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Behavioral Ecology Vol. 10 No. 6: 726-732
© 1999 International Society for Behavioral Ecology
A test of the sequential assessment game: the effect of increased cost of sampling
Department of Zoology, Division of Ethology, Stockholm University, 106 91 Stockholm
Address correspondence to O. Brick. E-mail: brick{at}zoologi.su.se .
Received 20 December 1998; revised 8 May 1999; accepted 10 May 1999.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The sequential assessment game describes a fight between two conspecifics as a statistical sampling process, allowing for specific predictions about fight duration and number of repetitions of a behavioral element depending on relative fighting ability. Fight duration and number of repetitions of a behavioral element correlate moderately to relative fighting ability. Variation in real contests depends on differences between the contestants in the ability to incur cost and the value of the contested resource. I hypothesized that an additional source of variation is differences between individuals in their perception of how dangerous it is to fight. To investigate this, I used the risk of predation to study the effect on the use of different agonistic behaviors in fights between males of the cichlid fish Nannacara anomala. In the group subjected to predation risk, the time until the most escalated behavior (mouth wrestling) was more variable and increased significantly on average. In addition, the duration of fights was significantly longer. In the predator treatment the use of visual assessment and tail beating varied more than in the control, giving a significant positive relationship between the use of low-intensity behaviors and time to mouth wrestling across the group. These relationships were less pronounced in the control group. The effect of predation risk on optimal information transfer is discussed based on the behavioral mechanism suggested by the sequential assessment game.
Key words: cichlids, fighting behavior, Nannacara anomala, predation risk, sequential assessment.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The sequential assessment game (Enquist and Leimar, 1983
,
1987;
Enquist et al., 1990;
Leimar, 1988;
Leimar and Enquist, 1984)
describes a fight between two contestants as an ongoing statistical sampling
process, which makes it possible to predict fight duration and number of
repetitions of a behavioral element depending on relative fighting ability
(e.g., relative weight). A large asymmetry in relative fighting ability can be
assessed using only low-intensity behaviors
(Enquist et al., 1987). A
small asymmetry between contestants is assessed either by using more
repetition of a behavior or more costly and informative behaviors
(Enquist and Jakobsson, 1986).
The model has been supported qualitatively and quantitatively by empirical
data (Hack, 1997;
Keeley and Grant, 1993;
Koops and Grant, 1993;
Leimar et al., 1991), but some
variation in contest behavior remains unexplained
(Enquist et al., 1990; see also
Koops and Grant, 1993;
Turner and Huntingford,
1986).
Two factors have been shown to influence the variation found in real
contests: differences between the contestants in the ability to impose cost on
the opponent and the value of the contested resource
(Austad, 1983;
Enquist and Leimar, 1987;
Grafen, 1987;
Maynard Smith, 1982;
Parker, 1974). Individuals may
also differ in inherent aggressiveness, which may be a source of variation
(Barlow et al., 1986). However,
in this study I consider another potential source of variation—that
individuals differ in their assessment of the risk associated with the fight.
Fighting behavior can cause loss of time and energy and can inflict injuries,
but there may also be other costs associated with fighting. The risk of
predation has been suggested as a potential cost of intense fighting
(Dow et al., 1976;
Jakobsson, 1987). However,
until recently no empirical studies existed to support this notion. Martel and
Dill (1993) found that
juvenile coho salmon significantly decreased their aggressive behavior toward
their own mirror image when they could smell a bird predator in the water.
Evidence has also been presented that escalated fighting behavior could
increase predation risk due to decreased vigilance in the willow warbler
Phylloscupos trochilus and in the South American cichlid fish
Nannacara anomala (Jakobsson et
al., 1995). Males of N. anomala also showed reluctance to
reescalate to mouth wrestling, a high-intensity behavior, after a sudden
introduction of a model predator and changed the performance of the mouth
wrestling after the introduction of a model predator
(Brick, 1998).
Based on these findings, I make two assumptions about the effect of
predation risk. First, I assume that the risk of predation influences the
overall cost of obtaining a sample of relative fighting ability. Second, I
assume that the animal's assessment of current risk of predation influences
its choice of behavior during agonistic interactions. Even if the cost of
predation has never been explicitly acknowledged by game theorists, Maynard
Smith (1974: 215) wrote,
"the cost of the contest is again measured by the expenditure of energy
and any other risks that may be associated with a protracted contest."
Thus, the objective of this study was to determine what effect an increased
risk of predation has on the sequential assessment of relative fighting
ability between male N. anomala. By using the risk of predation to
increase the cost of information acquisition, I was also able to test
predictions from the sequential assessment game
(Enquist and Leimar, 1987;
Enquist et al., 1990;
Leimar, 1988) of the use of
different agonistic behaviors in relation to increased cost of sampling.
Effects of increased risk of predation: predictions and
mechanisms
The first prediction, which does not originate from the sequential
assessment game per se, is that an increased risk of predation will lead to
increased variation in behaviors used and in duration of contests
(Table 1, case A). A
hypothetical mechanism of increased variation in behaviors when predation risk
increases is that animals differ in their assessment of how dangerous it is to
fight and use different behaviors according to the assessed risk
(Table 1, case A, prediction
1). Still, decreased vigilance during the most escalated behaviors
(Brick, 1998;
Jakobsson et al., 1995) would
make the animals hesitate to escalate, which leads to longer fighting times
(Table 1, case A, prediction
2). The sequential assessment game contains two parameters that can be
altered. The parameters are the cost of obtaining a sample of relative
fighting ability and the accuracy of the information about relative fighting
ability that is transferred during a fight. Increasing the cost of obtaining a
sample of relative fighting ability gives two opposite predictions on behavior
used and duration of fights: either shorter fights with high-intensity
behaviors or longer fights with low-intensity behaviors. The hypothetical
mechanism behind shorter fighting times facing an increased risk of predation
is that the animals want to minimize the time exposed to predation risk and
escalate to the most decisive behaviors to settle the fight as soon as
possible (Table 1, case B,
predictions 1 and 2).
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The hypothetical mechanism of longer fighting times is that animals choose
behavior so that the precision increases optimally for a given risk. Thus, to
compensate for an increased risk of predation, the animals could decide to use
more repetitions of a low-intensity behavior to accumulate more information at
a relatively lower risk and thus avoid escalated behaviors. Because the
information content in the low-intensity behaviors is limited, the animals
have to escalate to settle the fight, but the entire fight would take more
time, giving the opposite prediction on fighting times
(Table 1, case C, prediction 1
and 2). Increased risk of predation would then push the evolutionary stable
switching line toward longer fighting times
(Figure 1, case C). From a
biological point of view only case C should be considered plausible. Previous
studies have shown seriously decreased vigilance during the most escalated
behaviors, whereas animals that are engaged in low-intensity agonistic
behaviors are able to maintain their vigilance
(Brick, 1998;
Jakobsson et al., 1995). It is
therefore more likely that an increased risk of predation will lead to longer
fighting times and an increased use of low-intensity behaviors, rather than
fierce fighting.
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The second parameter in the model is the accuracy of the information about relative fighting ability transferred during a fight. If the risk of predation decreases the accuracy of the information, the sequential assessment game predicts that additional repetitions of a behavioral element are needed to increase the accuracy, compared to a contest without predation risk. This would lead to longer fighting times (Table 1, case D, predictions 1 and 2). The hypothetical mechanism to a decreased accuracy is that animals may have to divide their attention between the opponent and a potential predator. In fact, this is a special case of optimization of information transfer because increasing the number of repetitions can compensate for less accurate sampling. It was not possible within this study to distinguish between case C and D (Table 1). They are not mutually exclusive.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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All tests were carried out between 17 October 1995 and 2 April 1996 at Tovetorp Zoological Research Station in south-central Sweden. I used males of the South American cichlid fish N. anomala. The animals came from a stock of originally 250 animals purchased from a local dealer. When males from the brood started to show secondary sexual characters (approximately 6 months after hatching), I isolated them in holding aquariums (30 x 30 x 30 cm) for at least 2 months before they were used in a test. I fed the fish twice daily on live midge larvae and dry fodder to keep fighting ability, resource value, and the value of the future equal for all contestants. All aquariums contained a substrate of gravel and a flower pot made of clay. The temperature was held constant at 26°C and a 12:12 h light:dark cycle was maintained. The fish weighed between 1 g and 2.5 g. I matched the fish in pairs of equal weight. In 20 out of 27 pairs, the difference in weight was less than 1%. The weight difference in the remaining seven dyads were 6% in two dyads (1.5 g versus 1.6 g in both dyads), 7% in two dyads (1.4 g versus 1.5 g and 1.3 g versus 1.4 g), 8% in two dyads (1.2 g versus 1.3 g in both dyads), and 9% in one dyad (2.1 g versus 2.3 g). I used each fish only in a single contest.
Nine dyads were not exposed to any predator stimulus and were used as a
control group, group 1. To find an appropriate predator stimulus, I used two
treatment groups. One treatment group (n = 9) was subjected to a
model predator with no facial features except the rude shape of a forepart of
a fish. The other treatment group (n = 9) was subjected to a model
predator with eyes and an open jaw. Both model predators were grayish and
black and measured 15 x 7 x 6 cm (length x height x
width) (Brick, 1998). However,
the two treatment groups did not differ from each other in any of the
investigated variables, and I pooled them in the analyses, group 2. There was
no difference in weight asymmetry between the groups (Mann-Whitney U
test; n1 = 9, n2 = 18, U =
70, p =.59), nor was there a difference in absolute weight between
the groups (Mann-Whitney U test; n1 = 9,
n2 = 18, U = 279.5, p =.42).
Fighting behavior of Nannacara anomala
Fights between males of N. anomala start with low-intensity
behaviors which are gradually replaced by more dangerous and decisive
behaviors (Baerends and Baerends-van Roon,
1950; Jakobsson et al.,
1979). The fight is divided into three different phases, each
characterized by the use of a new behavioral element: lateral display, tail
beating, and mouth wrestling (Enquist and
Jakobsson, 1986; Enquist et
al., 1990). Bites often occur, and it has been suggested that one
fish can bite to force the opponent to escalate
(Enquist and Jakobsson, 1986).
The fish can also temporarily reverse the fighting sequence throughout the
fight (i.e., go from behavior of higher intensity to one of lower intensity).
Observations from large tanks suggest that N. anomala males try to
dominate a territory containing several females. However, males fight even if
there are no females in the tank, which suggests that the contested resource
is the alpha position (Enquist and
Jakobsson, 1986; Enquist et
al., 1990).
Experimental procedure
Twenty-four hours before a trial started, I moved two fish to the test
aquarium (30 x 30 x 30 cm). The test aquarium was divided into two
compartments of equal size by an opaque partition. Each compartment contained
a box in which each fish could be enclosed 5 min before the test started. For
the treatment group the models were then placed outside the test aquarium at a
distance of 25 cm, the mean distance at which contestants fled from an
approaching model predator in active mouth wrestling
(Jakobosson et al., 1995). The
opaque partition was taken away and the test started by remotely opening the
two boxes. I videotaped the fish from behind a blind.
Videotape analysis
I measured the duration of a fight from the first reciprocal agonistic
behavior until one of the fish won or for a maximum of 60 min. The
investigated variables were time until the initiation of each phase, the
duration of active visual assessment, and the number of tail beats. I
considered a behavioral phase complete once the reciprocal use of the next
behavior in turn appeared. If a dyad was still interacting through visual
assessment or tail beating after 60 min, I set the time until mouth wrestling
to the end of the experiment (censored data). The mouth wrestling phase was
considered complete if one of the contestants won the fight. The loser is
easily distinguished because he turns pale, folds his fins, and behaves
submissively (Enquist and Jakobsson,
1986). I also recorded inspection behavior. Inspection behavior
was defined as an approach alone or together toward the model predator in a
tentative manner while visually fixating the model predator
(Godin and Davies, 1995;
Magurran and Seghers, 1990;
Pitcher et al., 1986).
Statistical tests
Due to the non-normal distribution of the variation in the samples, all
tests used are nonparametric. I used the Mann-Whitney U test,
Kolmogorov-Smirnov two-sample test, and Spearman rank order correlation. In
addition, Gehan's Wilcoxon test for censored time series data (Statistica 5.1)
was used.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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General observations
Twenty-six of 27 dyads started the agonistic interaction with visual assessment and one dyad in group 1 began with tail beating. In group 1 all nine dyads escalated to mouth wrestling within the experimental period (60 min). In group 2, 12 of 18 dyads escalated to mouth wrestling. Three dyads escalated only to tail beating. In two of them, the reciprocal tail beating continued throughout the experimental period. In the remaining dyad, there was only one sequence of tail beating that lasted 5 s, but visual assessment continued, and one of the contestants delivered tail beats throughout the experimental period. The other fish did not surrender (i.e., did not signal its defeat). The remaining three dyads in group 2 performed only visual assessment. One dyad continued the visual assessment throughout the experimental period, while in the other two the interaction ceased after 21 s and 393 s, respectively. However, in both cases one of the contestants continuously followed its opponent that constantly backed off. Seven out of 9 trials in group 1 and 8 out of 18 trials in group 2 were settled. In 13 of the 15 terminated fights, the weight asymmetry was <1%. In the two remaining fights that were terminated, the size asymmetry was 7% (1.4 g versus 1.5 g) and 9% (2.1 g versus 2.3 g), one from each group. In both cases the lighter fish won.
In the breaks between agonistic behaviors, the dyads in group 2 spent a lot of time inspecting the model predator (Table 2). However, once the fish in the two groups had reached the mouth-wrestling phase, little inspection occurred. In group 2, inspection behavior was performed in 14 trials toward the exterior of the tank during the visual assessment phase, in 9 trials during the tail-beating phase, and in 3 trials during the mouth-wrestling phase. The corresponding numbers for group 1 were 1, 0, and 2.
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Escalation
A comparison between the groups shows that there was no difference in time
until the start of the fight (i.e., until the first reciprocal agonistic
behavior; Table 3). However,
escalation to mouth wrestling was slower in group 2
(Figure 2). Thus, it took
significantly longer for the dyads in group 2 to reach mouth wrestling
(Table 3). There was also a
significant difference in the distribution of time until mouth wrestling in
the two samples (Kolmogorov-Smirnov two-sample test: n1 =
9, n2 = 18, p >.025,
Figure 3). All the dyads in
group 1 had reached mouth wrestling before 30 min, in comparison with only
half of the dyads in group 2 (Figure
3). The duration of fights was significantly longer in group 2
compared with group 1 (Gehan's generalized Wilcoxon test for censored time
series: n1 = 9, median = 566 s, range = 295-2542 s,
n2 = 18, median = 3329.5 s, range = 194-3585 s, p
=.013).
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Behaviors used
Despite the significant difference between the two groups in time until
mouth wrestling and the significant difference in the duration of fights, the
duration of active visual and the number of tail beats before the onset of
mouth wrestling did not differ between the groups
(Table 3). However, the power
of these tests was low. There was only a 32% chance of rejecting the null
hypothesis at 
= 0.05 for the use of visual assessment and a 8% chance
to statistically detect a difference between the groups in the use of tail
beating. In both groups 1 and 2, there were positive relationships between the
use of low-intensity behaviors and time until the initiation of mouth
wrestling. However, in group 2 these relationships were more strongly
pronounced. This is because several dyads in group 2 used more low-intensity
behaviors before the onset of mouth wrestling (Figures
4 and
5).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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In agreement with case A, prediction 1, increasing the risk of predation significantly increased the variability in the use of different agonistic behaviors. Some dyads in the predation risk treatment used visual assessment and tail beating instead of escalating to mouth wrestling, while other dyads escalated to mouth wrestling like the dyads in the control group. The presentation of the model predator also significantly increased the time it took for the contestants to reach the mouth-wrestling phase and the duration of fights, supporting case A, prediction 2. After 30 min, all the dyads in the control group had reached mouth wrestling, while only half of the dyads had done so in the group subjected to increased risk of predation. A contributing factor to the slower escalation in the predation risk treatment was inspection behavior that occurred mostly during the low-intensity phases.
Because of the increased use of visual assessment and tail beating in some
of the dyads in the predator treatment, there was a significant relationship
between the use of low-intensity behaviors and time to mouth wrestling across
the group. In the control group, the relationship was less pronounced. As
hypothesized in case A, a possible mechanism behind the increased variation in
the group subjected to an increased risk of predation may be that individual
animals differ in their assessment of how dangerous it is to fight. If both
animals assess the danger to be high, they would agree to use only
low-intensity behaviors such as visual assessment or tail beating so that they
can maintain their vigilance. If the contestants differ in this respect and
one of the contestants starts to escalate, it is likely that the other
individual must also escalate to avoid getting bitten
(Enquist and Jakobsson, 1986).
Still, it would probably take a little longer before escalation occurred
compared to a dyad were both animals were likely to escalate quickly
(Leimar, 1988). If both
animals assess the danger to be low, they would agree to escalate in a way
similar to the dyads in a control group. If the animal's boldness
(Wilson, 1994) is known in
advance and the dyads are put together accordingly, the variation might
decrease within a group subjected to an increased risk of predation. This
prediction could easily be tested. However, the present study does not make it
possible to decide whether the variation indeed originates from differences
between individuals in boldness. It could also originate from differences
between the animals in their stress tolerance or from some other unknown
reason.
As already pointed out in the Introduction, the data do not give any
support to case B, predictions 1 and 2, that an increased risk of predation
would lead to less use of low-intensity behavior, faster escalation, and
shorter fights in order to minimize the time exposed to predation risk. The
explanation may be that even though animals may differ in their response to an
increased risk of predation, the price for lost mating opportunities in the
future would outmatch a smaller gain in fitness due to shorter fights and a
minimized time exposed to predation risk. However, there are circumstances
when fierce fighting could be expected
(Grafen, 1987).
A number of the dyads in the predator treatment group preferred to use
low-intensity behaviors, which ultimately led to longer fighting times on
average. There are two possible explanations for this. As suggested in case C,
animals may optimize information acquisition by the increased use of
low-intensity behaviors. Using low-intensity behaviors allows the contestants
to monitor the environment. However, the alternative suggestion, case D, is
also possible. Predation risk could degrade the accuracy of the information,
and the contestants could repeat the behaviors to increase the accuracy.
However, it is not possible from this experiment to uncover the mechanism.
Indeed, the suggested mechanisms are not mutually exclusive, and all the dyads
in the group subjected to an increased risk of predation may pay a cost in
terms of less accurate information being transferred during the fight. The
information available from visual assessment and tail beating is quickly
depleted (Enquist et al.,
1987), and "sloppy" mouth wrestling may result in
decreased accuracy in the information that is transferred. This could
ultimately lead to wrong decisions (i.e., the slightly lighter fish winning
the contest more often than expected during increased risk of predation). This
question deserves further attention.
To conclude, this study shows that an increased risk of predation leads to an increased variability in behaviors used and time until the initiation of the most decisive and dangerous behaviors in fights between male N. anomala. Increased predation risk also leads to longer fighting times on average. In addition, in some of the dyads, increasing the external acquisition costs changed the optimal sequence of information transfer in a way that can be interpreted in terms of the behavioral mechanism suggested by the sequential assessment game. The results indicate that individual differences in boldness contribute to the observed variation in real contests. A more accurate treatment and design of the experimental groups, taking into account individual differences in boldness, may lead to an even better fit between theoretical predictions and empirical data.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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I thank Olle Leimar, Björn Birgersson, and Magnus Enquist for discussions and improvements of earlier drafts of the manuscript. I am also thankful to Patsy Haccou for statistical advice and three anonymous referees for comments on the manuscript, Sven Jakobsson for support, and Nils Andbjer, Anders Bylin, and Susanne Strömberg for animal care. This study was supported by grants from the foundations Lars Hiertas Minne, Hierta Retzius stipendiefond, and Alice och Lars Silléns fond.
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