Behavioral Ecology
doi:10.1093/beheco/ars153
Advance Access publication 11 October 2012
Original Article
Movement in a selfish seal herd: do seals follow
simple or complex movement rules?
Alta De Vos and M. Justin O’Riain
Zoology Department, Private Bag X3, Rondebosch 7701, Cape Town, South Africa
The selfish herd hypothesis predicts that animals can reduce their relative predation risk by moving toward their neighbors.
However, several computer simulation studies have found that smaller herds, rather than large, compact aggregations form
when animals move in this manner and that larger herds are only achieved by following more complex movement rules, thought
to be unrealistic for real biological systems. Despite much theoretical work, predictions on how animals move to reduce their
predation risk have seldom been tested in natural systems. Here we investigate the movement patterns of fur seals (Arctocephalus
pusillus pusillus) within 7 groups as they move through a zone of high risk to the relative safety of their foraging grounds. We
assess different movement rules against all the individuals in the study and identify whether such an individual’s movement at a
snapshot in time plausibly reflects a follow (1) of a rule or not (0). Our results suggest that seals traversing high predation risk
areas use simple movement rules, rather than complex averaging rules, to reduce their domains of danger. Simple movement
rules that serve to decrease an individual seals’ domain of danger resulted in the formation of compact groups as predicted by
the selfish herd hypothesis. Importantly, individuals dropped these simple movement rules where predation risk is low, which
coincided with a reduction in mean group compaction. Despite our small sample size, our results provide empirical support for
the central predictions of the selfish herd hypothesis. Key words: cape fur seal, groups, movement rules, predators, prey, selfish
herd. [Behav Ecol]
Introduction
P
rotection from predators is considered to be an important driving force in the evolution of sociality in many
species (Parrish and Hamner 1997; Lima 1998; Bednekoff
and Lima 2004). One popular explanation for how grouping
may have evolved in response to predation is the selfish herd
hypothesis (Hamilton 1971), an individual-based model that
explains how differential risk amongst previously ungrouped,
loosely associated prey individuals could drive the evolution
of groups.
In Hamilton’s simplest model, prey individuals are attacked
by a hidden predator. The predator attacks the nearest prey
individual from where it randomly appears within a group,
creating “domains of danger” for individual prey animals.
A domain of danger is the area around an individual encompassing all the locations at which an emerging predator will
be the “closest” to that prey individual. The larger this area,
the greater the individual’s predation risk relative to that of
its’ neighbors. By moving toward neighboring individuals an
individual can reduce this “domain of danger,” which, translates into a lower predation risk and ultimately greater fitness (Hamilton 1971). If all members of a group attempt to
reduce their domains of danger by moving toward their nearest neighbors, a more compact group should be the result.
Several studies document attempts by group members to
lower their domains of danger, which is a key prediction of
the selfish herd hypothesis (Parrish 1989; Ens et al. 1993;
Watt et al. 1997; Spieler and Linsenmair 1999; Viscido et al.
Address correspondence to A. De Vos. E-mail: alta.devos@gmail.
com.
Received 24 October 2011; revised 27 July 2012; accepted 27 July
2012.
© The Author 2012. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved.
For permissions, please e-mail: [email protected]
2002). However, computer simulation studies have failed to
find large, tight aggregations resulting from using the movement algorithms proposed by Hamilton’s hypothesis (Morton
et al. 1994; Viscido et al. 2002; Morrell and James 2008).
Indeed, Hamilton himself found that a rule of approaching
the nearest neighbor does not result in large, dense aggregations (Hamilton 1971), a limitation he proposed could be
remedied by groups seeing the collective benefit of moving
toward other groups.
In keeping with Hamilton’ individual-based model, many
subsequent studies have instead proposed that individuals
may use more complex assessment rules, such as averaging
the positions of many neighbors (Morton et al. 1994; James
et al. 2004; Reluga and Viscido 2005; Morrell et al. 2011a).
However these rules have often been criticized as being
too complicated for animals to follow in real-life situations
(Reluga and Viscido 2005; Morrell and James 2008). The
search for a movement rule that can satisfy both simulated
central compaction and subsequent biological verification
is what has been referred to as the “dilemma of the selfish
herd” (Viscido et al. 2002; Reluga and Viscido 2005).
Several theoretical computer simulation studies have
subsequently investigated animal movement within the context
of the selfish herd, under the broad theme of simple and
complex rules (Krause and Tegeder 1994; Morton et al. 1994;
Viscido et al. 2002; Morrell and James 2008; Morrell et al. 2011a,
2011b). Here, we define “simple rules” as rules in which animals
only use information from 1 or 2 nearest neighbors when
making movement decisions, whereas “complex rules” require
animals to use information from multiple other individuals.
Two simple rules have been investigated in simulation
studies. Firstly, moving toward a nearest neighbor in space
(Hamilton 1971; Viscido et al. 2002; Morrell and James 2008;
Morrell et al. 2011a) and secondly, moving toward a nearest
neighbor in time (Krause and Tegeder 1994). In the latter,
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De Vos and O’Riain • Movement rules in selfish seal herds
the time it takes for an individual to turn toward a nearest
neighbor is recorded in addition to the time it takes to close
the spatial distance between two individuals.
More complex averaging rules considered to date have
been relatively uncomplicated modifications of simple nearest
neighbor rules, where animals move into the space between
two nearest neighbors (Hamilton 1971), or even more complex rules where animals move toward multiple (2, 3, and 5
have been considered) nearest neighbors in space (Morton
et al. 1994; Viscido et al. 2002; Morrell and James 2008; Morrell
et al. 2011a). One more sophisticated addition was the proposal of the local crowded horizon rule (Viscido et al. 2002;
Morrell et al. 2011a, 2011b). This rule is based on an animal’s
perception of its group members, where an animal’s movement decision is dependent on many different neighbors, but
with importance weighted by distance from neighbor.
The scientific community has not achieved consensus on
an optimum movement rule, where optimum is defined by
a decrease in domain of dangers of group individuals given
the ability of all animals in a group to follow a specific rule
(Viscido et al. 2002). Morton et al. (1994) showed that moving toward a nearest neighbor (a simple rule) represented a
significant improvement to random movement. However, in a
subsequent simulation based on a similar system, individuals
that considered more neighbors when deciding where to move
to were better at forming larger, compact groups, suggesting
that a more complex rule would carry greater benefits. Viscido
et al. (2002) showed that the most complex averaging rules
produced the densest aggregations and therefore, the highest decrease in predation risk. In these studies, complex rules
appear to be more advantageous than simple or optimal target
rules in producing aggregations of animals. Other studies have,
however, shown that following simple rules (which are thought
to be within the capability of animals to follow) may result in
the formation of large groups (Krause and Tegeder 1994).
Many results suggest that multiple movement rules may be
drivers of aggregation and that specific rules may be more
beneficial under different environmental conditions. Wood
and Ackland (2007) found that flock dynamics, the size and
density of a group, and ecological variables all had a significant effect on which movement rules were most beneficial
in producing compact aggregations. Similarly, Morrell and
James (2008) and Morrell et al. (2011a) showed that complex
rules are most successful at reducing risk in small, compact
groups whereas simpler rules are most successful in larger,
low-density populations, and when predators attack quickly
after being detected by their prey.
A major limitation to the understanding of selfish movement rules has been that, with the exception of a single study
on small fish (Krause and Tegeder 1994), investigations on
real-time trajectories of animals have been limited to computer simulations.
In this paper, we aim to remedy this deficiency by investigating movement rules of cape fur seals as they cross an area of elevated great white shark predation risk to their foraging grounds.
Earlier work in this system has demonstrated that white sharks
target seals at random, leaving individuals with larger domains
of danger more at risk than those with smaller domains of danger (De Vos and O’Riain 2010) and that seals traversing across
a dangerous area change their position relative to neighboring
individuals (i.e., they jostle) (De Vos 2010).
Specifically, we investigate (1) how individual seals in a
group move relative to their neighbors when they are in a high
versus low predation risk area, (2) whether individual movements are best explained by simple or complex movement
rules, (3) whether the movement patterns of individual seals
result in a reduction of that individuals domain of danger, and
(4) if all members of the group use the same movement rule,
this results in the formation of small compact groups. We do
not explore all possible rules that animals could follow and
acknowledge that these results present only the consequences
of local rules. As different rules may sometimes result in an
animal moving in the same vector direction, and it is not possible to assess intent, it is not possible, unlike in modeling studies, to judge the rules as mutually exclusive from one another.
Rather we hope to shed some light on how selfish movement
rules in real animals when under predation risk.
METHODS
Study site
We collected behavioral data in the water around Seal Island
in False Bay, South Africa (Figure 1). Seal Island is a granitic
outcrop about 2 hectares in area, with a maximum elevation
of 6 m. The island is the second largest cape fur seal breeding colony in South Africa and is the largest colony (between
36 000 and 77 000 individuals) that is based on an island
(Kirkman et al. 2007).
The water around the island has limited refugia. There is
no kelp around the island, and it has sharp drop offs to the
northwest, west, and south of the Island. To the south of the
Island is an area dubbed the “launch” pad, a shallow outcrop
of rock where seals typically aggregate before leaving the
island and traversing the high predation risk zone en route to
their feeding grounds to the south (Figure 1).
We collected data during the high predation season (Kock
and Johnson 2006), which equates to the austral winter,
between the months of May and September. During these
months white sharks aggregate around the breeding rookeries of the cape fur seal (Arctocephalus pusillus pusillus) on the
south coast of South Africa, predating heavily upon these
marine mammals (Martin et al. 2005; Kock and Johnson
2006; Laroche et al. 2008).
Sharks predominantly attack surface swimming seals from
depth and as consequence breach the surface waters (Martin
et al. 2005; Laroche et al. 2008). Prior to launching these attacks,
sharks swim in the mid-water column (Laroche et al. 2008), concentrating their searching activity to the south and west of the
rookery (Martin et al. 2005; Laroche et al. 2008) where most
attacks have been recorded to date (Martin et al. 2005; Laroche
et al. 2008). Adult female seals typically feed far from the island,
but being central place foragers, have to return to the rookery at regular intervals to feed their young of the year (David
et al. 1986; Gamel et al. 2005). The young themselves venture
out to sea at the start of the austral winter to supplement their
milk-based diet (David et al. 1986; Gamel et al. 2005).
Seals are frequently attacked within 1.5 km of the island,
but only rarely beyond this (Laroche et al. 2008). There is
also a safe zone immediately next to the island (without
food resources, but potentially important for behavioral
thermoregulation). We collected data both within the
“danger zone” stretching to a 1.5 km radius from the island
and the “safer” water beyond this ring (Figure 1).
Aerial data collection
To answer questions on the spatial geometry of the seal
groups leaving Seal Island, we followed 7 independent groups
of seals (71 individuals, in groups of three [3], five [5], nine
[9], ten [10], eleven [11], sixteen [16], and seventeen [17])
using a Robinson R44 helicopter.
Seal groups were filmed with a handheld high-definition
digital video camera (Sony PD150 digitial DVcam) from the
moment they left the safe shallow water at the south end of
the island for a distance of approximately 2 km from the
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Behavioral Ecology
Figure 1 Google Earth images showing the study site, Seal Island, False Bay. The seals move from the “launch pad” within a “safety zone” (top right
insert) around a breeding rookery (indicated with a triangle on all 3 images) to the foraging grounds in a southwesterly direction (solid
arrow). The solid ring around the island denotes the zone in which cape fur seals are primarily at risk to great white sharks. The points
marked with a helicopter denote the points inside the “danger zone” (IDZ) and outside the “danger zone” (ODZ) where snapshots of seal
movement were assessed.
island. The duration and route traversed by the group was
recorded with a handheld GPS (Garmin e-trex).
Seals appeared to be unaware of the helicopter unless the
shadow of the aircraft passed directly over them. Southwell
(2005) found that a helicopter flying directly over and lower
than 130 m altitude had no effect on the behavior of 3 species of seals (crabeater, leopard, and Ross) and 2 species of
penguins (Adélie and emperor).
A similar result was obtained for this study. Shadows elicited classical antipredator behavior (a rapid change in movement patterns of affected seals) and these events were thus
excluded from the subsequent analyses on group geometry
and behavior. When possible, we simply requested that the
pilot avoid casting a shadow on the group to exclude any
observer effects on the seal group(s) under observation.
Aerial follows were subsequently analyzed using video software (Moviemaker) to freeze-frame groups and estimate
distances between seals. Adult female seals are on average
136 ± 14.1 cm in length and were thus used as the metric upon
which other measurements within the group (e.g., distances
between individuals) could be estimated. Although there
might be some error contingent upon using this measure,
we used a paired statistical evaluation of group geometries
and thus the comparisons were between the same individuals
within and outside of the danger zone. We calculated domains
of danger, described in more detail below, and compared average domains of danger inside versus outside the danger zone,
and before and after an animals’ assessed movement. Analyses
inside the danger zone were performed after groups had split.
Constructing Voronoi tessellations
In the simplest case of a Voronoi diagram (also known as a
Dirichlet tessellation), we are given a set of points s in the
plane. Each site s has a Voronoi cell, consisting of all points
closer to s than to any other sites (Okabe 2000). Tessellations
were constructed by plotting seal positions as a single point
on a 2D grid and using the Voronoi scatter plot function in
Stat soft to draw appropriate Voronoi diagrams. We used the
midpoint along a seal’s dorsal body length as the coordinate
around which we constructed the tessellations.
The area around each individual, also called the domain of
danger, was calculated by superimposing 0.25 × 0.25 m2 cube
grids onto the diagrams and summing the grids. Seal groups
are not edgeless, but bounded by either a limited predator
attack or predator detection range (James et al. 2004). We
present results calculated by binding Voronoi tessellations
with 1 predator body length, taken as 3 m beyond edge
individuals (the average estimated length of white sharks at
Seal Island; Kock and Johnson 2006). Sharks attack seals by
stalking them at depth and then intercepting them either
vertically or at 45° at the surface (Martin and Hammerschlag
2012). We thus assume that by the time a shark hits the
surface it would have appeared within 1 body length of any
individual it is likely to attack. Additionally, we chose 1 body
length as the binding metric to be consistent with De Vos
and O’Riain (2010), a study that demonstrated a significant
relationship between seals’ domains of danger and their
relative predation risk at Seal Island.
Aerial follows were subsequently analyzed using video
software (Moviemaker) to freeze-frame groups and estimate
distances between seals. Adult female seals are on average
136 ± 14.1 cm in length and were thus used as the metric upon
which other measurements within the group (e.g., distances
between individuals) could be estimated. We calculated
domains of danger, described in more detail below, and compared average domains of danger inside versus outside the
danger zone, and before and after movement rules.
193
De Vos and O’Riain • Movement rules in selfish seal herds
Movement rules analysis
To assess which theoretical movement rules (Table 1,
Figure 2) best predicted seal movement, we used the freezeframed function in the software package Moviemaker, to
allow for the sizing of individuals and to calculate domains of
danger as described above.
Groups were freeze-framed circa 500 m from the island.
The exact point at which we took a snapshot was the first point
at which all individuals in a group could be distinguished and
measured. At this point we also identified n nearest neighbors
for each individual. Distances between neighbors (d) were
computed by measuring the shortest distance between the
dorsal body midpoints of seals.
We took a second snapshot 5 s after this first frame,
remeasured individuals, and plotted new positions for
them. We chose to use 5 s as this was judged, from earlier
observation, to be sufficient time for 1 seal porpoise in any
direction. We then assessed these subsequent positions
against original seal positions to establish whether theoretical movement rules were followed (1) or not (0). How
we did this matching is described in more detail under the
subheading below.
We repeated this procedure outside the danger zone: We
freeze-framed groups at circa 2000 m from the island, at the
first point at this distance in which all individuals within a
group could be identified and measured, and took a subsequent snapshot 5 s later. Outside of the danger zone, groups
no longer comprised all the members they had before, so our
sample size for this analysis was smaller (n = 55).
constitute a follow (score 1). The focal target (or point) was
determined by the predictions of the movement rules under
investigation (Figure 2, Table 1).
We then constructed a vector through this focal target
(Figure 2) and calculated the initial distance (d1) between the
focal individual and the focal target. We measured the angle
of that line with the focal individual (α1) and also calculated
its domain of danger.
After calculating domains of danger, we played the clip for
5 s and obtained a second position for the focal individual.
Next, we drew a line along the dorsal axis of the second position of the focal individual. We measured the subsequent
distance between this position and the nearest point (d2) on
the focal point vector constructed initially and measured the
angle with this line (α2). We again constructed and measured
its domain of danger.
For all the rules bar the forward trajectory rule we took that
if d2 < d1 and α2 ≤ α1, the rule would be assigned a value of
1. If d2 ≥ d1 and α2 > α1, the rule would be assigned a value
of 0. In other words, a very small angular difference between
real and theoretical trajectories would mean that the animal
is following the rule, and the rule would be assigned a value
of 1. For the forward trajectory rule, we scored 1 against a
focal individual if the individual ventured less than 15° off its
projected vector in any forward direction.
Every rule that was followed was given a score of one (1),
whilst every rule that was not followed was given a score of
zero (0). Where an individual followed more than 1 rule,
both, or all rules we allocated a score of one (1).
Rule matching
Group size and density
To match a focal individual to a theoretical movement rule,
we drew a line along a focal seal’s dorsal length. Next, we
identified and ranked its nearest neighbors.
For every movement rule, we calculated a focal point
toward which a seal would have to move in order for it to
To calculate group size we counted the number of seals
observed within the group at the start of the movement rule
analysis (see above). Group density was measured as the
mean of all the individual domains of danger within a group.
We used group density as at the first instance from which
Table 1 Movement rules considered for individuals in this study
Rule
Proposed by
Prediction
Simple rules
Nearest neighbor
Time minimization
Hamilton (1971)
Krause and Tegeder (1994)
An individual moves toward the nearest individual in space
An individual moves toward the nearest individual in time (takes account
of the time taken in turning toward a neighbor)
An individual moves into the space between their 2 nearest neighbors
An individual moves into the space between their 2 nearest neighbors in
time
Hamiltonian
Hamiltonian in time
Complex rules
n closest neighbors
Hamilton (1971)
Modification of Hamilton
(1971)
Morton et al. (1994)
n closest neighbors
in time
Local crowded
horizon
Modification of Morton
et al. (1994)
Viscido et al. (2002)
Group center
Nonselfish herd rules
Forward trajectory
This study
An individual moves toward the average location of several (n) nearest
neighbors. We investigate 3 nearest neighbors
An individual moves toward the average location of 3 nearest neighbors in
time
An individual moves toward the area with the densest concentration of
conspecifics. The influence of neighbors on the focal animal varies with
the distance of the neighbors relative to the focal individual. We use the
perception function suggested by Viscido et al. (2002) and Morell and
James (2008), as being the most biological likely: f(x) = 1/(1+kx), where x is
the distance from the focal individual and k = 0.375. Thus, individuals close
to the focal individual have a strong influence on movement direction,
whereas distant group members exert a much weaker influence. We only
considered individuals to the front of focal individuals in this analysis
An individual moves toward the center axis of the group
Modification of random movement
rule, e.g., Viscido et al. (2002)
An individual moves in a forward trajectory and does not approach any
neighboring individual
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Behavioral Ecology
Focal individual:
Initial Postion
Focal individual:
Subsequent Position
Assessed neighbor
Nearest Neighbor (NN):
Individual moves toward the nearest individual
in space.
N Nearest Neihbor (3NN):
Individual moves toward the average location of
several (n) nearest neighbors. We assesses three
nearest neighbors (Morton et al. 1994)
Foacal target and vector
Hamiltonia (HT):
Individual moves into the space between their two
nearest neighbors (Hamilton, 1971)
Group Centre (GC):
Individual moves toward the centre axis
of the group.
Forward Trajectory (FT):
Individual moves in a forward trajectory and does
not approach any neighbouring individual.
Figure 2 A graphical explanation of the spatial movement rules explored in this study (the time minimization and crowded horizon rules are explained
in text in Table 1 and have not been included here).
movement rules were assessed in all 7 groups (and thus the
density which informed the movement rule results).
All statistical tests are 2-tailed. Parametric means are given
with standard errors of the mean and rank-based values of
locations with standard errors of the median (Wilcox 2005).
Statistical analyses
We performed exploratory descriptive statistics prior to running all statistical tests to test relevant assumptions of normality of distributions, homogeneity of variances, independence,
linearity, and colinearity of variables.
If data were normal or could be transformed to normality,
parametric statistics were used following Quinn and Keough
(2002). In all other cases we used the robust rank-based nonparametric equivalents following Wilcox (2005). To analyze
2 sample data sets (all datasets were paired) we employed
paired t-tests and nonparametric Wilcoxon paired tests. In
instances where a single categorical variable predicted a continuous response variable we employed single factor ANOVA’s
or a nonparametric Kruskal–Wallis to test the null hypothesis of no differences between the means and medians, and
post hoc Tukey and rank-based Tukey tests to infer significant differences between groups. To test differences between
observed proportions we employed the Cochran’s Q test for
assessing matched proportions.
To analyze the relationship effect of group size on density,
we employed a generalized linear model (GLM), after satisfying the assumptions of a normally distributed response variable. To assess the interaction between complex, simple, and
forward trajectory rules and group density, we employed a
generalized linear mixed model (GLMM). As the response
term for this analysis (following of movement rule = 1, not following the movement rule = 0) was binary, we specified a logit
link function to correct for unknown error terms. Estimators
were fitted using Grauss–Hermit approximations and stepwise regression was not required as there was no colinearity
between variables (group size was not included in the model).
We used the Wald-F statistic to draw statistical inferences.
RESULTS
Can the selfish herd movement rules explain seal behavior
within groups?
There was significant variation in the probability that a movement rule was followed (Cochran Q test, Q = 69.464, df = 8,
P < 0.000001) that could be explained by different movement
rules. The “nearest neighbor in time” and the “Hamiltonian
in time” rules described 54.29% (Cochran Q = 7.692,
P < 0.01) and 62.83% (Cochran Q = 11.267, P < 0.001) of all
movement vectors. Other movement rules fared little better
than front trajectory movement (23.28%) and “group center” (25.71%) rules, ranging from 9% to 38.46% in describing seal movement. Outside the danger zone, the “forward
trajectory rule” could explain 82.14% of all seal movement,
significantly more (Cochran Q = 143.946, P < 0.00001) than
any other movement rule (<14.44%) (Figure 3).
Inside the danger zone, all selfish herd rules followed were
associated with a significant decrease in individual domain of
danger (all paired tests are Wilcoxon matched-paired t-tests).
Individuals whose behavior could be described by the nearest neighbor rule decreased their domains of danger from
3.362 ± 1.236 to 2.122 ± 1.236 m2 (z = 2.241, n = 21, P < 0.05),
nearest neighbor in time from 2.672 ± 1.211 to 1.654 ± 0.922 m2
(z = 3.603, n = 38, P < 0.001), Hamiltonian from 2.167 ± 1.396
to 0.751 ± 0.795 m2 (z = 3.636, n = 18, P < 0.001), Hamiltonian
in time from 1.44 ± 0.633 to 0.887 ± 0.426 m2 (z = 3.034,
n = 24, P < 0.01), 3 nearest neighbors from 1.910 ± 1.488
to 0.460 ± 0.427 m2 (z = 2.366, n = 7, P < 0.01), and 3 nearest neighbors in time from 1.488 ± 0.765 to 0.476 ± 0.262 m2
(z = 3.206, n = 16, P < 0.01). Individuals whose behavior could
195
Inside danger zone
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Outside danger zone
FT
GC
NN
NNT
H
HT
3NN 3NNT LCH
Movement rule
Mean domain of danger (m2)
Figure 3 The proportion of seals whose movement could be described by
different movement rules, inside (white bars) and outside (grey
bars) the danger zone. We consider the front trajectory rule (FT)
and the group center (GC) rules as rules against which selfish herd
rules can be judged. We consider the nearest neighbor in space
(NN) and time (NNT), the Hamiltonian in space (H) and time
(HT), three nearest neighbors in space (3NN) and time (3NNT),
and the local crowded horizon rule (LCH).
8
7
6
5
4
3
2
1
0
Before movement
After movement
FT
GC
NN
NNT
H
Movement rule
HT
3NN
3NNT
Figure 4 The mean domain of danger of seals before and after following
a specific movement rule. Movement rules assessed are the front
trajectory rule (FT), the group centre rule (GC), the nearest neighbor
in space (NN), nearest neighbor in time (NNT), Hamiltonian in
space (H) and time (HT), three neighbors in space (3NN) and time
(3NNT) rules, and the local crowded horizon (LCH) rule. Error bars
represent standard error at the 95% confidence interval.
be described by a forward trajectory movement rule had significantly larger (Wilcoxon matched-pairs test, z = 2.45, n = 18,
P < 0.05) domains of danger (1.694 ± 1.799 vs. 3.334 ± 4.078
m2) after following this rule (Figure 4).
There was significant variation in the change in the
size of the domain of danger (Kruskal–Wallis, H = 29.017,
P = 0.0012) associated with the different movement rules.
Most movement rules, with the exception of the “group center” rules, reduced average domains of danger significantly
more successfully (multiple comparison of mean ranks, all
P < 0.028) than front trajectory movement rules (Figure 5).
Mean change in domain of danger (m2)
Proportion of seals
De Vos and O’Riain • Movement rules in selfish seal herds
3
2
1
0
-1
Complex rules
Simple rules
GC
NN
NNT
H
HT
3NN
3NNT
LCH
FT
-2
-3
Figure 5 The mean change in the size of the domain of danger associated
with different movement rules. Error bars represent standard
error at the 95% confidence level. The forward trajectory (FT),
Group center (GC), nearest neighbor (NN), nearest neighbor time
(NNT), Hamiltonian (H), Hamiltonian in time (HT), three nearest
neighbors (3NN), three nearest neighbors in time (3NNT), and
local crowded horizon (LCH) rules are shown.
from the “front trajectory” rule (also 23.38%). Simple rules in
time could, in turn, explain significantly more seal movement
(Cochran Q = 24, n = 77, P < 0.00001) than complex rules in
time (77.92% vs. 46.7.5%).
Although there was significant variation in the mean change
in individual domain of danger (Kruskal–Wallis H = 25.412,
P = 0.0001) associated with different movement rules, there
were no significant differences (multiple comparison of mean
ranks, P > 0.1) between rules of different complexities, or
rules that considered nearest neighbors in time and those
that considered nearest neighbors in space. The forward trajectory rule was, however, less successful at reducing domains
of danger than all selfish herd rules (multiple comparison of
mean ranks, P < 0.01), but there was no significant difference
between this rule and the group center rule (Figure 6).
The effect of group size and density
Group densities were significantly lower (F1,7 = 0.306,
P = 0.024) at smaller group sizes (Table 2). There was a significant effect of group density (Wald F = 6.040, P < 0.05)
and movement rule (Wald F = 27.206, P < 0.00001) on the
probability that a seal movement rule was followed. There
was also a significant interaction between group density and
movement rule (Wald F = 6.8.61, P < 0.05). We found that
while there was a significant interaction for group density and
complex rules (Wald F = 6.8.06, P < 0.01; complex rules could
describe more group movement at higher densities), there
Do simple or complex rules in space or time best
explain seal movement?
Rules where animals consider their nearest neighbors in
time could explain a significantly larger proportion of seal
behavior (Cochran Q = 26.133, P < 0.000001 for simple rules;
Q = 16.2, P < 0.0001 for complex rules) than those where animals considered their nearest neighbors in space (77.93%
vs. 41.56% for simple rules and 46.7.5% vs. 23.37% for complex rules). Movement rules where animals did not consider
specific neighbors but just aimed for the group midline only
explained 23.38% of seal movement, which was no different
Figure 6 The proportion of seals whose behavior could be explained
by complex and simple selfish herd rules in space (simple and
complex) and time (time complex and time simple), compared with
simple dilution rules (Group) and forward trajectory rules (FT).
196
Behavioral Ecology
Table 2 GLM of the effect of group size on group density (as measured by
mean domain of danger in m2) (n = 7, r2 = 67.33%)
Model term
Effect
df
F
SE
P
Intercept
Group size
180.024
66.158
1.000
1.000
28.042
10.306
6.420
6.420
0.003
0.024
Table shows parameter estimates (effect), standard errors (SE),
associated test statistic (F), and significance (P-value).
was no significant effect of the interaction between group
density and simple rules or between group density and forward trajectory rules on the model (Table 3).
Discussion
We provide support for the predictions of the selfish herd
hypothesis by showing that selfish herd rules can explain
individual seal movement better than forward trajectory
rules (i.e., individuals do not approach neighboring individuals), and that these movement rules are, on average, associated with reduced domains of danger for individuals inside
a zone of high predation risk. Moreover, selfish herd rules
explained only 14% of seal movement vectors outside this
“danger zone,” an area associated with low predation risk and
low group compaction (De Vos 2010). Additionally, the rule
that seals should move toward the center of the group did
not describe individual movement any more than the forward
trajectory rule did (Figure 4). Together these results suggest
that individuals have evolved movement rules that conform to
the predictions of the selfish herd hypothesis.
Importantly, these results follow on from the empirical validation of the critical prediction of the selfish herd hypothesis,
namely, that an individual’s domain of danger is proportional
to its relative predation risk (De Vos and O’Riain 2010). It
also informs earlier behavioral results at this island that
showed that seals jostled in groups (changing position relative to other seals) within the danger zone during winter
when predation levels are high, but not during the comparatively safe summer, and furthermore did not jostle outside the
danger zone during either season (De Vos 2010).
Analysis of movement patterns within groups suggests that
seals at Seal Island are using simple movement rules to reduce
predation risk. Seal movement is best explained by moving
toward their nearest neighbors, or into the spaces between 2
neighboring individuals. We found that rules where individuals considered nearest neighbors in time (individuals in front
of them), rather than in space, offered a better explanation
Table 3 The effect of group density and simple, complex, or forward
trajectory rules on predicting seal movement
Model term
Estimate
df
Wald
SE
P
Movement rules
Density
Rule × density
Simple × density
Complex × density
FT × density
Intercept
0.902
−0.121
1.000
1.000
2.000
1.000
1.000
1.000
1.000
27.206
6.040
6.861
2.590
6.806
2.590
5.119
0.326
0.049
0.068
0.069
0.073
0.068
0.226
0.000001
0.013985
0.032368
0.248226
0.009087
0.107539
0.023668
0.078
−0.1891
0.111
0.512
The table shows a GLMM analysis with a binomial error structure
and a logit link function. Table shows parameter estimates (estimate),
standard errors (SE), Wald statistic, and significance (P-value).
for observed seal movement within the danger zone, a finding that should be kept in mind in future studies modeling
individual-based animal movement.
Although we found no differences in the success (decrease
in domains of danger) of different selfish herd rules (see
Morrell and James 2008; Wood and Ackland 2007) ecological factors may well provide an explanation for the result that
simple rules described seal behavior in groups better than
complex rules (Figure 6). For example, limited visibility below
water and the porpoising of seals may limit the spatial information that each seal could gather on other group members.
Thus, seals may not have adequate information to make complex decisions (based on where its 3 neighbors, or the most
crowded area of a horizon is). If seals do not have a “crowded
horizon” (Viscido et al. 2002; Reluga and Viscido 2005; Morrell
et al. 2011a, 2011b) on account of limited visibility of other
group members (Martin and Hammerschlag (2012) estimates
a 4.8 m downwards recognition distance under sunlit conditions), this system may not be appropriate for assessing the
local crowded horizon rule, or at least requires that a much
adjusted perception function be used. The suggestion that the
level of information that individuals have on group members
may influence the use of simple or complex movement rules is
supported by the results on group size and density (Table 3).
Whereas simple rules provided a more robust description
of seal movement than complex rules at all group sizes and
densities, complex rules matched seal behavior better at high
densities compared with low densities. At higher group densities, individuals may have better information on group members because they are in closer proximity to each other, thus
allowing the use of more complex rules.
Although only a snapshot of how real animals move relative
to their nearest neighbors, this study is informative in that
it mimics the hypothetical conditions under which the selfish herd hypothesis was developed in a real biological system
(Hamilton 1971). Under these conditions, where the domain
of danger is validated as a construct of risk (De Vos and
O’Riain 2010), and where there are no confounding foraging
or social- and age-class effects (the latter is likely, although
not validated in this system), individuals move toward their
nearest neighbors or the spaces between 2 nearest neighbors
to reduce their relative domains of danger, in accordance
with the central prediction of the hypothesis.
The “dilemma of the selfish herd” is that simple rules (as
predicted by the selfish herd hypothesis) do not seem to
result in large, compact groups observed in nature. However,
our results show that prey individuals do follow simple rules
that reduce their domains of danger in compact groups, an
important contextualization is that the mean group size at
Seal Island is only about 10 (De Vos 2010). In fact, both larger
groups in this study fissioned into 2 smaller compact groups
whilst still within the danger zone (personal observation). As
in theoretical studies, it seems large groups, a phenomenon
that the selfish herd is often invoked to explain, did not result
from simple movement rules.
Thus, it is not clear that the results from this study can be
extrapolated toward more complex systems where social and
foraging factors do play a role, or where individuals have better information on other group members and have access to
information on “crowded horizons.” However, it does provide
a rare empirical insight into how animals move relative to
each other in selfish herds.
Funding
Funding for this research was provided by the National
Research Foundation and the University of Cape Town.‍
De Vos and O’Riain • Movement rules in selfish seal herds
The authors wish to thank Philip Richardson and Andy Casagrandry
for the filming of seals in this study. We also wish to thank Louis
van Wyk for piloting the initial aircraft and the Department of
Environmental Affairs & Tourism for a permit to carry out this
research (V1/8/5/1). We would like to thank 2 anonymous reviewers
for vastly improving the quality of this manuscript.
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