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Behavioral Ecology Vol. 12 No. 3: 348-352
© 2001 International Society for Behavioral Ecology
Bystander effects and the structure of dominance hierarchies
Department of Biology, Life Sciences Building, University of Louisville, Louisville, KY 40292, USA
Address correspondence to L.A. Dugatkin. E-mail: lee.dugatkin{at}louisville.edu .
Received 11 January 2000; revised 11 September 2000; accepted 28 September 2000.
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ABSTRACT |
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Prior modeling work has found that pure winner and loser effects (i.e., changing the estimation of your own fighting ability as a function of direct prior experience) can have important consequences for hierarchy formation. Here these models are extended to incorporate "bystander effects." When bystander effects are in operation, observers (i.e., bystanders) of aggressive interactions change their assessment of the protagonists' fighting abilities (depending on who wins and who loses). Computer simulations demonstrate that when bystander winner effects alone are at play, groups have a clear omega (bottom-ranking individual), while the relative position of other group members remains difficult to determine. When only bystander loser effects are in operation, wins and losses are randomly distributed throughout a group (i.e., no discernible hierarchy). When pure and bystander winner effects are jointly in place, a linear hierarchy, in which all positions (i.e.,
to 
when N = 4) are clearly defined, emerges.
Joint pure and bystander loser effects produce the same result. In principle
one could test the predictions from the models developed here in a
straightforward comparative study. Hopefully, the results of this model will
spur on such studies in the future. Key words: aggression, bystander, observer, hierarchy, dominance.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMODELSRESULTSDISCUSSIONREFERENCES |
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Given the ubiquity of aggression in even the most cooperative of animal societies (Archer, 1988
;
Dugatkin, 1997a;
Gadagkar, 1997;
Huntingford and Turner, 1987)
it should come as no surprise that theoreticians and empiricists have a
long-standing interest in understanding both proximate and ultimate factors
influencing aggression and dominance hierarchies. Behavioral ecology models of
aggression partition the effects that influence fighting into two
compartments—intrinsic and extrinsic factors (Landau,
1951a,b).
Intrinsic factors, as the label implies, typically refer to traits that
correlate with an animal's fighting ability in terms of physical
prowess—that is, its resource holding power or RHP
(Parker, 1974). The most
common of these factors is some measure of size
(Archer, 1988;
Huntingford and Turner,
1987).
Extrinsic factors are encapsulated by what have come to be known as winner
and loser effects (Landau,
1951a,b;
see Chase et al., 1994 for a
review of empirical work on winner and loser effects). Winner and loser
effects are usually defined as an increased probability of winning at time
T, based on victories at time T-1, T-2, and so on,
and an increased probability of losing at time T, based on losing at
T-1, T-2, and so on, respectively. I shall refer to these as
"pure" winner and loser effects to contrast them clearly with
terminology I introduce below. Exactly how winner and loser effects influence
fighting behavior is not well understood for many systems, but
endocrinological changes after victory or defeat are the likely proximate
mechanisms (Nelson, 1995). For
example, in copperheads, when compared to winners, losers have elevated levels
of plasma corticosterone, but decreased levels of plasma testosterone
(Schuett, 1997).
Much of the theoretical work on aggression focuses on intrinsic factors.
Extrinsic effects have been the subject of less attention, and studies to date
tend to examine winner and loser effects in terms of their impact on pairwise
interaction, rather than on dominance hierarchies. I have recently modeled the
effect of pure winner and loser effects on hierarchy structure per se
(Dugatkin, 1997b). When winner
effects alone were important, a hierarchy in which all individuals held an
unambiguous rank was found. When only loser effects were important, a clear
alpha individual always emerged, but the rank of others in the group was
unclear because of the scarcity of aggressive interactions. Increasing winner
effects for a given value of the loser effect increases the number of
individuals with unambiguous positions in a hierarchy and the converse is true
for increasing the value of the loser effect for a given winner effect. In
addition, pure winner and loser effects have ramifications for intervention
behavior and coalition formation (Dugatkin,
1998a,b;
Johnstone and Dugatkin,
2000).
While pure winner and loser effects examine how the actual experience of
contest outcome can affect fighting abilities, there two related types of
extrinsic factors—audience and bystander effects—that have not
been the subject of any formal mathematical modeling. Audience effects occur
when individuals change their fighting behavior as a result of being watched
by others (Doutrelant et al.,
2001; Evans and Marler, 1984;
McGregor and Peake, 2000). The
bystander effect, which we shall be focusing on here, refers to the case in
which an individual changes its estimation of the fighting abilities of others
based on what it observes. Given that fighting costs can often be significant
during animal contests (Archer,
1988; Abbott and Dill,
1985; Enquist et al.,
1990; Huntingford and Turner,
1987) selection should, whenever possible, favor any assessment
that curtails such costs. Despite their potential importance, bystander
effects have not been the subject of a great deal of empirical work, although
they have been demonstrated in chickens (Chase,
1982a,b,
1985;
Coultier et al., 1996),
rainbow trout (Oncorhynchus mykiss,
Johnsson and Akerman, 1998)
and fighting fish (Betta splendens;
Oliveira et al., 1998).
Chase's "jigsaw model" (Chase,
1980,
1982a) was the first serious
attempt to place bystander effects into a theoretical framework. Chase
developed a three-player scenario, wherein a bystander (C) observes an
interaction between the two other group members (A and B). Subsequent to this
C interacts with either A or B. In such scenarios, there are four possible
dyadic outcomes: (1) double dominance where A defeats C, (2) double
subordinance in which C defeats B, (3) bystander dominates initial dominant,
wherein C defeats A; and (4) initial subordinate dominates bystander, wherein
B defeats C.
Chase's models found that regardless of the direction of the third
relationship, double dominance and double subordinance led
to transitive, linear hierarchies (A
B, BC, AC, or AB,
CB, AB) while bystander dominates initial dominant and
initial subordinate dominates bystander always lead to intransitive,
relatively nonlinear hierarchies. Chase's experimental work with chickens
demonstrated that double dominance and double subordinance were indeed the
most likely outcomes, suggesting that bystander effects tend to stabilize
dominance hierarchies (Chase,
1982a,b;
this also held true when examining triadic interactions in four-person
hierarchies; see Chase,
1985).
Chase's jigsaw model, though suggestive, leaves many questions about bystander effects and dominance hierarchies unanswered. This is in part due to the fact that these verbal models contain no explicit parameters that can be manipulated. In particular, Chase did not examine "bystander winner" and "bystander loser" effects independently (see more below), but only considered the effects on hierarchy formation when both are present. Furthermore animals did not assess each other's RHP in Chase's model work, nor were bystander effects combined with pure winner and loser effects to examine their joint effects. Here, spurred by Chase's seminal work on bystander effects, I develop models that explicitly address the issues raised. It is important, however, to note that the models presented here do not examine the evolution of bystander effects. Rather, given that the literature suggests that winner, loser, and bystander effects may play a role in animal social behavior, the models ask what impact these effects have on hierarchy formation.
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MODELS |
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TOPABSTRACTINTRODUCTIONMODELSRESULTSDISCUSSIONREFERENCES |
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General rules and parameters
As in Dugatkin (1997b
),
individuals in a group of size N are randomly paired in potentially
aggressive contests. For simplicity, I will examine groups in which N
is even. The simulation proceeds through time intervals, T =
1,2,...Tmax, and during each interval N/2
interactions occur. At the start of a simulation, each player is assigned a
number that measures the individual's assessment of its own fighting ability.
This value can be thought of as a player's estimate of its own RHP. A player's
assessment of itself at time T is labeled RHPplayer i,
self, T.
Aggression in these simulations encompasses both chases (where one player
opts to fight, while its opponent does not) and actual fighting. In an
encounter, players are aggressive if:
 | (1) |
(where 
0) will be called the "aggression threshold"
(Mesterton-Gibbons and Dugatkin,
1995). For example, if = 0, animals will always fight
regardless of who their opponent is, if = 0.5, they will fight another
individual whose RHP they assess to be up to twice as great as their own, and
if = 1, they will fight anyone with an RHP that they assess to be
smaller than or equal to their own. Given this, three outcomes are possible
when player i meets player j: (1) Both player i and
j meet the aggression threshold and both decide to fight. In such
cases, one individual wins and one loses. (2) Player i meets the
aggression threshold, while player j does not, or vice versa. In this
case, we will say that one player "attacked," while the other
player "retreated." Attackers are considered to have won such
interactions. (3) Neither player i nor player j meets the
aggression threshold, and hence neither opts to fight. This will be referred
as a "double kowtow."
If both players opt to be aggressive (i.e., a fight occurs), the
probability that player i will defeat player j is given as:
 | (2) |
) and that of
its potential opponent, but the probability of winning an aggressive
interaction, given that one occurs, is dependent only on each individual's
assessment of its own RHP (i.e., player i's
assessment of j does not affect player i's
probability of victory).
Tmax was set to 250, group size (N) was either
four or eight, was set at either 0.25, 0.5, 0.75, or 0.9, the initial
RHP value for each group member was set at 100 (i.e., all group members
started out with the same RHP value) and each combination of parameters was
run 10 times.
Model I: bystander effects only
The bystander effect comes in two flavors—bystander winner (BW) and
bystander loser (BL). If a bystander raises its estimation of the fighting
ability of one of its group mates because it has just seen that group mate
emerge victorious in an aggressive interaction, bystander winner effects are
in play. Conversely, should a bystander see another individual lose a fight
and then subsequently devalue the fighting ability of such a loser, bystander
loser effects are at work. Both effects can be in operation
simultaneously.
I will assume that all pairwise interactions in a group are
observed by all other group members. Let us consider BW effects
first. Imagine an interaction between players j and k at
time T. Should j either win a fight or attack k
(and thus have k retreat), each bystander (i.e., every
individual in the group beside j and k), now changes their
estimation of j's RHP as follows:
 | (3) |
Now imagine the same interaction when only BL effects are modeled. Each
bystander should now change its estimate of k's RHP as follows:
 | (4) |
Model II: bystander and pure winner/loser effects
Model II considers the case in which, in addition to bystander effects,
pure winner (W) and loser (L) effects are also at work. I shall examine this
by modeling the case where either BW and W are both in play (and BW = W), BL
and L are both in operation (and BL = L), or BW, W, BL, and L are all
operating (pure winner and loser effects alone were examined in
Dugatkin, 1997b).
Again, consider the situation raised above. If BW and W are both in play,
not only do bystanders change their assessment (as in Equation 3), but now:
 | (5) |
 | (6) |
BW/W and BL/L were each increased from 0 to 0.5 (in increments of 0.1). In all simulations, an animal was considered dominant to another if it defeated that individual in greater than 50% of the encounters between the pair. All computer simulations were constructed using TrueBasicTM.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMODELSRESULTSDISCUSSIONREFERENCES |
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As in prior work on winning and losing, (Dugatkin, 1997b
) varying
either (the aggression threshold) or N (group size) does not
qualitatively affect the results presented below (i.e., the same general
patterns were uncovered regardless of or N), and so I shall
focus on = 0.5 and N = 4. In addition, repeated simulations
with the same set of parameter values were very consistent in their
outcomes. When bystander winner effects alone are at play, each group has a clear omega (bottom-ranking individual), but the ranking of other group members is difficult to determine (Table 1). To understand this pattern, recall that all individuals begin with an RHPi self, 1 of 100. During early interactions, one individual (let's call him D in accordance with Table 1), by chance, loses a majority of its early interactions. Others in the group observe this and now act as if D has the same (or close to the same) RHP it began with (i.e., 100), while they all view each other's RHP as larger than 100 (because most group members will have won some early fights). This quickly devolves into a situation in which upon encounter everyone attacks D (who always retreats), but never attack each other. In this scenario, most aggressive interactions are of the "attack-retreat" rather "both individuals opt to fight" variety.
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= 0.5, 250
interactions (including double kowtows which score zero for each player
involved in such an interaction)
The scenario is dramatically different when only bystander loser effects are in operation. Now, wins and losses are randomly distributed throughout a group (Table 2). In contrast to the bystander winner case in which most aggressive interactions are "attack-retreat," now individuals always fight when they meet. The lack of a clear hierarchy in such groups can be understood as follows: When bystander loser effects are in operation, individuals change the RHP value they assign to others, but only in a negative direction, and they never change the estimation of their own RHP. As a result, when two players meet, each assess the other to have an RHP lower than their own and they both tend to opt for fighting. The results of such fights are random, in the sense that each of the protagonist's RHP always remain at 100 (i.e., RHPj, self, T = 100 for all T), and thus Equation 3 assures such randomness.
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While it is not possible to be precise, for values of between 0.1 and
0.5, bystander loser effects appear to be stronger than bystander winner
effects. For example, when N = 4 and BL = 0.1, BW must be set at 0.5
to produce a typical BW hierarchy (only a clear omega), but when BW =.1, a Bl
of 0.2 produces a typical BL set of interactions (wins and losses distributed
equally through a hierarchy) (Table
3). This pattern is found for different values of N and
and could be interpreted as evidence that bystander loser are more
powerful than bystander winner effects. It is worth noting that empirical work
on pure winner and loser effects often finds that of the two, pure loser
effects tend be more potent (Chase et al.,
1994).
|
Model II examined three cases—joint pure and bystander winner
effects, joint and pure bystander loser effects, and all four effects in play
simultaneously. All three cases produced a linear hierarchy in which all
positions (i.e., to when N = 4) were clearly defined,
and most interactions were of the attack/retreat variety (Tables
4 and
5). The clearly defined linear
hierarchy is due to each individual having the exact same information
regarding RHPs. That is, if individual A assesses its own RHP as R, then when
joint effects are in play, all other individuals also assess A's RHP as R,
hence there is agreement about everyone's RHP. This in turn creates a social
environment in which most interactions are of the form
"attack-retreat" and individuals fall into rank quickly.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMODELSRESULTSDISCUSSIONREFERENCES |
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In conjunction with prior work (Dugatkin, 1997b
), it is now
clear that the nature of pure winner, pure loser, bystander winner, and
bystander loser effects (and their interactions) can have a profound effect on
hierarchy formation (or the lack of it). Depending on which effects are in
play, a variety of hierarchy forms are possible
(Table 6). For example, under
the models presented here we have seen that, depending on the parameters, one
might expect only a clear bottom-ranking individual, a clearly defined
hierarchy or no hierarchy at all (where wins and losses are randomly
distributed among individuals).
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Unfortunately, the published data on bystander effects are not of the form
that can be plugged into the equations presented in this article. In
principle, however, future experimental work could easily be constructed in a
way to allow use of the equations presented here. For example, to measure
bystander winner effects, for simplicity, one would begin in a system where no
pure winner effects are in play and simple pairwise aggressive bouts were used
to determine the value of . Then individual i would be pitted
against individual j (where i and j were of known
RHPs) in part 1 of a trial, and any aggression that took place would be
recorded. Then, at some point at which i and j had forgotten
the initial encounter (this will vary across systems), i and
j would be re-paired in part 2 of a trial, but only after i
had been a bystander to a fight in which j emerged victorious. If
repeated with many pairs of individuals, the difference between i's
behaviors in different parts of a trial could be used to gauge WL. Similar
sorts of experiments (but with i observing j lose) could be
run to examine pure loser effects.
Once the sorts of experiments outlined above are complete, one could then
further test the predictions from the models developed here in a comparative
study in which hierarchy formation would be examined in species that had
documented various combinations of bystander winner, bystander loser, pure
winner, and pure loser effects. The types of hierarchies uncovered could then
be compared to the results presented here and in Dugatkin
(1997b). Unfortunately, the
data for such comparisons do not yet exist. That is, although bystander
winner, bystander loser, pure winner, and pure loser effects are evident in a
wide variety of taxa (e.g., insects;
Alexander, 1961;
Burk, 1979; molluscs;
Zack, 1975; fish;
Beaugrand and Zayan, 1985;
Francis, 1983;
Frey and Miller, 1972;
Johnsson and Akerman, 1998;
Oliveira et al., 1998; birds;
Drummond and Osorno, 1992;
reptiles; Schuett, 1996, 1997
and rodents; van de Poll and Smeets,
1982), and despite some controlled studies of these phenomena
(Bakker and Sevenster, 1983;
Bakker et al., 1989;
Beacham and Newman, 1987;
Beaugrand and Zayan, 1985;
Burk, 1979; Chase,
1982a,b,
1985;
Chase et al., 1994; Cloutier
et al., 1995,
1996; Francis,
1983,
1987;
Frey and Miller, 1972;
Hollis et al., 1995;
Johnsson and Akerman, 1998;
Oliveira et al., 1998;
Schuett, 1996, 1997), no work
to date has documented both pure and bystander winner and loser
effects and the detailed nature of behavioral interactions when
individuals are in groups. Hopefully, the results of this model will
spur on such studies in the future.
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ACKNOWLEDGEMENTS |
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I wish to thank D. Dugatkin and R. Earley for suggestions on earlier versions of this article.
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