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royalsocietypublishing.org/journal/rspb
Research
Cite this article: Lambert PJ, Herbert-Read
JE, Ioannou CC. 2021 The measure of spatial
position within groups that best predicts
predation risk depends on group movement.
Proc. R. Soc. B 288: 20211286.
https://doi.org/10.1098/rspb.2021.1286
Received: 9 June 2021
Accepted: 23 August 2021
Subject Category:
Behaviour
Subject Areas:
behaviour, ecology, evolution
Keywords:
group living, virtual prey, domain of danger,
collective behaviour, selfish herd,
Gasterosteus aculeatus
Author for correspondence:
Poppy J. Lambert
e-mail: poppyjulielambert@gmail.com
Electronic supplementary material is available
online at https://doi.org/10.6084/m9.figshare.
c.5598182.
The measure of spatial position within
groups that best predicts predation risk
depends on group movement
Poppy J. Lambert
1
, James E. Herbert-Read
2,3
and Christos C. Ioannou
4
1
Comparative Cognition Unit, Messerli Research Institute, University of Veterinary Medicine Vienna, University of
Vienna, Medical University of Vienna, Vienna, Austria
2
Department of Zoology, University of Cambridge, Cambridge, UK
3
Aquatic Ecology, Department of Biology, Lund University, Lund, Sweden
4
School of Biological Sciences, University of Bristol, Bristol, UK
PJL, 0000-0002-0573-7891; JEH-R, 0000-0003-0243-4518; CCI, 0000-0002-9739-889X
Both empirical and theoretical studies show that an individual’s spatial
position within a group can impact the risk of being targeted by predators.
Spatial positions can be quantified in numerous ways, but there are no direct
comparisons of different spatial measures in predicting the risk of being
targeted by real predators. Here, we assess these spatial measures in
groups of stationary and moving virtual prey being attacked by three-
spined sticklebacks (Gasterosteus aculeatus). In stationary groups, the limited
domain of danger best predicted the likelihood of attack. In moving groups,
the number of near neighbours was the best predictor but only over a limited
range of distances within which other prey were counted. Otherwise,
measures of proximity to the group’s edge outperformed measures of
local crowding in moving groups. There was no evidence that predators pre-
ferentially attacked the front or back of the moving groups. Domains of
danger without any limit, as originally used in the selfish herd model,
were also a poor predictor of risk. These findings reveal that the collective
properties of prey can influence how spatial position affects predation risk,
via effects on predators’targeting. Selection may therefore act differently
on prey positioning behaviour depending on group movement.
1. Introduction
Animals often form groups to lessen their risk of predation [1,2]. The risk of pre-
dation, however, is not distributed evenly across the different spatial positions
an individual might occupy within the group. Risk can be higher for individ-
uals on the group’s edge rather than in the centre (also known as marginal
predation [3–5]), for individuals positioned further from their near neighbours
[6–8], or for those at the front or back of moving groups [9–11]. The majority of
evidence for the different risk afforded by different spatial positions comes from
observational studies of real predators targeting real prey, and from how prey
respond by changing their position in groups in response to predatory attacks
[7,8,12–14].
Measures to define prey position within groups fall into two broad categories:
those describing centre-edge positioning and those describing the degree of local
crowding. Previous studies have tended to focus on one or the other, even though
these measures tend to be correlated as individuals on the edge of groups have
reduced local crowding. We are therefore limited in our understanding of
which measures are particularly important in determining the predation risk
faced by prey in different spatial positions. Such a comparison is challenging
because it is difficult to accurately measure prey spatial positions during a suffi-
cient number of (often unpredictable) attacks. Additionally, the spatial position
within groups of real prey is known to be determined by a number of additional
confounding factors, such as parasite load, boldness and the ability to acquire
© 2021 The Author(s) Published by the Royal Society. All rights reserved.
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food [15–20]. While models of virtual predators attacking
simulated prey allow for unconfounded investigations of the
effect of spatial position on risk (e.g. [21]), these models have
to make assumptions about how predators behave [6]. Finally,
groups vary in their collective properties, such as whether
groups are stationary or moving, and these collective proper-
ties can impact predation risk and foraging success [22–24].
However, whether such properties affect which measures of
spatial position best predict predation risk is unknown.
To address these challenges, we presented simulations of
virtual prey to three-spined sticklebacks (Gasterosteus aculeatus).
Prey groups of 20 individuals were either stationary (with only
small, uncoordinated ‘jitter’motion) or had relatively slow
directional movement (in addition to the jitter motion). The
spatial positions of targeted and non-targeted prey were defined
according to different measures previously used in the literature,
and the success of each measure in predicting the likelihood of
predation (i.e. attack) was assessed with an information criterion
model comparison approach. We predicted that centre–edge
measures of spatial position would better predict predation
risk in moving groups due to the greater encounter rate with
moving groups, especially at the front of the prey group [10].
By presenting real predators with virtual prey, the limitations
of studies using predators attacking live prey, and simulated
predators targeting simulated prey, can be overcome [3,9,25].
2. Material and methods
(a) Subjects and housing
Three-spined sticklebacks (G. aculeatus) were caught from the River
Cary in Somerton, UK (51.069990 latitude, −2.758014 longitude) in
November 2017 and were transported by car to the University of
Bristol. They were housed in 40 × 70 × 34 cm (width × length ×
height) glass tanks on a flow-through recirculation system, with
plastic shelters and plants for environmental enrichment, and
kept at 14°C under a 11 : 13 light : dark cycle. Approximately 40
individuals were housed in each tank. The experiment was run
from October to November 2018. Fish were fed with defrosted
bloodworms before and throughout the experiment. During the
experiment, they were fed after testing each day.
(b) Experimental set-up
Two-dimensional virtual prey were presented to the fish on
the front wall of a testing arena, so that the fish’s approach
was typically from the third dimension (i.e. perpendicular to
the two-dimensional spread of the group). This minimized the
bias of the fish to attack individuals on the edge of the group
because they are the first to be encountered [3]; Romenskyy
et al. [8] showed that for three-dimensional prey groups,
information about the spatial position taken from only a
two-dimensional plane can predict the likelihood of predation.
The testing arena (55 × 40 × 35 cm, L × W x H) was filled to a
depth of 25 cm with water from the recirculating system that the
fish were housed in. The walls of the back, side and bottom of
the arena were covered with opaque white plastic. A screen made
from a white translucent film (Rosco gel no. 252) was placed
inside the front wall of the tank. When the simulated prey were pro-
jected onto thisscreen, they were visible to the predatory fish, while
the predatory fish was also visible through the screen (figure 1).
A projector (BenQ MW523) was positioned 82 cm in front and
below the bottom level of the tank to minimize the bulb’sglare
on the glass. Two strip lights were placed outside the tank
behind the back wall to illuminate the arena from the rear. This
ensured that the projected prey were not visible to the fish on the
rear tank wall, while prey were still visible to the fish on the front
screen. A camcorder (Panasonic VX870) was positioned directly
in front of the tank, behind and above the projector. Videos were
recorded at a resolution of 3840 × 2160 pixels at 25 frames per
second. The entire experimental set-up was enclosed by black cur-
tains to visually isolate the experiment from the testing room.
(c) Virtual prey simulations
We generated two types of prey simulations in MatLab 2018b
[26] (electronic supplementary material, figure S1): stationary
groups and moving groups (electronic supplementary material,
movies S1 and S2). Once projected onto the screen, the virtual
prey appeared as red dots approximately 3 mm in diameter, a
typical size of stickleback invertebrate prey. The prey could
appear in an area of 350 × 240 mm and in the moving simulations
moved across the screen at 11 mm s
−1
. The size and speed of prey
were set to elicit predatory responses from the fish (e.g. as in [9]).
We gave the prey of both types of simulation a small jitter
motion, to make them appear more lifelike. See electronic
supplementary material for simulation details.
(d) Prey presentation and identification
Each focal fish was presented with a unique prey simulation play-
ing on a loop. Each loop lasted 40 s, with the first 10 s containing no
prey, followed by 20 s of the prey being presented (the prey loomed
in at the start over 1.67 s, and then loomed out over 1.67 s at the end
240 mm
(1115 px)
T511324
350 mm
(1605 px)
Figure 1. Experimental set-up. Frame from an experimental trial showing
the moment a stickleback attacks one of the virtual prey. Virtual prey (red
and yellow dots) have been overlaid on this image, which are not visible
in the camera footage (see electronic supplementary material, movie S3).
The yellow prey indicates which prey was attacked, although all prey were
projected as red dots in the trials. The white outline represents the projection
area where prey could appear. The black oblong in the top right-hand corner
of the arena shows the trial number and the time stamp of the simulation.
These time stamps were used to determine the locations of the prey in the
calibration videos, where prey were visible. The inset illustrates the measures
of spatial position calculated from the prey positions. The grey lines show the
Voronoi polygon for each prey. The large circle shows a radius around a prey
within which its number of near neighbours is counted, and the shaded area
of this circle shows that prey’s limited domain of danger. The solid line
around the group shows the convex hull. The double-headed arrow between
two prey shows the nearest neighbour distance, and the single-headed arrow
shows a distance to the group centroid (the red filled circle). The dashed
vertical lines and double-headed arrow show a distance to the front of
the group (the prey furthest to the left). The dotted lines and red arc
show an angle of vulnerability. (Online version in colour.)
royalsocietypublishing.org/journal/rspb Proc. R. Soc. B 288: 20211286
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of these 20 s) and followed by 10 s without any prey, resulting in
20 s between each prey presentation. Each focal fish was exposed
to the loop 15 times (approx. 10 min trials), although we only
used the first attack from each trial. A time stamp and playback
identification number were shown in the top right corner of the
simulations, but this was not visible to the fish as it was masked
off from the fish’s field of view by black tape (figure 1). To infer
which prey had beentargeted in the trials, before each trial, we pro-
jected the identical simulation the fish was to receive but with prey
projected as white dots, and with the strip lights turned off. These
‘calibration’videos allowed us to subsequently identify the
locations of prey, so we could infer which prey had been targeted
by matching the time stamps between the calibration video and the
prey videos at the time of attack (electronic supplementary
material, movie S3).
(e) Experimental procedure
Each subject participated in two trials: once in the stationary prey
condition and once in the moving prey condition. Fish were ran-
domly assigned to one of two testing groups. One of the testing
groups received the stationary prey condition first, and the other
group received the moving prey condition first. The two trials for
the same individual fish were separated by at least 24 h. Within
the moving prey condition, approximately half of the subjects
were randomly assigned to receive the group moving from
right to left ( from the subject’s perspective) across the front of
the tank, and the other half received prey moving left to right.
Trials were generally alternated between the stationary and
moving playbacks. Focal fish (n=126) were given 10 min to
acclimatize in the testing tank before any prey were projected.
(f) Analysis and statistics
Only the first attack of eachtrial was used in the analysis [9]. An attack
was defined when the stickleback orientated towards the screen and
pecked (often more than once) at the screen. Where two prey were
close to one another and we could not distinguish which of two
(and in one trial, three) prey was the target, one prey was selected
at random; this occurred in 8 of the 74 trials with an attack.
At the frame of the attack (i.e. whenthe fish made contact with
the screen with its mouth open), we identified the time stamp of
the simulation. We then manually tracked the position of all the
prey in calibration videos at this time stamp using a bespoke
script in MatLab [26]. This gave us the xand ycoordinates (in
pixels) of all the prey in the group, which were used to calculate
the measures of spatial position (figure 1, table 1). All were calcu-
lated using R v. 3.6.0 [28]; the R code for these calculations and the
statistical analysis are available in the electronic supplementary
material. The distribution of, and correlations between, these
measures are shown in electronic supplementary material, figure
S2 (for stationary groups) and electronic supplementary material,
figure S3 (for moving groups).
At the frame of each attack, we also classified whether one-third
of the body of the fish (as viewed by the camera) was inside or out-
side of the perimeter of the prey group, defined by the convex hull
(figure 1). This was used as a proxy for the direction that the pred-
ator approached the group, where being inside the perimeter
suggests an approach perpendicular to the group’s two-dimen-
sional plane. The classifications were made blinded to whether the
prey were moving or not. We compared whether the prey’smove-
ment (i.e. stationary or moving) affected the probability that the
fish’s body was inside or outside of the group’s perimeter using a
chi-square test of independence (i.e. whether the approach direction
changed depending whether the prey group was moving).
To determine how well each measure of the spatial position
predicted the risk of an individual prey being targeted, we used
binomial generalized linear models (GLMs) with the default
logit link function. The response variable was whether an individ-
ual was targeted (1) or not (0), and the explanatory variable was
one of the measures of spatial position. A model for each measure
of spatial position was constructed, separately for the stationary
and moving groups; the data from the two conditions were ana-
lysed separately to avoid pseudoreplication, given that we could
not keep track of fish identities across the two conditions. The like-
lihood of each model given the data was compared using the
Akaike information criterion corrected for small samples sizes
(AICc), as in [9]. A null model without an explanatory variable
was also included to test whether the predictive power of
models accounting for spatial position exceeded that of a null
model after accounting for the extra parameter in these models.
The limited domain of danger (LDOD) and the number of near
neighbours both require a maximum radius around the prey to be
defined. For the LDOD, this is the distance beyond which a
Table 1. Measures of spatial position used in our analysis. The distance from front measure was only applied to prey in moving groups.
measures of local crowding
Voronoi polygon area (i.e. domain of
danger) [6]
Area around an individual prey that is closest to that individual and not another individual. The Deldir function
in the deldir R package was used. The four corners of the projection area (figure 1) were used as the
boundaries.
limited domain of danger [27] As above, although the domains of danger are limited to a maximum distance from each individual prey.
nearest neighbour distance The distance between the focal prey and the closest other prey in the group.
number of near neighbours The number of other prey within a predefined distance. This distance was the radius of a circle centred around
each prey.
measures of prey position defined by reference to the group centre or periphery
distance to the group centroid Distance from the mean xand ycoordinate of all prey in the group.
on the convex hull? The convex hull is the polygon with minimum area that encloses all prey positions (thus also known as the
minimum convex polygon). Calculated using the chull function in R. Each prey was classified as being either
on this convex hull perimeter or not.
angle of vulnerability [21] Determined by calculating the angles from the prey as the vertex to all possible pairs of other prey (creating a
triad); the largest of these angles where no other prey were located within it was the angle of vulnerability.
distance from front The distance of each prey from the front of the group, where the leading individual is given a distance of zero.
royalsocietypublishing.org/journal/rspb Proc. R. Soc. B 288: 20211286
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predator will not attack the prey, even if that prey is the closest [27],
and for the number of near neighbours, the distance within which
near neighbours are counted [21]. We thus included in the AICc
comparisonsmodels for the LDOD and number of near neighbours
calculated using varying radius sizes, ranging from 10 to 500 pixels
in 10-pixel increments. This parameter scan avoided any apriorior
post hoc choice of the radius size and allowed us to examine whether
the radius size influenced the ability of the LDOD and the number
of near neighbours to predict predation risk.
3. Results
The test fish attacked the virtual prey in 35 trials with stationary
prey (out of 123 trials) and in 39 trials with moving prey (out
of 126 trials). When attacking stationary groups, a substantial
proportion of the fish’s body was within the group’s perimeter
in 16 trials and 12 trials when attacking moving prey. Although
there was a greater probability of approaching within the
group perimeter when attacking stationary prey (0.46 versus
0.31), this difference was not statistically significant
(chi-squared test of independence: x
2
= 1.17, d.f = 1, p= 0.28).
In stationary groups, the targeted prey was best predicted
by the LDOD over a wide range of radius sizes (approx. 50 to
500 pixels); there was only a small range of radius sizes
(approx. 50 to 100 pixels) where the number of near neigh-
bours model outperformed it (specifically when LDOD
radius sizes were smaller than 50 or greater than 300 pixels)
(figure 2a). Greater local crowding was associated with a
reduced predation risk (figure 3a). In contrast with the impor-
tance of the LDOD in predicting risk, the Voronoi area (i.e.
the domain of danger bounded by only the projection area)
was a relatively poor predictor of being targeted (figure 2a;
electronic supplementary material, table S1). Measures of
proximity to the group’s edge as predictors of risk were
less well supported but were generally greater than 2 AIC
units less than the null model [29], suggesting that a prey’s
angle of vulnerability, whether it is or is not on the convex
hull edge, and the distance from the prey to the centroid,
still have explanatory power in predicting predation risk
(figure 3a; electronic supplementary material, table S1).
For moving groups, the measures of spatial position that
best predicted which prey were targeted were not consistent
with the results from stationary groups. Although the number
of near neighbours was the best predictor of risk when the
radius size was optimized at 150 pixels, for much of the range
of radius sizes examined, the angle of vulnerability and the dis-
tance to the group centroid (both measures of proximity to the
group edge) had lower AICc values, and thus were better pre-
dictors of risk (figure 2b; electronic supplementary material,
table S1). Whether prey were on the convex hull edge was
less predictive of risk, but this had a lower AICc value than
the remaining measures of local crowding (the LDOD, nearest
neighbour distance and Voronoi size (domain of danger)).
Prey closer to the edge of the group were more likely to be
targeted (figure 3b). The measure of spatial position relative
to the front of the group (distance from the front), was a poor
predictor of risk as it performed worse than the null model.
4. Discussion
Our results demonstrate that even when comparing two
relatively similar prey group types, where one group had
directional movement and the other did not, the selection of a
target by predators was altered enough that the risk of being tar-
geted was best predicted by different measures of spatial
position. Measures of local crowding best-predicted risk in
stationary groups, with the LDOD [27] outperforming all
other measures. Although similar, the Voronoi area was a rela-
tively poor predictor of risk, which lends substantial support
to the more biologically realistic LDOD [27] in contrast with
the unlimited domain of danger as originally formulated by
Hamilton [6]. In moving groups, the best predictor of risk was
the number of near neighbours but only for a small range of
radius sizes within which neighbours are counted; more gener-
ally, measures of whether the prey were closer to the group edge
performed best, rather than measures of local crowding.
Althoughthese results areconsistent with the predators encoun-
tering individuals near the edge of the group more when the
prey are moving, we also found that prey’s proximity to the
front of the group was a poor predictor of risk, unlike a recent
study also using sticklebacks [9]. There was also no evidence
that whether groups were moving or not affected whether
they were more likely to be approached from outside the
group. The radius that minimized the AICc for the LDOD and
number of near neighbours was substantially larger when
groups were moving, possibly because moving objects have
0
0
5
10
15
20
25
30
35
0
5
10
15
dAICcdAICc
100 300 500
D to front
null
null
Voronoi
Voronoi
NND
NND
N near neighbours
N near neighbours
LDOD
LDOD
on convex hull
on convex hull
D to centroid
D to centroid
angle of vulnerability
angle of vulnerability
radius size (pixels)
(b)
(a)
Figure 2. Model comparison results for stationary (a) and moving (b) groups
based on the difference in the Akaike information criterion corrected for small
sample sizes (dAICc) between the most likely model given the data (0 on the
y-axis) and each other model. In the model names, D represents distance,
N represents number, LDOD represents limited domain of danger and NND
represents nearest neighbour distance. As the dAICc for the limited
domain of danger and number of near neighbours models are dependent
on the radius size used to calculate these variables, dAICc values are plotted
against radius size. For all other measures of spatial position, there is only
one model (and hence dAICc value). Line colours for the different models
correspond between the panels and figure 3. (Online version in colour.)
royalsocietypublishing.org/journal/rspb Proc. R. Soc. B 288: 20211286
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higher salience [30], which suggests that the radius size is
context specific.
Individual prey in groups vary in multiple aspects of how
they appear to predators, including their direction and speed,
and how variable such parameters are over time and between
individuals. Group-level variables are also diverse, such as the
group’s shape, the spatial arrangement of individuals and the
degree to which individuals change position within the group
[31–34], which can depend on species and ecological context
[35–37] and also vary over time within the same group and con-
text [24,38]. Given our results with groups which differed only
with respect to their directional movement, multidimensional
variation in individual and collective properties of prey may
make it difficult to generalize whichmeasure of spatial position
accurately predicts the risk of prey being targeted. Indeed, our
findings are likely to have been different had other aspects of
the prey group differed, such as the speed of movement. A
lack of generalization between groups with different properties
could help explain the surprising result in our study of no evi-
dence that prey at the front of a moving group were more at
risk, in contrast to other experiments with virtual [9] and real
[10] prey. Further differences in the aspects of spatial position
important in predicting risk may come from variation between
predators, for example, in the attack strategy of different
species [21,39], in hunger or experience between individuals
of the same species [40], or from consistent personality differ-
ences between individuals within the same population [41].
For prey in groups spread over two, rather than three, dimen-
sions, another likely source of variability is whether the
predator is attacking in the same, or perpendicular to, the
plane of the prey group, which remains a relatively neglected
question in predator–prey interactions [5].
Our findings, where the predictive success of spatial
measures differed for attacks on stationary groups and
groups with directional movement, suggest that there may be
no single best measure of spatial position for describing preda-
tion risk. Instead, the spatial measure that most predicts risk
might be dependent upon the prey’s collective behaviour.
This has implications for the selection pressure acting on
prey in terms of the movement rules they should follow
when locating themselves within the group [13,42]. For
example, our results suggest that when a group is relatively
still, such as when they are resting or foraging within a
patch, individuals should occupy areas which are more
crowded to minimize their LDOD, regardless of whether this
area falls near the edge of the group. However, occupying
the optimal spatial position within the group may be con-
strained by cognitive abilities in determining where to move
to, and the behaviourof other individuals in the group [42–44].
Ethics. All procedures were approved by the University of Bristol
Ethical Review Group (UIN UB/16/047).
Data accessibility. The data are provided in the electronic supplementary
material [45].
Authors’contributions. P.J.L.: investigation, methodology, project adminis-
tration, writing-original draft; J.E.H.-R.: conceptualization, data
curation, methodology, project administration, software, supervision,
writing-review and editing; C.C.I.: conceptualization, formal
analysis, funding acquisition, project administration, resources,
supervision, visualization, writing-review and editing.
All authors gave final approval for publication and agreed to be
held accountable for the work performed therein.
Competing interests. We declare we have no competing interests.
Funding. This work was supported by Natural Environment Research
Council Independent Research Fellowship NE/K009370/1 and
Leverhulme Trust Grant no. RPG-2017-041 V awarded to C.C.I.
J.E.H.-R. was supported by the Whitten Lectureship in Marine
Biology and a Swedish Research Council grant: 2018-04076.
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