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Behavioral Ecology
doi:10.1093/beheco/arj060
Advance Access publication 24 March 2006
Toward an individual-level understanding of
vigilance: the role of social information
Andrew L. Jackson and Graeme D. Ruxton
Department of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences,
University of Glasgow, Glasgow G12 8QQ, UK
A gregarious lifestyle affords the benefit of collective detection of predators through the many-eyes effect. Studies of vigilance are
generally concerned with exploring the relationship between vigilance rates and group size. However, a mechanistic understanding of the rules individual animals use to achieve this group-level behavior is lacking. Building on a previous modeling approach,
we suggest that individuals reconcile their own private information against the social information they receive from their group
mates in order to decide whether to feed or be vigilant at any one time. We present a novel modeling approach utilizing a Markov
chain Monte Carlo process to describe the transition between vigilant and nonvigilant states. Many of our assumptions are based
qualitatively on recently published experimental observations. We vary the amount of social information and the fidelity with
which individuals process this information and show that this has a profound effect on the individual vigilance rate, the individual vigilant bout length, and the proportion of vigilant individuals at any one time. A wide range of group-level vigilance
patterns can be obtained by varying simple behavioral characteristics of individual animals. We find that generally, increasing the
amount of, and sensitivity to, social information generates a more cooperative vigilance behavior. This model potentially provides
a theoretical and conceptual framework for examining specific real-life systems. We propose analyzing individual-based data
from real animals by considering their group to be a connected network of individuals, with information transfer between them.
Key words: collective behavior, computational model, group living, information transfer, network. [Behav Ecol 17:532–538 (2006)]
he link between group living and antipredator benefits is
a long-standing and fundamental area of ecological research (Pulliam 1973; Krause and Ruxton 2002). These benefits are focused around three main factors: 1) dilution of risk
(Dehn 1990), 2) confusion effect (Milinksi 1990), and 3) collective detection (or many-eyes effect, Treherne and Foster
1980; Lima and Zollner 1996). It is the latter concept of collective detection that we are concerned with in this paper; specifically, how the amount of time spent vigilant for predators (an
activity often referred to as ‘‘scanning’’) is traded off against the
amount of time spent performing other essential tasks such
as feeding. Generally, research in this field has focused on
finding evidence for the prediction that individual vigilance
should decline with increasing group size (Cresswell 1994;
Lima and Zollner 1996; Roberts 1996; Bednekoff and Lima
1998; Beauchamp 2001)—for the most part with some success.
Given that individuals in groups likely respond to changes
in their internal state and to external stimuli, individual-based
studies are required to explore the mechanisms underlying
collective, group-level behaviors. Carefully designed experimental approaches such as that presented by Fernández-Juricic
and Kacelnik (2004) are yielding instructive empirical findings. Similarly, ground-up or forward-engineering approaches
have already demonstrated their ability to elucidate the fundamental and minimum set of rules/interactions required to
generate collective behavior in ant-trail organization (Couzin
and Franks 2003) and fish shoaling (Aoki 1982; Couzin et al.
2002). Vigilance has not been entirely neglected in this regard: Bahr and Bekoff (1999) provided a foundation model
built around a cellular automaton where each individual
T
Address correspondence to A.L. Jackson who is now at Medical
Research Council Social and Public Health Sciences Unit, 4 Lilybank
Gardens, Glasgow G12 8RZ, UK. E-mail: [email protected].
Received 4 May 2005; revised 13 February 2006; accepted 20
February 2006.
The Author 2006. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved.
For permissions, please e-mail: [email protected]
tended to do the opposite of that of its immediate neighbors.
Their model makes simplifying assumptions about how individuals interact with one another and shows how a group-level
(collective) vigilance behavior can be achieved through sets
of local interactions governing the behavior of individuals.
The key assumption underlying their model centered around
individuals’ abilities to determine what state their immediate neighbors were in (feeding or vigilant); moreover, it required that they be able to count (to a greater or lesser extent)
how many of their neighbors were in each state. Although
Beauchamp (2002) and Lima and Zollner (1996) failed to find
evidence for such monitoring of one’s neighbors in finches
and dark-eyed juncos, respectively, recent work by FernándezJuricic and Kacelnik (2004) on starlings provides much
promise. Their work suggests that not only do flocking starlings pay attention to their neighbors’ behavioral states but
also that ‘‘. . .this response intensified with the number of
conspecifics displaying a certain behaviour’’ and that responsiveness diminished with increasing distance between
individuals—compelling evidence that group-level vigilance
is affected, if not driven, by sets of overlapping local interactions between individual members (much like the fish-shoaling
models of Aoki 1982; Couzin et al. 2002). Furthermore, several
studies of primates have shown that proximity to neighbors
affects individuals’ behavior (reviewed in Treves 2000), although it is less clear from these studies whether individuals
are actually paying attention to the behavioral states of their
neighbors or simply their presence.
Our model builds on the fundamental concepts introduced
by Bahr and Bekoff (1999), specifically that individuals tend
to adopt the behavior opposite to that of the majority of their
neighbors and that the overall behavior of the group is built
from simple interactions between neighboring individuals. We
make some fundamental developments to their more strategic
model in order to introduce a higher level of biological realism by incorporating the key findings of Fernández-Juricic and
Kacelnik (2004). Individuals in our model are not restricted to
Jackson and Ruxton • Social information and vigilance
nodes on a grid lattice, rather they are located randomly in
space. We explore the effect of increasing the distance over
which individuals draw influence from their group mates in
contrast to just inspecting their immediate neighbors. When
deciding whether or not to feed or be vigilant, individuals
reconcile their own tendency (private information) to be vigilant for a nominal period of the time against the tendency to
do the opposite of the majority of their neighbors (social information). We introduce a sensitivity function that alters the
ability of individuals to process the social information they
receive from their neighbors. We show that increasing the
amount of and accuracy with which individuals can utilize
social information leads to a greater degree of cooperation
between individuals. We describe how the mean individual
vigilant bout length, mean individual proportion of time
spent vigilant, and proportion of vigilant individuals per unit
time are affected by the rate at which feeding individuals inspect their neighbors, how many neighbors they draw inference from, and with what degree of accuracy they can process
this information.
MODEL DESCRIPTION
N ¼ 500 individuals are allocated a random position within
a square area of 5000 units2 (side length therefore is 70.71
units). Each individual in the group is stationary and cannot
move about the group. At any one time, each individual occupies one of two mutually exclusive states, namely, vigilant
(equates to scanning) or feeding. Individuals are independently assigned to one or other of these states randomly, each
with 50% probability at the start of each simulation. The
group is modeled in a toroidal manner with periodic boundary conditions such that opposite sides of the group are
wrapped and the distances between individuals adjusted accordingly. This arrangement essentially allows us to consider
our results as being a representative section of a larger group
with no edge-related effects.
During the course of the simulation, individuals switch between feeding and being vigilant. The process of switching
between these states is modeled as a Markov chain Monte
Carlo (MCMC) process. Only one individual is allowed to
switch state at any one time, and time between switching
events is calculated using the standard theory of stochastic
processes (Grimmett and Welsh 1986). The rate of switching
is determined analytically from an individual’s current state
(private information) and also the current state of its neighbors (social information). In the most simple case, individuals
will feed if the majority of individuals in the group are vigilant
and will be vigilant if the majority of individuals in the group
are feeding. However, two factors limit an individual’s ability
to determine which state to adopt: 1) the influence of neighbors declines with distance (Fernández-Juricic and Kacelnik
2004) and 2) individuals are limited in their ability to reconcile the social information they receive from neighbors when
deciding whether to be vigilant or feed.
1. Influence declines with distance between individuals
As suggested by the field observations of Fernández-Juricic
and Kacelnik (2004), closer neighbors exert more influence
on a focal individual and more distant neighbors exert little, if
no influence at all. A simple declining linear function is used
to calculate the ‘‘influence matrix’’ that describes how the
distance between individuals (d) affects how information
about other group members is weighted (there are of course
alternative functions such as S shaped; however, given the
generality of this paper and the lack of data on a real system,
it is reasonable to adopt a linear function). Maximum influ-
533
Figure 1
The mean number of groups (filled triangle), the mean number of
vigilant neighbors (open circle), and the mean group size (filled
circle) as a function of the maximum detection distance for a
‘‘supergroup’’ containing 500 individuals. Results are averaged
across 500 randomly drawn group arrangements using the settings
described in the methods. Error bars have been omitted for clarity,
and the lines connecting the data points are linear interpolations
between data points and are illustrative only.
ence (I ¼ 1) is felt at a distance of zero units between individuals, and this influence declines linearly toward no influence
(I ¼ 0) at distance dmax. Varying dmax alters the distance over
which individuals are influenced by their neighbors and also
how many of its neighbors are of influence. Influence values
are adjusted according to the periodic boundary conditions.
It would also be possible to incorporate habitat obstruction
when wiring the network. Habitat obstruction may affect the
shape of the influence function or simply reduce certain connections to zero if visual contact is completely obscured.
When each individual considers changing state, its desire to
be vigilant (DV) and also its desire to feed (DF) are calculated:
X
IF ;
ð1aÞ
DV ¼
DF ¼
X
IV ;
ð1bÞ
where IV and IF are the subsets of influence values for a focal
individual’s vigilant and feeding neighbors, respectively. The
group can therefore be viewed as a fully connected network
with information transfer between individuals. The connections between the nodes (individuals) are weighted such that
they are stronger for closer nodes and zero for distant nodes
that are greater than dmax units apart.
The network structure describing the flow of information
between individuals is greatly affected by the maximum detection distance (dmax) such that what may appear to be a large
single group of individuals may in fact be itself a collection of
smaller isolated units. Some care must therefore be employed
when interpreting both this model and indeed real systems.
Figure 1 describes how group size, the number of independent groups, and the number of visible neighbors an individual has are affected by increasing the maximum detection
distance. When dmax ¼ 0, the group is made up of 500 individuals (groups of size 1). Intuitively, as dmax increases, individuals have more visible neighbors, mean group size
increases, and the number of independent groups decreases
whereupon the overall supergroup becomes a single network
entity when dmax is greater than 5 units on average.
Behavioral Ecology
534
accurate information from their surroundings—an aspect
Fernández-Juricic and Kacelnik (2004) rightly point to as
a key feature for any model of vigilance. Low-sensitive animals can be thought of as struggling to determine which posture their neighbors are in (head up or down), as having
difficulty in counting the neighbors they have, or as having
a tendency to ignore the information they are receiving from
their neighbors.
The MCMC process
Figure 2
The probability of being vigilant (PV) as a function of the difference
in the desires to feed and be vigilant (jDV DF j) for the case DV .
DF, for three values of sensitivity (v ¼ [0.1, 10, 100]). The high and
low values used in this analysis as marked.
SVF ¼ ð1 PV Þ:
1. Limits to processing social information
There is good evidence from psychology experiments that
animals may vary in their ability to determine either how many
neighbors they have or what their neighbors are doing—limits
to perception and attention, including counting, are reviewed
in Shettleworth (1998). We introduce a sensitivity function to
reflect the ability of an individual to determine whether or
not the desire to be vigilant outweighs the desire to feed (i.e.,
DV DF?). The probability of being vigilant (PV) is calculated
as follows:
If
DV DF ;
Using an MCMC process avoids the problem of simultaneous
updating that occurred in the Bahr and Bekoff (1999) cellular
automata model—for some of the parameter space, their
model adopts highly unrealistic, strongly synchronized behaviors (AL Jackson and GD Ruxton, unpublished data). Some
consequences and problems associated with simultaneous
updating are discussed in Ruxton (1996) and Ruxton and
Saravia (1998). The rate at which each individual switches
states is determined analytically in each iteration. ‘‘Vigilant’’
individuals change to the feeding state at a rate simply
given by
We assume that feeding individuals do not consider switching
states unless they interrupt their feeding bout temporarily to
inspect their neighbors: this occurs with rate J and equates to
the jumpiness of feeding individuals in the model of Bahr and
Bekoff (1999). Jumpiness is the propensity to break a feeding
bout and consider changing state (as introduced in Bahr and
Bekoff 1999) and corresponds to individuals with narrow
visual fields in Fernández-Juricic et al. (2004). ‘‘Feeding’’ individuals have a rate of switching to the vigilant state given by
PV ¼ 0:5 1 0:5ð1 expðv 3 jDV DF jÞÞ; ð2aÞ
else,
PV ¼ 1 ½0:5 1 0:5ð1 expðv 3 jDV DF jÞÞ:
ð2bÞ
This function means that when the difference between the
desires to feed and scan are small, individuals find it difficult to tell them apart and PV / 0.5 (see Figure 2), and
when the difference is great, they can easily tell them apart
and PV / 1 or 0 depending on which desire is larger. The
constant v in the equation alters the sensitivity of each individual: as v / 0, so individuals become insensitive and
struggle to exploit the difference between the two tendencies
(PV / 0.5), and as v / N, individuals become hypersensitive
and are able to detect even very slight differences between the
two tendencies (PV / 1 or 0). Note that the corresponding
probability of feeding (PF) is PF ¼ 1 PV. We consider two
values of v ¼ [0.1, 100], respectively, corresponding to low
and high sensitivity—intermediate values produce results that
are intermediary between those described below. This imperfect ability to determine between the desires to feed and be
vigilant reflects the different abilities of individuals to draw
ð3aÞ
SFV ¼ JPV :
ð3bÞ
At the beginning of each iteration, the appropriate switching
rate (SFV or SVF) is calculated for all individuals in the group.
The single event that occurs in this iteration (an event being
one individual switching state) is selected stochastically from
all possible events: each switching event occurs with a probability proportional to each individual’s rate of switching state
Si. The total event rate R is given by the sum of all the event
rates
R¼
NF
X
1
SFV 1
NV
X
SVF :
ð4Þ
1
Time is advanced by Dt, determined by drawing randomly
from an exponential distribution with mean 1/R (Grimmett
and Welsh 1986). The chosen individual then switches to the
appropriate alternative state, the switching rates recalculated,
the process repeated for 5000 iterations to remove any transient effect of initial conditions, and subsequently evaluated
for a further 10 000 iterations during which the following results are recorded: 1) mean proportion of vigilant individuals,
!
Figure 3
Three panels per box show 1) the proportion of vigilant individuals at any one time, 2) the mean individual vigilant bout length, and 3) the
mean proportion of time spent vigilant. Box plots show the median and 25% and 75% interquartile ranges with outliers (1) over 4000 iterations
of a single simulation. Results per panel are presented as a function of maximum detection distance (dmax). Each row represents a different
combination of sensitivity (low v ¼ 0.1, high v ¼ 100) and jumpiness (low J ¼ 0.1, high J ¼ 1) as indicated. Note the different y axis scales in the
bout-length plots for low jumpiness. Note also that in the bottom right panel, one individual recorded a mean vigilant bout length of 120 time
units for dmax ¼ 17: the y axis has been restricted to 70 time units for clarity of the main results.
Jackson and Ruxton • Social information and vigilance
535
Behavioral Ecology
536
2) mean individual vigilance bout length, and 3) mean individual proportion of time spent vigilant.
This model examines a simple setup where individuals reconcile their own private information against social information they derive from their neighbors. In the extreme case,
where individuals pay no attention to their neighbors—either
because there are no individuals within their zone of influence (e.g., dmin ¼ 0) or because they are completely insensitive (v ¼ 0)—they essentially rely on their own private
information and ignore their neighbors’ behavior. In our
model, private information tends to make individuals switch
from vigilant to feeding (SVF) with P ¼ 0.5 and from feeding
to vigilant (SFV) with P ¼ J 3 0.5 (thus, individuals with lower
values of J are inherently more likely to feed). However, as
detection distance and sensitivity increases, individuals begin
to draw more information, more accurately, from their neighbors. Ultimately, they tend to do the opposite of what their
neighbors are doing. Although alternative behavioral rules
obviously exist at least theoretically—such as private information based on food intake rates, hunger levels, a simple
greater propensity to scan/feed, or alternatives to the majority
rule—it is impossible to explore all these possibilities in a single analysis. We have chosen what we feel to be the salient
points of such a system of vigilance, drawing guidance from
studies such as Fernández-Juricic and Kacelnik (2004) and
concepts from Bahr and Bekoff (1999), and explored the
effect of some ecologically important parameters.
The results below are for a single randomly drawn square
arrangement of 500 individuals (i.e., same group structure,
different behavioral parameters). The effect of maximum detection distance (dmax: x axis), jumpiness (J: panel columns),
and sensitivity (v: panel rows) were investigated in this singlegroup arrangement in separate simulations. The particular
architecture used resulted in a single fully connected supergroup when the detection distance dmax 5 (cf. Figure 1).
Although each box plot in Figure 3 represents results obtained from a single-group architecture only (and all box plots
shared this architecture), repetition using different randomly
allocated results yields very similar results (certainly they are
qualitatively identical). The particular architecture used herein
was drawn randomly and was not chosen for any particular
reason. By comparing the effect of jumpiness and sensitivity
on a single-group structure, the understanding of model
predictions is clearer and easier to comprehend.
RESULTS
In general, we find that intuitively the mean proportion of
vigilant individuals and the mean proportion time spent vigilant for individuals correlate on a 1:1 basis. However, the
trends observed in the variation around these means need
not correlate. Furthermore, the mean vigilant bout length
need not correlate with either proportion individuals vigilant
or proportion time spent vigilant such that a given level of
vigilance can be achieved with either several short vigilance
bouts or few long ones.
When feeding individuals always consider changing state
(i.e., when J ¼ 1), the group tends toward a state where
50% of individuals are vigilant regardless of sensitivity (v) or
maximum detection distance (dmax). Specifically, when private
information dominates these jumpy individuals’ behavior (low
sensitivity and small detection distances: Figure 3a), 50% of
the group tend to be vigilant at any one time and there are
large deviations around this tendency. However, as dmax increases, so the variance about the central tendency for 50%
vigilant individuals decreases—this trend is more pronounced
for highly sensitive individuals (v ¼ 100, Figure 3b).
A change in the behavior of the system occurs when feeding
individuals inspect their environment less frequently (i.e.,
when they consider breaking their feeding bout 10% of the
time, J ¼ 0.1, Figure 3c,d). As expected, when individuals rely
solely on private information (dmax ¼ 0), they spend approximately 10% of their time being vigilant, and there are approximately 10% of them vigilant at any one time; they also exhibit
short vigilant bout lengths of approximately 2 time units (the
observed values are in accordance with the analytic prediction
of exponentially distributed vigilant and feeding times with
mean 1/SFV ¼ 1/SVF ¼ 1/0.5 ¼ 2 time units, Grimmett and
Welsh 1986). As the zone of influence of neighbors increases
(dmax increases), so the proportion of vigilant individuals also
increases and so too does the mean individual vigilant bout
length and the mean proportion of time spent feeding. The
shape of this response is affected by the sensitivity of individuals in the group. These relationships are relatively weak in
low-sensitivity groups (Figure 3c) but are strong and S shaped
in high-sensitivity groups (Figure 3d).
The changes in behavior of the system with detection distance could and indeed are likely to be affected by the network structure of the group. As shown in Figure 1, the group
is only a single fully connected system when dmax 5 and
comprises several isolated subgroups for values lower than
this. However, this does not explain all the observed trends
as they persist above this threshold value. Furthermore, we
might have expected to see sudden changes in the system’s
behavior as the number of subgroups comprising the supergroup increases in large steps with detection distance. In contrast, the trends describing the effect of detection distance on
the response variables are smooth (especially noticeable in
Figure 3c,d), suggesting that detection distance itself is responsible for much of the changes in the system’s behavior
rather than being solely due to changes in the connectivity of
the group.
DISCUSSION
The number of vigilant individuals at any one time in a group
is likely to be the important factor in determining the success
of collective detection (many-eyes effect, Krause and Ruxton
2002). Purely random switching between feeding and vigilance (dmax ¼ 0, J ¼ 1), such as when individuals use only
private information, produces higher variance around the
central tendency for 50% vigilant individuals than when social
information is incorporated into their decision (dmax . 0).
Such variable collective behavior means that at times there
are many more vigilant individuals than 50% and, similarly,
at others there are many fewer. If we consider a hypothetical
scenario and arbitrarily assume that collective detection of
a would-be predator is guaranteed when 50% of individuals
are vigilant (appropriate for our model), then it is in the
interests of all individuals that this vigilance rate be maintained consistently over time. The variation around the central tendency indicates to what extent the individuals are
cooperating in terms of their vigilance behavior. The smaller
the variation, the more cooperative the group. The larger the
variation, the more they are acting as independent solitary
individuals with respect to the goal of achieving a collective
50% vigilance rate. By obtaining more information, more
accurately from their neighbors, individuals are capable of
substantially reducing the amplitude of these oscillations
through better coordination of their vigilance. Although the
adaptive benefits of cooperative vigilance strategies have been
studied extensively, mechanistic explanations are less common (Beauchamp 2003). Previous explanations have suggested that individuals do not parasitize their group mates
vigilance because personal detection of a predator provides
Jackson and Ruxton • Social information and vigilance
more protection than relying on secondhand information
(Fitzgibbon 1989; Scheel 1993; Cresswell 1994).
Feeding individuals are not likely to be able to search
for and handle food while simultaneously inspecting their
neighbors. Reducing individuals’ tendency to break their
feeding bout (J , 1) introduces inertia into the system and
generates a propensity for less than 50% vigilant individuals as
more individuals end up temporarily ‘‘stuck’’ feeding while
they ignore their neighbors. When individuals rely solely on
private information (dmax ¼ 0), we observe that approximately
10% of individuals are vigilant at any one time and that
they themselves spend approximately 10% of their time vigilant. This is as we would expect because feeding individuals
only consider switching states at a rate of J ¼ 0.1. However, as
these relatively inert individuals (low jumpiness) pay more
attention to their neighbors with greater accuracy, social information dominates their personal tendency for feeding, and
the mean proportion of vigilant individuals and the mean
individual time spent vigilant increase. This rate of increase
is influenced strongly by how sensitive the individuals are,
such that a group of highly sensitive individuals can achieve
a much greater number of vigilant members for the same
detection distance as their less sensitive counterparts. The increase in the proportion of vigilant individuals is accompanied by increasing vigilant bout lengths: this is in contrast to
the short vigilant bouts observed in the jumpy individuals.
This suggests that some individuals are acting as long-term
sentries within the group while their neighbors feed, until
such a time as enough feeding individuals lookup, see that
most of their neighbors are feeding, and so they take up sentry duty. This concept is further upheld by the observation
that several individuals become outliers with respect to their
vigilant bout length such that for low jumpiness and high
sensitivity there are several individuals that are vigilant for
on average more than 30 time units. Bednekoff (1997,
2001) covers sentinel behavior in more detail and shows under which circumstances it is favorable and evolutionarily stable. Although the within-flock sentry behavior we observe in
our model is somewhat different from the away-from-flock
sentinel behavior that he describes, the principles are similar.
The key difference is that our sentries are emergent properties of our model, arising simply as a result of the dynamics of
the flock, rather than requiring some level of sentinel behavior be imposed on them.
Furthermore, this model’s behavior suggests some dependency on group size (AL Jackson and GD Ruxton, unpublished data). However, this effect is weak and will involve
detailed analyses before we understand the mechanism behind such subtle changes in the system’s behavior. Some modification to the basic private information rule or to the rule
governing social information use may be required to capture
the well-described patterns of decreasing individual vigilance
rates with increasing group size observed in real situations
(Krause and Ruxton 2002). Our model is similar to that of
Bahr and Bekoff (1999) in that we assume that individuals
tend to do the opposite of that of their neighbors. This is in
contrast to the findings of Fernández-Juricic and Kacelnik
(2004) on starlings, which suggested a tendency for individuals to copy their neighbors. When such a copying rule is used
in our model, we find that eventually all individuals end up
feeding for the majority of time (indeed all the time in many
cases) as long as they pay some attention to their neighbors
(AL Jackson and GD Ruxton, unpublished data). Such behavior seems contrary to the concept of vigilance behavior and
warrants further consideration in future studies. Perhaps,
a copying rule may be favored in purely foraging situations
and an opposing rule in antipredator vigilance. Indeed, it
would be interesting to combine individual-based models of
537
group foraging (e.g., Beauchamp and Fernández-Juricic 2005)
with those of group vigilance and allow movement of individuals in an environment containing different distributions of
food. Rather than speculate about the alternatives, we feel
that further experimental work will drive our knowledge
and modeling in this regard.
We hypothesize that the group is essentially a connected
network of individuals, with individuals themselves having
internal state-dependent rules governing vigilance rates,
against which they reconcile the social information they yield
from their neighbors. By wiring such a network from video
analyses, it should be possible to reverse engineer the underlying rules by elaborating on methods employed in, for example, Fernández-Juricic and Kacelnik (2004). Hidden MCMC
approaches may provide a means to obtain the switching rates
individuals follow for moving between states (Durbin et al.
1998). The input into such models would be the observed
sequence of vigilance/feeding states adopted, and the output
would be estimates of the unknown probabilities of moving
between the states.
Modeling vigilance as we have done opens up a range of
avenues of research. Introducing a predator to the system
would allow us to explore information sharing between individuals regarding predator detection, using concepts such
as the Trafalgar effect (Treherne and Foster 1981). Position
adopted within the group will also be interesting to pursue
as it is often associated with differential costs and benefits
(Krause and Ruxton 2002) and often with different rates of
vigilance (Terhune and Brillant 1996; Rattenborg et al. 1999;
de Oliveira et al. 2003; Randler 2003). Indeed, analyses of
single-simulation runs (AL Jackson and GD Ruxton, unpublished data) suggest that the different influences felt by individuals in different locations within the group affects their
feeding–vigilant switching rates, suggesting that an effect of
group size, density, or shape as well as heterogeneity of position
within a group will alter the system’s behavior. It is also clear
from our analyses that it is important to bear in mind the connectivity of the entire group as it may in fact be a collection of
several smaller independent groups rather than a single entity.
Elucidating the underlying individual-level mechanisms
that drive collective vigilance behavior will be challenging for
both theoreticians and experimentalists alike—as analogous
complex molecular networks are proving (Nicholson et al.
2004). A combination of forward- and reverse-engineering
approaches (e.g., Bahr and Bekoff 1999 and Fernández-Juricic
and Kacelnik 2004, respectively) working in tandem will be
the key to dissecting, understanding, and reconstructing
mechanistic models of vigilance.
A.L.J. was funded by a research scholarship from the Institute of
Biomedical and Life Sciences, University of Glasgow. We thank two
anonymous referees for their thorough and insightful comments that
improved this paper—most notably for pointing out that the group
may not be a single entity. Thanks also to Daniel Haydon and Ashley
Ward for their useful input.
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