Behavioral Ecology Vol. 8 No. 6: 583-587
Winner and loser effects and the structure of
dominance hierarchies
Lee Alan Dugatkin
Department of Biology, life Sciences Building, University of Louisville, Louisville, KY 40292, USA
In the literature on dominance hierarchies, "winner" and "loser" effects usually are denned as an increased probability of winning
at time T, bated on victories at time T-l, T-2, etc, and an increased probability of losing at time T, based on losing at T-l, T% etc,
respectively. Despite some early theoretical work on winner and loser effects, these factors and how they affect the structure of
dominance hierarchies have not been examined in detail. I developed a computer simulation to examine winner and loser effects
when such effects are independent of one another (as well as when they interact) and when combatants assess each other's resourceholding power. 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 dear alpha individual always emerged, but the rank of others in die group was often
unclear because of die scarcity of aggressive interactions. Increasing winner effects for a given value of the loser effect increase the
number of individuals with unambiguous positions in a hierarchy and die converse is true for increasing the value of die loser effect
for a given winner effect Although winner and loser effects have been documented in a number of species, no study has documented
both winner and loser effects (using some controlled, padrwise testing system) and die detailed nature of behavioral interactions when
individuals are in groups. I hope die results of this model will spur such studies in die future. Key words: aggression, dominance
hierarchies, resource-holding power, winner and loser effects. [Behav Ecol 8:583-587 (1997)]
B
ehavioral biologists' interest in die nature of dominance
hierarchies can be traced back at least as far as Schjelderup-Ebbe's (1922) seminal work on this subject in chickens.
Part of die fascination widi hierarchy formation probably
stems from the difficulty in understanding why an animal
would ever "accept" a role other than that of alpha individual
in die group (Alice, 1951; Dugatkin, 1995; Reeve and Ratnicks, 1993; Vehrencamp, 1983). For this and many other reasons, (e.g., die specific costs and benefits associated with various positions in a hierarchy), hierarchy formation has been
studied in a wide array of taxa (Archer, 1988; Huntingford
and Turner, 1987; Jackson and Winnegard, 1988) and has
been die subject of a number of dieoretical treatments (Appleby, 1983; Chase, 1974; Dugadun, 1995; Landau, 1951a,b;
Reeve and Ratnieks, 1993; Rothstein, 1992; Vehrencamp,
1983).
Bodi "extrinsic" and "intrinsic" factors (Landau, 1951a,b)
may influence hierarchy formation. Intrinsic factors typically
refer to some correlate of an animal's fighting ability, in terms
of physical prowess—Le., its resource-holding power (RHP;
Parker, 1974). In contrast, extrinsic factors typically are encapsulated by things such as winner and loser effects (Landau,
1951a,b) but also include other factors such as territory possession. Winner and loser effects are usually defined as an
increased probability of winning at time T, based on victories
at time T-l, T-2, etc., and an increased probability of losing
at time T, based on losing at T-l, T-2, etc., respectively. It is
important to note that winner and loser effects are not necessarily two sides of die same coin, as in any given system, one
can exist without die other. For example, animal X may be
more likely to defeat animal Y'tC it has just defeated animal Z
(winner effect), but diis does not necessarily mean that animal Z is more likely to be defeated during its next interaction
(Le., no loser effect need exist).
The tendency to win or lose a fight after a prior victory or
defeat has been documented in the blue gourami (MacroReceived 31 May 1996; revised 27 January 1997; accepted 2 February 1997.
1045-2249/97/J5.00 O 1997 International Society for Behavioral Ecology
podus operations; Francis, 1983,1987; Frey and Miller, 1972),
diree-spined sticklebacks (GasUrosUus aculeatur, Bakker and
Sevenster, 1983), pumpkinseed sunfish (Ltponds gibbonis,
Beacham and Newman, 1987), swordtails (Xiphophorus htlUri, Beaugrand et al., 1996), and other species, and such
effects often last for at least 24 h (see Chase et al., 1994, for
a review). The winner and loser effects found in these studies have, however, been die subject of sparse theoretical
treatment, given their potential importance in die structuring of hierarchies.
In a pair of influential papers, Landau (1951a,b) examined how extrinsic and intrinsic factors might explain die
presence of die linear hierarchies he believed were so common in nature. Landau (1951a,b) created an index of linearity which he labeled H (0 a H 2: 1), where greater values
of H indicate more linear hierarchies (see Appleby, 1983,
for an alternative measure). Landau found that except under extreme conditions, intrinsic factors alone could not
produce die hierarchies he believed were representative of
nature. However, once extrinsic factors were added to die
model, hierarchies were much more similar to those found
in nature. In Landau's model, extrinsic factors were incorporated by taking a fixed hierarchy and using Markov chains
to examine die effect of reversing some of die positions in
such a hierarchy.
Despite die importance and impact of Landau's (1951a,b)
paper on research in die area of dominance hierarchies, a
number of critical questions surrounding winner and loser
effects and how they interact remain unanswered some 40
years after die original papers were published. In particular,
Landau (1951a,b) did not examine winner and loser effects
independendy, but only considered the effect on hierarchy
formation when both are present Furthermore, animaW did
not assess each other's RHP in Landau's work. Is it possible
that when RHP is assessed (i.e., individuals can gauge the
fighting abilities of others, as well as themselves) diat winner
and loser effects can, when separated, have different implications for hierarchy formation? If so, what sort of differences exist and through what means are these differences
manifested? Here, I develop a model to examine these questions.
Behavioral Ecology VoL 8 No. 6
584
THE MODEL
Roles and i nxnetera
Consider a group of N animals, within which randomly chosen pairs of individuals are pitted against one another in potentially aggressive contests. For simplicity and because all interactions modeled are pairwise, I will examine groups in
which Nit even. Discrete time intervals, Tm 1,2,... T,^, are
simulated, and at each interval, N/2 interactions occur (Le.,
all group members are involved in contests). At die start of a
computer simulation, each animal is assigned a score that
measures die individual's assessment of its ownfightingability.
This score is analogous to a player's estimate of its own RHP.
Individuals are aware not only of their own initial RHP value,
but those of an other group members as welL An individual's
assessment of die RHP of others does not change dirough
time, and this value is labeled RHPo<hcr. This assumption may
be reasonable given that such assessment is likely based stricdy
on size, which is assumed to remain relatively constant in this
model. An individual's assessment of its own RHP, however,
does change dirough time as a result of (1) whedier it wins
or loses a fight, and/or (2) whether it retreats from an opponent or whedier its opponent retreats (see below). A player's assessment of itself is labeled B H P ^ i Mjt_ T (as noted
above, T is a counter that is initialized at 1 and increases by
a single unit after each pairwise encounter).
In each contest, an animal can choose to either be aggressive or leave. Players use a simple rule to determine which
option to employ. Individuals assess their own RHP and that
of their opponent and choose to be aggressive if:
its aggressive approach, it increases its own RHP by a factor
of W, and so
DTjp
a
/I
4. TflA DUD
/fl\
This wfll be referred to as the winner effect The effect of W
on RHP is unbounded (Le., it has no upper bound and, in
principle, can produce very large values of BWP(lUf^l t . ^ 7).
Conversely, when a player loses a fight or retreats from an aggressive act by an opponent, RHP is lowered by a factor L and
As such, L measures loser effects (and its impact has a lower
bound of PHP . u u tA T m 0). Neither winner nor loser effects
decay wim timeTltfaimportant to note diat this model does not
incorporate any specific interactions, nor does it require individual recognition per se. Rather, an individual simply recognizes
die RHP of other* and self. RHP,*^, t rf T changes based on an
relevant prior interactions, but no memory of interactions with
specific other group members is part of die model.
In aU simulations, winner and loser effects are independent
of one another in the sense diat individuals in a given run of
a simulation may be affected by winner effects alone, loser effects alone, both winner and loser effects, or neither. I assume
diat winning a fight and having an opponent retreat before a
fight have die same effect on W and diat losing afightor
retreating have the, same effect on Z. This assumption could,
of course, be relaxed and one could have one W value for
winning afightand one for having your opponent retreat before any aggressive interactions take place (and similarly for L).
W and L were each increased by from 0 to 0.5, in increments of 0.1. T^, was set to 1000, group size was set at either
N = 4, 6, 8, or 12, and die initial RHP value for each group
member was set at 10 (i.e., all group members started out with
where RHP^y., A ^ j/RHP,,^., wiU be referred to as "relative
die same RHP value). These values were meant to span die
RHP" and <J> (where 4>SO) wiU be called the "aggression
group sizes diat are most commonly found in hierarchies in
threshold" (see Mesterton-Gibbons and Dugatkin, 1995, for nature (Archer, 1988) and to incorporate a reasonably large
more on this idea). For example, if <t> •=• 0, animals will always number of behavioral interactions. It is important to note diat
fight, regardless of who their opponent is; if 4> ~ 03, they
Landau's index of linearity could not be calculated for most
wiU fight anodier individual whose RHP they assess to be up
runs, as this index requires aggressive interactions between all
to twice as great as their own, and if <X> ™ 1, they will fight pairwise combinations of individuals and many hierarchies
anyone with an RHP tiiey assess to be smaller than or equal
did not produce all such combinations (see Results).
to their own. Given this, three outcomes are possible when
An animal was considered dominant to anodier if it deplayer 1 meets player j
feated diat individual in greater than 50% of die encounters
1. Both player t and j meet the aggression threshold and
between die pair. AU computer simulations were constructed
both decide to fight.
using TrueBasic®.
2. Player 1 meets die aggression threshold, while player j
does not, or vice versa. In this case, we will say diat one player
RESULTS
was aggressive, but that die other player "retreated."
3. Neither player i nor player _/ meets die aggression threshSeparating winner and loser effects had a dramatic impact on
old, and hence neither opts to fight. This will be referred to
die distribution and type of encounters among group memas a "double kowtow."
bers and on die type of hierarchy formed. When winner efIf both players opt to be aggressive (i.e., fight or display), die
fects alone were examined, a hierarchy in which an individuals
probability diat player i will defeat player j is given as:
held an unambiguous rank was found (Figure 1). When examining loser effects in die absence of winner effects, a dear
alpha individual always emerged, but die rank of others in die
group was unclear (Figure 1) because of die scarcity of fights
From Equations 1 and 2 we then see diat an animal's deand aggressive/retreat interactions between such individuals
cision about being aggressive is determined by its assessment
and the primacy of double kowtows.
of its own RHP (Jackson, 1991) and diat of its potential opIncreasing winner effects for a given value of die loser effect
ponent, but die probability of winning an aggressive interacraised die number of individuals with unambiguous positions
tion is dependent only on each individual's assessment of its
in a hierarchy, and die converse was also true (Figure 1), alown RHP (i.e., player fi assessment of j does not affect player
though in neither case was the effect linear. Changing group
it probability of victory). In essence, Equations 1 and 2 make
size had little effect on die results described above (Figure 2)
die assumption diat an individual is privy to its own win/loss
in that increasing group size raised die number of dearly
record aad net that of its opponent (these values determine
filled slots in a hierarchy (due to there being more members
whedier one opts to be aggressive), but diat die win/lose recper group), but did not change die general pattern found for
ord of an opponent affects die outcome of any fight diat takes
winner and loser effects. Lowering die aggression threshold
place.
had a mild impact on hierarchies, occasionally increasing die
When player i wins a fight or has its opponent retreat from
Dugatkin • Winner and loser effect! and dominance hierarchies
585
Winner Effect
0.1
02
A B C D
- 146 136 140i
8 8 172,'
168|
21 170
6 18 7
0 0 0
171 . 171 163
C 0 0 . 0
D 0 0 0 .
161 195 IX
0 . 2 0
0 0 . 0
10 159 153 -
. 156 168 174
. 156 178 149
0 . 0 0
0 0 . 0
0 0 1 -
A
0.1
B
A
0.2
B 0 . 3 3
C 0 0 . 0
D 0 0 0 -
A B C D
I • 146 172 160i
| 6 - 168 158J
J7
i 2
-
i
- 177 173 157
0 - 0 0
0
0 - 0
0 0
0 1
0
157 173
1 3
0.4
O3
1 0
0 0
. 148
0 •
A B C D
- 4 158 16*i
161 - 146 172J
6 2 - 183j
0
1 3 - 1
152 171 159
0 . 0 0
0 0 . 0
4 179 171 .
147
0
1
2 173 149
. 160 IS*
0 . 0
0 3 -
03
A B C D
- 165 171 182i
0
- 141 2
0
8 - 0
0 155 176 - 158 171 3
0 - 0 0
0
0 - 0
153 167 170 .
0
143
188
0 0 0
- 0 0
183 - 155
147 0 -
A B C D
172 0 0
0 0
j 182 144 - 1641
U61 176 1
i i
173
171
0
0 0 0
- 0 165
147 - 154
0
0 -
- 158 177 165
2 - 175 159
0
0 - 0
0 0
0 -
Loser Effect
0 0
0 4
. 163
0 -
0 1 0
178
164 133
0 0 . 0
1 0 5 -
. 0
0 .
163 184
0 0
0 1
0 0
. 158
0 -
. 3 0 6
0 . 0 0
160 170
170
0 1 0 -
. 0 0
162 . 176
0 0 173 164 159
0
1
0
-
0 1 0
. 168 174
0 - 0
0 0 .
. 183 156 162
0 . 0 0
0 2 - 0
0 2 0 .
. 0 0 0
170 - 166 195
0
0 - 0
7 2
2 -
- o. 0 0
162 160
161
0 0 - 0
0 0 0 .
. 0 0 0
170 - 171 166
0
0 - 0
2 0 2 -
. 0 0
0
0
1 2 .
172 177 166
0
0
0
-
A . 1 0 0
B 0 . 0 0
C 139 170 - 168
. 180 169 171
0 . 0 0
0 1 - 0
0 2 1 -
0
0
0
155 165 188
. 0 0
1 . 0
3 3 -
. 159 173 171
0 . 0 0
0 4 . 5
0 0 0 -
. 61 55
0
0
0 0 .
153 159 167
0
0
0
A - 0 3 1
B 181 . 172 154
C 0 0 . 0
D
0.4
0.5
0
142
C 0
D 0
A
B
D
0
0
0
0
0
-
-
.
6
15<5
0
0
.
178
0
•
0
0
0
-
160 166 195
. 0 0
0 . 0
1 0 -
Figure 1
Winner and loser effects on hierarchy structure: group size - 4, * - 1, snd 1000 potential interactions (including double kowtows which
score zeros for each player involved in such an interaction). Entries in rows represent the number of times the row player was aggressive to a
column player, and data in columns shows the number of times cohimn players are aggressive to a row player. For example, for tbe case of a
winner effect - 0.2 and a loser effect - 0, individual A was aggressive to individual B 146 times, while B was aggressive to A 6 times. Shaded
box - no dominance hierarchy, dashed box — all positions in hierarchy are clear, single-line box = only alpha individual is clearly
discernible; double-line box - only alpha and beta individuals are clearly discernible.
number of clear hierarchy positions filled (Figure 2). This
effect was primarily due to the decreased number of double
kowtows (and hence the increased frequency of aggressive interactions) when the aggression threshold is lowered.
Although it is difficult to gauge the relative strength of winner versus loser effects, loser effects appear to be somewhat
more important with respect to their effect on hierarchy formation. For example, in a group of eight individuals, a dear
ranking of all eight is possible when winner effects alone are
in play. However, a moderate loser effect combined with a
stronger winner effect allows only the top two to four individuals in a hierarchy to be unambiguously ranked (Figure 2).
DISCUSSION
The most salient result of the model outlined here is that
when RHP of self and others is assessed, the type of hierarchy
predicted depends critically on whether winner effects exist
alone, loser effects exist alone, or some combination is acting
in a system. Winner effects alone produce hierarchies in
which the rank of aO individuals can be unambiguously assigned, whereas loser effects alone produce hierarchies in
which a dear alpha individual exists, but the relation among
other group members remains uncertain. What causes this
difference? It appears that winner effects create a situation in
which pairs of individuals primarily interact by righting or by
aggressive/submissive interactions, and thus assigning position in die hierarchy is flirty straightforward. Loser effects,
however, quickly produce individuals that are not going to be
aggressive both because of their low estimate of their own
RHP after a few losses and their decision to be aggressive or
not based on <t>. Hence, most interactions will end in double
kowtows. Of course, such double kowtows will be difficult to
record, and even if they could be recorded, they would tell
the investigator nothing about an individual's position in a
hierarchy. Without a fight or a chase sequence, double kowtows may be quite subtle and hard to quantify. However, in
some spedes with ritualized combat that indudes sequential
assessment (e.g., Nannacara anomala. Enquist et aL, 1987,
1990; FronttTvlla pjnmitda. Leimar et aL, 1991), double kowtows might be more easily observed.
The model presented here differs from others in the growing literature on dominance hierarchies in that it simultaneously examines RHP, winner and loser effects, and their
impact on hierarchy structure. However, some excellent models already in the literature examine some subset of these variables. For example, Parker (1974), Maynard Smith and Parker
(1976), and Parker and Rubinstein (1981) examined assessment strategies but did not incorporate winner and loser effects or their implications for hierarchy structure. In addition.
586
Behavioral Ecology VoL 8 No. 6
A
Winner effect
0 0.1
Loser
effect
O2 O3 0.4
05
Winner effect
0.2 O3 0.4 O5
Winner effect
0 0.1
0
0.1
0 Ol
O2 O3 0 4
0
0
4
4
4
4
4
0
6
6
6
6
6
0
8
8
8
8
8
0
12
12
0.1
1
2
1
2
2
2
2
2
3
3
3
3
2
4
3
4
4
4
1
5
5
5
6
6
O2
1
1
1
2
2
2
1
2
3
2
3
3
2
2
3
3
4
4
1
3
5
5
7
4
03
1
1
1
1
1
2
2
1
2
2
2
3
1
2
3
4
3
4
2
3
4
4
7
5
0.4
1
1
1
1
1
1
1
2
1
3
3
2
1
2
1
2
3
4
1
3
3
4
3
5
O5
1
1
1
1
2
1
1
1
1
2
2
3
1
1
1
2
3
3
1
1
3
3
4
3
O2 03
0.4 0 5
Winner effect
G
E
Loser
effect
0.5
12 12 12
0
0
4
4
4
4
4
0
6
6
6
6
6
0
8
8
8
8
8
0
12
0.1
2
3
3
3
3
3
3
4
4
4
5
4
3
5
5
6
6
6
3
6
8
8
10
9
0.2
2
2
2
3
2
3
2
3
4
4
4
4
2
3
4
5
4
1
6
6
6
7
7
03
2
1
2
2
2
2
2
2
2
2. 3
3
1
3
3
3
4
4
1
4
4
5
6
6
0.4
1
2
2
2
2
2
2
2
1
2
3
3
2
2
2
3
3
4
1
2
3
4
5
5
0J
1
1
1
1
2
2
1
2
2
2
3
3
1
2
2
3
2
4
1
2
3
4
4
4
12 12
12 12
Figure X
The number of individuals in a group that can be anigned a clear rank order position. (A) N « 4, <t> «* 1.0, B) N » 6, <I> •= 1.0, (C) N «• 8,
<I> - 1.0. (D) N - 12, <D - 1.0, (E) N - 4, * - 0.5, (F) ?v" - 6, * - 0.5, (G) A/ - 8,1> - 0.5, (H) N - 12, <& - 0.5. See text for more
^/•taiu and Figure 1 for «^tail« on distribution of interactions in A.
although Landau's (1951a,b) initial work on winner and loser
effects was followed in great detail by Chase (1974, 1982),
these models concentrate on Landau's index of linearity (H)
and do not examine how winner and loser effects operate
when RHP is assessed and individuals can choose not to engage in any interaction, nor do these models examine how
winner and loser effects produce dramatically different kinds
of hierarchies.
From a behavioral endocrinological/mechanistic perspective, the fact that winner and loser effects can make such a
difference on the type of hierarchy uncovered may not be
extremely surprising, as aggressive and submissive behaviors
are not typically under the control of the same exact suite of
hormones (Leshner, 1978), thus allowing for the large differences seen in hierarchy structure when "^mining each effect
in isolation of the other. It should be noted, however, that we
actually know very little about underlying mechanisms involved in any specific example of documented winner and
loser effects, nor do we truly understand how such mechanisms are translated into complex behavioral interactions. As
such, I use the terms winner and loser "effects" only within
the contexts of the parameters I examined in this model and
do not claim to understand how such effects manifest themselves in any given system.
It is .important to note that this model does not examine
the evolution of winner and loser effects, but rather the ramificatiens of these effects, should they exist. Future models
examining the evolution of winner and loser effects themselves will no doubt be informative.
Given this caveat, the question remains as to how one could
test the predictions of the model presented here. In principle.
this could be done in a straightforward comparative study that
would employ species that had documented winner or loser
effects and within which one could gather the behavioral data
on aggressive interactions—a dear prediction being that species with individuals that were subject to winner effects would
show very definable hierarchies, while species in which loser
effects were found would show only dear alpha, and perhaps
beta, individuals. Unfortunately, the data for such a comparison do not yet exist That is, although the general phenomena of prior contests affecting the outcome of subsequent interactions is evident in a wide variety of taxa (insects: Alexander, 1961; Burk, 1979; molluscs: Zack, 1975; fish: Beaugrand
and Zayan, 1985; Francis, 1983; Frey and Miller, 1972; birds:
Drummond and Osomo, 1992; rodents: van de Poll et al.,
1982), and despite controlled studies on both winner (Bakker
and Sevenster, 1983; Bakker et al., 1989; Burk, 1979; Chase et
aL, 1994; Frey and Miller, 1972) and loser effects (Francis,
1983, 1987; Beaugrand and Zayan, 1985; Beacham and Newman, 1987; Bakker et aL, 1989), no study has documented
both winner and loser effects in a single spedes (using some
controlled, pairwise testing system; see Chase et al., 1994) and
the detailed nature of behavioral interactions when individuals are in groups. I hope the results of this model will spur
such studies in the future.
I thank J. Beacham, I. Chase, A. Dugatkin, D.Dugatkin and H.K.
Reeve, L. Wolf, and two anonymous reviewers for suggestions on earlier versions of this paper.
Dugatkin • Winner and loter effects and dominance hierarchies
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