al., 2007) supporting SITA seems
a very promising avenue to track temporal changes in the
proportion of resources fueling consumers and potential
energy pathway dynamics.
SITA contributes to achieving the synthetic challenge
inherent to high spatio-temporal resolution datasets,
independently of the size of the study area and/or the
length of the time series. This ability to deal with large
datasets seems especially relevant in the context of
isoscape dynamics in widespread and/or intensively stud-
ies area, as shown for SI dynamics in the northeast
Pacific water body (EA6).
Differences in SITA metrics can be tested statistically
as illustrated with circular statistics for direction-based
metrics (EA1). Users are encouraged to use complemen-
tary statistical approaches, such as regression or correla-
tion tests, to explore the relationship and the strength of
the relationship between distance-based metrics and
other explanatory variables under natural, anthropo-
genic, or experimental conditions.
Representing spatio-temporal dynamics in
stable isotope ecology
The recent CTA extension (Sturbois et al., 2021) showed
the importance of plotting trajectory metrics in specifi-
cally designed figure concepts, adapted for the represen-
tation of dynamics. Building on this, and on previous
attempts in SI ecology (Agostinho et al., 2021;
Cucherousset et al., 2013; Schmidt et al., 2007), we pro-
posed here two new figure concepts specifically devoted
to the representation of dynamics at large spatio-
temporal scales: the ITM and the TH (Figures 10 and 11).
Here, we have chosen the figure concepts that we
deemed the most suitable for each ecological application.
We believe that these entire figure concepts are strongly
complementary and that users should explore all figure
concepts and metrics, finally selecting the ones most
adapted to the relevant hypotheses.
To improve the representation of dynamics through
trajectory diagrams, users could innovate in the repre-
sentation of trajectory metrics. For example, the custom-
ization of diagram traditionally used in SI ecology with
arrows, density curve, net changes, and trajectory clus-
ters together brings new perspectives in the visualiza-
tion of ecological dynamics (EA1, EA2, EA4, and EA5).
Trajectory roses offer innovative ways to represent
directions. We went beyond the arrow diagrams pro-
posed by Schmidt et al. (2007)byusingthetrajectory
rose that allows representation of both angle distribu-
tion and length (EA3), or favoring the contrasted distri-
bution of angles among different groups (trajectory
cluster, population, anthropogenic factors, etc.) using a
circular bar plot structure (EA1). We also developed the
initial TM concept (Sturbois et al., 2021) devoted to the
representation of trajectory metrics in synthetic maps
(EA5), by the proposition of the ITM especially designed
to illustrate SI dynamics at very large scales (EA6).
Largely inspired by wind and current map, the ITM
appears particularly relevant to detect patterns charac-
terizedbydifferencesinthenatureandmagnitudeofSI
dynamics. To complement the representation of
ECOLOGICAL MONOGRAPHS 21 of 26
dynamics at high spatio-temporal resolution, we pro-
pose the TH concept, which provides synthetic perspec-
tives to represent both the magnitude and the nature of
changes and detect potential long-term SI cycles in large
areas (EA6).
We believe that these entire figure concepts are far
from being exhaustive and we suggest that users inno-
vate in the representation of trajectory metrics and in
the customization of R codes provided here (DataS1:
SITA_R_Codes; Sturbois, Cucherousset, et al., 2021b).
Assumption, applications, and limitations
of the proposed framework
Ecologists are increasingly using sophisticated methods for
dealing with measured data (Fry, 2013)andSIecologyisno
exception. While it is always tempting to favor approaches
providing quantitative analyses, it is important to keep in
mind the biological meaning of associated assumptions,
and their inherent simplifications (Layman et al., 2012). If
the SITA framework and the associated graphical represen-
tations constitute potential management and decision-
making tools, we urge users interested in sharing this
synthetic tools with stakeholders or managers that interpre-
tation must be done carefully in the hands of experienced
multivariate/SI ecologists (Sturbois et al., 2021).
“A carpenter would never use a screwdriver to pound a
nail”(Layman & Post, 2008): SITA concepts and metrics
were not intended as a universal tool to be applied in all
situations or as a substitute for other available methods
(Buckley, Day, Case, et al., 2021; Buckley, Day, Lear,
et al., 2021), but as a new tool for the SI ecologists that
could be useful in situations suitable for trajectory analy-
sis. Similar to all analytical tools, there is a high likeli-
hood that the SITA framework may be applied to
datasets to which it is not well suited or that inexperi-
enced users may misinterpret the results. Indeed, there is
a considerable history of this in the SI literature con-
cerning, for example, mixing models (Fry, 2013; Jackson
et al., 2009; Phillips, 2001; Phillips et al., 2014). Users
must consequently be aware of the assumptions, fields of
application, and limitations associated with the SITA
framework as described in this section.
Despite the speed of changes that allows dealing with
variations in frequency of surveys, we encourage users to
establish sampling strategies, implying synchronous sam-
pling and similar frequency of surveys (De C
aceres
et al., 2019; Sturbois, De C
aceres, et al., 2021). It is an
essential condition to use at best the SITA framework.
Multivariate ecological methods are descriptive by
nature. Despite SITA providing accurate measurements
and representations of dynamics in stable isotope
ecology, it shares limitations with CTA (De C
aceres
et al., 2019; Sturbois et al., 2021). Consequently, SITA
outputs must be completed by a strong examination of
input datasets (stable isotope raw data or structural and
functional indices) to improve the ecological interpreta-
tion of observed dynamics. Similarly, SITA may be com-
plemented with additional analyses (Buckley, Day, Case,
et al., 2021) to statistically test for other aspects of
changes or to provide statistical backgrounds.
Note that ordination spaces are specifically con-
structed for each given data set. Therefore, any data
transformation on the raw data or sampling decision is
likely to affect trajectories and, subsequently, all metrics
to be calculated. This effect should be tested before any
overall transformations of raw data, such as scaling
and/or baseline correction of SI values, or any biomass or
abundance weighing prior to indices calculation.
Despite the SITA framework being not limited in
terms of the number of components considered in metric
calculations, some of the applications only considered
part of the variability, if Ω
δ
or Ω
γ
contained more than
two dimensions (reporting angles Ɵ,ωin a 0–360sys-
tem, angle αcalculation). In this context, performing
SITA requires a careful interpretation of the multivariate
space to assess the consequences of such reduction.
SITA also shares numerous limitations inherent to
stable isotope properties and analysis (Fry, 2008;
Garvey & Whiles, 2017). Dynamics of basal source SI
values influence the corresponding SI compositions of
consumers (Matthews & Mazumder, 2004) and poten-
tially the metrics used to describe the variability, and the
food web structure and functioning. However, SITA
offers the possibility to explore both source and consumer
dynamics. Additionally, many other factors are known to
influence food assimilation and finally the isotopic com-
position of consumers such as fractionation variability or
the type of tissue analyzed (Fry, 2008).
In complex ecosystems characterized by similar SI
composition of basal sources and in underdetermined
cases in which multiple outcomes are feasible from isotope
tracer measurements, different feeding pathways may lead
to similar positions in δspace (Fry, 2013;Layman
et al., 2007), a situation that cannot be disentangled by
SITA and necessitates complementary approaches. For the
opposite, SITA will be more relevant when differences in
stable isotope values of basal sources induce contrasted
positions of consumers. When performed at the population
level, mean stable isotope values are used as input in
SITA, which has the drawback of hiding the stable isotope
composition variability at intraspecific levels (Bearhop
et al., 2006; Matthews & Mazumder, 2004). In this case,
intrapopulation variability could be shown as confidence
intervals in trajectory diagrams or maps.
22 of 26 STURBOIS ET AL.
The metrics allow a real-time measurement of
dynamics, and a qualitative and quantitative assessment
of the potential degree of success in achieving conserva-
tions objectives or the impact of natural or anthropogenic
changes in environmental conditions. All factors inherent
to multivariate and stable isotope analyses, individually
or combined, may influence SITA metric calculations,
and we urge users for a careful check of such potential
bias before defining their sampling design, performing
SITA, and interpreting results. Alternatively, conclusions
may lead to an incomplete picture and can mislead the
description of dynamics with potential misdirecting con-
servation actions or overstating conservation progress.
Exporting trajectory analysis to other kinds
of ecological data
Taking into account the strengths and limitations of
the proposed framework, we consider that SITA brings
insightful perspectives into the analysis of high-
resolution temporal datasets using stable isotopes
and/or other tracers in integrating organism tissues.
Even though the SITA framework has been here
defined based on stable isotope data, and builds on the
CTA framework for community data, any other multi-
dimensional input data are likely to be suitable for this
approach. For instance, using trajectory analysis on
multitrace element data, including SI or not, would
provide appealing insights into subpopulation migra-
tory patterns in fish populations based on otolith
chemistry (Elsdon et al., 2008; Trueman et al., 2012).
Similar applications can easily been foreseen at the
individual scale from tree rings, in a dendrochronology
context (Sleen et al., 2017), or from environmental sig-
nals recorded in bivalves shells (Butler et al., 2019), or
bone growth layers (Merrett et al., 2021;Turner
Tomaszewicz et al., 2016). As shown at the scale of the
northeast Pacific water body (EA 6), sea water SI com-
position can be tracked to large spatio-temporal scales
and may be tested for long-term or seasonal SI trajecto-
ries in rain and snowfall (Aizen et al., 2005;Tian
et al., 2018), or ice (Schotterer et al., 1997; van Trigt
et al., 2002;Werneretal.,2018). Other tracers are also
increasingly used in association with SI, such as con-
taminants (Dietz et al., 2004,2021) or fatty acids
(Madgett et al., 2019), and the absence of limitation in
the number of dimensions supporting SITA constitutes
an important strength to improve the analysis of such
complex multivariate datasets. As experimental studies
involve very controlled protocols, SITA metrics can
also be particularly relevant to depict experimental tra-
jectories (EA3).
We hope that trajectory analysis using the new ecotraj
package will contribute to the assessment of natural or
man-induced environmental changes using the responses
of chemical composition in biological archives, both in
contemporary or archeological studies at local, to
regional and global, scales. On a broader front, there are
claims for an extension of the trajectory analysis concept
to other fields in ecology. In this perspective, the adapt-
ability to different type of ecological questions (composi-
tional, functional, structural, trophic, etc.) given by the
choice of the space of analysis Ω(i.e., raw variables and
dissimilarity metric choice) constitutes the major strength
of the approach. We strongly believe that coupling eco-
logical trajectory analysis frameworks with traditional
methods of analysis in studies dealing with long-term
integrative data sets could bring interesting perspectives
for a better understanding of ecosystem functioning,
trends in ecosystems quality, and past and present global
changes.
ACKNOWLEDGMENTS
We are very grateful to the editor and anonymous
reviewers who significantly contributed to improve the
quality of the article. We acknowledge the Agence de l’eau
Loire-Bretagne (grant number 180212501), the Région Bre-
tagne (grant number OSIRIS PFEA621219CR0530023), the
Europe for the European Maritime and Fisheries Fund
(grant number FEAMP 621-B) and the Ministère de la
transition écologique et solidaire (grant number EJ
No. 2102930123) who funded this research as part of the
ResTroph Baie de Saint-Brieuc research program. This
work was carried out as part of the PhD thesis of
A. Sturbois for Université de Bretagne Occidentale. This
research was also funded by the Spanish Ministry of Econ-
omy (CGL2017-89149-C2-2-R) and all EA were supported
by complementary funds described in the respective arti-
cles. Particularly, the fur seal work was financially and
logistically supported by the French Polar Institute (IPEV,
program no. 109, C. Barbraud). The gravel pit lake study
was supported by the Office Français de la Biodiversité
(STABLELAKE and SOLAKE projects).
CONFLICT OF INTEREST
The authors declare no conflict of interest.
DATA AVAILABILITY STATEMENT
Data are available as follows: Bestion et al. (2019b), Zenodo,
https://doi.org/10.5281/ZENODO.3475401;Espinasseetal.
(2020), Dryad, https://doi.org/10.5061/DRYAD.D2547D7Z6;
Sturbois et al. (2021a), Zenodo, https://doi.org/10.5281/
ZENODO.5519696.Code(Sturboisetal.,2021b)isavail-
able on Zenodo at https://doi.org/10.5281/ZENODO.
5519693.
ECOLOGICAL MONOGRAPHS 23 of 26
ORCID
Anthony Sturbois https://orcid.org/0000-0002-9219-
4468
Julien Cucherousset https://orcid.org/0000-0003-0533-
9479
Miquel De C
aceres https://orcid.org/0000-0001-7132-
2080
Nicolas Desroy https://orcid.org/0000-0002-9047-5637
Boris Espinasse https://orcid.org/0000-0002-7490-5588
Yves Cherel https://orcid.org/0000-0001-9469-9489
Gauthier Schaal https://orcid.org/0000-0003-3860-1517
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How to cite this article: Sturbois, Anthony,
Julien Cucherousset, Miquel De C
aceres,
Nicolas Desroy, Pascal Riera,
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2022. “Stable Isotope Trajectory Analysis (SITA): A
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