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Behavioral Ecology Vol. 13 No. 2: 260-267
© 2002 International Society for Behavioral Ecology
Kleptoparasitism and the distribution of unequal competitors
Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Address correspondence to I.M. Hamilton, who is now at the Department of Biology, Concordia University, Montréal, QC H3G 1M8, Canada. E-mail: ihamilt{at}vax2.concordia.ca .
Received 16 October 2000; revised 18 May 2001; accepted 1 June 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Kleptoparasitism is an important means by which many animals obtain limited resources. The success of kleptoparasitism may be influenced by a number of factors, including competitive differences among individuals and the spatial distribution of prey and hosts. I used ideal free distribution (IFD) theory to predict the spatial distribution of kleptoparasites and their hosts between two patches differing in quality and to predict how the use of kleptoparasitism was influenced by the relative searching and fighting abilities of classes of competitors. Unlike previous IFD models incorporating kleptoparasitism, I allowed competitors to choose between attempting kleptoparasitism or searching for undefended prey. When the rates of resource inputs into the patches were high, the model predicted little use of kleptoparasitism. If competitive types were equally able to displace others from resources, then those individuals that were poorer at searching for food were more likely to kleptoparasitize. If competitive types differed in their abilities to displace others, kleptoparasites were exclusively those individuals that were best able to do so. Regardless of their competitive type, a higher proportion of individuals in the high-quality patch were kleptoparasitic, while the total density of competitors in the high-quality patch was lower than that expected based on the ratio of resource inputs. These predictions differ from previous IFD models of kleptoparasitism, suggesting that the mechanisms involved in searching for and obtaining resources can influence the spatial distribution of animals.
Key words: habitat use, ideal free distribution, producer-scrounger model, searching efficiency, simulation model.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Among the fundamental decisions that a foraging animal must make are how to obtain food and where to forage. When animals forage in the presence of others, they may have the option of attempting to usurp resources from successful foragers rather than finding food on their own. This is referred to as kleptoparasitism, and it is an important component of many social foraging systems (Brockmann and Barnard, 1979
). The use of kleptoparasitism reflects a variety of social
and ecological factors, including dominance status
(Barta and Giraldeau, 1998),
the net benefits of alternative options
(Barnard and Sibly, 1981;
Barta and Giraldeau, 1998) and
the availability of opportunities for kleptoparasitism
(Brockmann and Barnard,
1979).
Opportunities for kleptoparasitism will be greater when there is a high
density of potential hosts relative to prey. In birds, kleptoparasitism is
more common when handling times are long, so that there is a high density of
handlers, and the density of competitors relative to food is high (reviewed in
Brockmann and Barnard, 1979).
In a patchy environment, opportunities for kleptoparasitism will depend on the
distribution of potential hosts among patches, which may reflect avoidance of
kleptoparasites (Parker and Sutherland,
1986). Social factors interact with these ecological variables to
determine the net benefits of kleptoparasitism. Kleptoparasitism is often more
prevalent among either high-ranked or low-ranked individuals
(Barta and Giraldeau, 1998;
Brockmann and Barnard, 1979).
Kleptoparasitism by high-ranked individuals may be attributed to their greater
ability to displace hosts (e.g., Harris's sparrows, Zonotrichia
querula: Rohwer and Ewald,
1981). However, low-ranked individuals may use kleptoparasitism if
they are otherwise prevented by dominants from obtaining resources (e.g., kelp
gulls, Larus dominicanus: Steele
and Hockey, 1995).
For many years, the ideal free distribution (IFD) of Fretwell and Lucas
(1970) and its subsequent
modifications have been used to interpret the interplay between behavior,
including kleptoparasitism, and the spatial distribution of animals among
patches differing in intrinsic quality. The basic assumptions of all IFD
models are that individuals have perfect knowledge of the quality of all
patches (ideal), they are able to move among patches at no cost to their
fitness (free), and that the quality of patches is changed (usually decreased)
as competitor density in that patch increases. The IFD is the Nash equilibrium
distribution of individuals among patches, at which no individual can improve
its payoff by unilaterally moving.
There have been several attempts to model ideal free habitat use by unequal
competitors using intraspecific kleptoparasitism (e.g.,
Holmgren, 1995;
Korona, 1989;
Parker and Sutherland, 1986),
which predict either a range of stable distributions of competitors
(Holmgren, 1995;
Korona, 1989), or no stable
equilibrium (Parker and Sutherland,
1986). However, these models assumed that kleptoparasites always
kleptoparasitized when encountering a host, ignoring the possibility that the
payoff for kleptoparasitizing may be so low that that individual should switch
to searching for prey (Stillman et al.,
1997). Incorporating kleptoparasitism as a tactical decision of a
potential attacker may have important consequences for the predicted
distribution of individuals.
In this article, I present a model predicting the use of kleptoparasitism by unequal competitors and the distributions of kleptoparasitic and nonkleptoparasitic individuals among patches. I allowed the form of competition to be a decision made by foraging individuals. I examined how variation in scramble competitive ability, the probability of winning a kleptoparasitism attempt, and the rates that resources are input into the patches influence these predicted distributions.
The model
The model describes a system in which there are two patches that differ in
the rates that prey enter. The prey dynamics in each patch are those of a
continuous input system (Parker and
Sutherland, 1986). That is, upon entry into a patch, prey are
captured immediately by a predator, but not consumed immediately. The
probability that a predator captures a prey item in each time unit depends on
the rate of prey input and competition with other predators in the patch.
Individuals select one of the two patches in which to forage and use one of two forms of competition: searching or kleptoparasitism. Searchers wait for undefended prey to enter the patch and do not initiate interactions with other foragers. Kleptoparasites attempt to steal prey from handling individuals (hosts). Therefore, there are a total of four tactics that an individual can play: searching in the more productive patch, kleptoparasitizing in the more productive patch, searching in the less productive patch, and kleptoparasitizing in the less productive patch.
I incorporated competitive differences between individuals by dividing the population into competitive types that differ in either their abilities to find and capture prey (searching efficiency) or in their probabilities of winning should they attempt kleptoparasitism (fighting ability). Individuals cannot change these competitive abilities. These differences may therefore reflect differences such as body size, age, or species.
Model payoffs
All parameters used in the model are shown in
Table 1. To solve for the
payoff for choosing each tactic, I used the mechanistic framework of Ruxton
and Moody (1997) and Holmgren
(1995). For each competitive
type (i), patch (j), and form of competition (k,
kleptoparasites: k = 1, searchers: k = 2), I divided the
population into four states: searching for prey or handlers
(sijk), handling
(hijk), fighting and eventually winning
(wijk), and fighting and eventually losing
(lijk)
 | (1) |
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Prey enter each patch at the rate Rj. Patch 1
is assumed to be the more productive patch; i.e.,
R1 > R2. Prey
density in the patch, xj, changes as a function
of the input rate of resources (Rj) and the rate
of encounters between searchers and prey. This latter rate is simply the
densities of searchers (k = 2) and prey
(xj) multiplied by their searching efficiency
(CWi). Searching efficiency may be thought of as
a function of the speed with which the animal scans the patch and its ability
to detect and capture prey. Thus, the rate of change in the prey density
(xj) is:
 | (2) |
At equilibrium, Equation 2 must equal zero. Solving for
xj at equilibrium
(x*j) yields:
 | (3) |
The rate of transition from searching to handling
(Cijk) is the density of searchers, multiplied by
the density of food and the competitive weight of searchers:
 | (4) |
 | (5) |
Upon capture of an item, searchers become handlers
(hijk). If uninterrupted, handlers process prey
for Th time units before ingesting it. During
this time, handlers remain in the patch where they captured prey, and are
vulnerable to attack by any kleptoparasites in that patch. The transition from
handling back to searching is:
 | (6) |
Kleptoparasites (k = 1) attempt to steal food from handlers.
However, they are in competition with other kleptoparasites for opportunities
to steal food. The probability that a kleptoparasite will encounter a handler
is a function of the densities of handlers and the searching efficiency of the
kleptoparasite. The probability that the kleptoparasite will obtain the item
is a function of its fighting ability, Fi, the
fighting ability of the attacked handler, Fq, and
the handler's ownership advantage, A:
 | (7) |
Kleptoparasites are assumed to encounter and attack handlers randomly. For
kleptoparasities, the rates of transition from searching to fighting (and
either winning, EW, or losing, EL) are:
 | (8) |
 | (9) |
 | (10) |
 | (11) |
Fighting takes time and ends with one winner and one loser. Winners become
handlers, while losers return to searching for prey or hosts. The time spent
fighting by winners and losers, respectively, is Tw and
Tl. In most simulations, I assumed that
Tl was equal to Tw. The rates of
transition from fighting to winning or losing are:
 | (12) |
 | (13) |
 | (14) |
 | (15) |
 | (16) |
 | (17) |
The above equations were iterated for 50 time units, which was sufficient
to reach steady state (no change in the proportion of the population
searching, handling, and fighting within each competitive type and tactic
between time steps). At steady state, per capita intake rate for individuals
of a given competitive type and tactic (Iijk) is the
proportion of the individuals of interest that are currently in the final time
step of handling (i.e., the probability that an individual is ingesting prey
each time step):
 | (18) |
Finding the evolutionarily stable strategy by simulation
To find the evolutionarily stable distribution of individuals among
tactics, I started the simulations with a random proportion of each
competitive type in each of the four possible tactics and solved for per
capita intake rate as described above. I then allowed individuals to
reproduce, with the contribution of a particular tactic to the next generation
being its fitness (intake rate, Iijk, relative to mean
intake rate for all tactics) multiplied by its current representation in the
population. I assumed that density-dependent processes kept population sizes
constant. To test for stability, each generation a small proportion (
=
0.001) of individuals joined or left each particular tactic (with probability
of 0.5 for each). This perturbation may represent either mutation over
evolutionary time or individuals switching tactics over ecological time
(Houston and McNamara, 1987;
Hugie and Grand, 1998). I
considered stability to have been reached when all intake rates (for the same
competitive type) were within 0.5% of each other and distributions returned to
equilibrium upon perturbation for four consecutive generations.
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RESULTS |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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I ran five simulations for each of a variety of combinations of searching efficiencies, fighting abilities, ownership advantages, and resource input rates (Table 1). Increasing density had the same effects on the distribution of individuals among tactics as decreasing overall patch input rates. Simulations reached a stable equilibrium within 10-200 generations. The results are summarized in Table 2.
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Frequency of kleptoparasitism
At high resource input rates, only a small proportion of individuals were
kleptoparasitic. As resource input rates decreased, this proportion increased
asymptotically (Figures 1 and
2). When competitive types
differed in their abilities to win a contest that they initiated (fighting
ability, F), only those individuals with high fighting abilities used
kleptoparasitism (Figure 1a). There was a unique, stable proportion of these individuals that used
kleptoparasitism. This proportion increased as their relative fighting weight
increased and ownership advantage decreased
(Figure 1b).
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When competitive types differed in their abilities to search for resources or hosts (CW), both individuals with high and low searching efficiencies used kleptoparasitism. Those with relatively low searching efficiencies were more likely to use kleptoparasitism (Figure 2a). The mean proportion of better searchers that used kleptoparasitism decreased with increasing resource input rates (Figure 2a). The mean proportion of poorer searchers using kleptoparasitism decreased with both increasing resource input rates and increasing use of kleptoparasitism by better searchers. This resulted in the highest use of kleptoparasitism by poorer searchers being at intermediate resource input rates, when most or all of these individuals were kleptoparasitic (Figure 2a).
When competitors differed in searching efficiencies, there was not a
unique, stable proportion of individuals using kleptoparasitism for all
simulations with the same parameters. However, if competitors were weighted by
their searching efficiencies, there was a unique, stable proportion of the
total competitive weights (sensu
Parker and Sutherland, 1986)
in the population that were kleptoparasitic. This proportion increased with
decreasing ownership advantage and with increasing differences in searching
efficiencies between competitive types
(Figure 2b).
Distribution between patches
When competitive types differed in fighting abilities, there was a unique,
stable distribution of competitors between patches for each combination of
parameters. When competitive types differed in their abilities to search for
prey or hosts, there was no single distribution of individuals between patches
that was stable in all simulations for the same set of parameters. In this
case, when individuals were weighted by their searching efficiency, there was
a unique, stable distribution of competitive weights between patches (as in
Parker and Sutherland,
1986).
When there were no kleptoparasites in the population, the distribution of
individuals (or competitive weights when individuals differed in searching
efficiency) between patches matched the distribution of resource inputs into
the two patches (as in Parker and
Sutherland, 1986; Figure
3). Matching resource inputs were therefore found when resource
input rates and ownership advantage were high.
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When kleptoparasites were present in the population, the distribution of individuals or competitive weights tended to undermatch the distribution of resource inputs (Figure 3). In other words, foragers tended to overuse the patch with lower resource input rates. This overuse of the poorer quality patch became progressively greater as the number or competitive weight of kleptoparasites in the population increased (Figure 3). Thus, there was greater undermatching of resource inputs when resource input rates were low and there were greater differences in fighting or competitive abilities. Regardless of whether competitors differed in fighting or searching efficiencies, a greater proportion of individuals in the high-quality patch used kleptoparasitism (Figure 4).
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When competitors differed in their abilities to win contests, individuals with high fighting abilities were more likely to use the high-quality patch than were individuals with lower fighting abilities (Figure 5a). When ownership advantage was high and kleptoparasitism therefore relatively rare, most or all individuals with high fighting abilities (and therefore most or all kleptoparasites) were confined to the high-quality patch (Figure 5a). When competitive types differed in searching efficiencies, they did not consistently differ in which patch they tended to use (Figure 5b).
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Sensitivity to time costs
I examined the influence of increasing handling time (by 5 time units),
increasing fighting time (by 5 time units), and changing the relative fighting
times of winners and losers on these distributions. Qualitatively, the
patterns described above did not change with changes in handling or fighting
time. The proportions of individuals or competitive weights that were
kleptoparasitic increased when handling time was increased and decreased when
fighting time was increased. I also increased the fighting time of losers of
contests relative to winners of contests. This may occur if losers must move
from the location of the fight before they can return to searching. However,
changing the relative fighting times of losers and winners had no effect on
the equilibrium proportion of kleptoparasites.
In all cases, there was the same negative relationship between the proportions of individuals or competitive weights that were kleptoparasitic and those in patch 1 described above. This meant that there were fewer competitors in patch 1 when handling time was increased and more when fighting time was increased.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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This model adds further realism to the existing theoretical framework of patch selection by kleptoparasites by allowing an individual to choose whether to kleptoparasitize when it has the opportunity. It makes testable predictions regarding how the use of kleptoparasitism and of patches differing in quality change with respect to changes in attributes of prey (such as handling time) and competitors (such as relative competitive and fighting abilities). These predictions are summarized in Table 2.
Although both intra- and interspecific kleptoparasitism have long been
recognized as an important alternative resource acquisition tactic,
particularly in birds (Brockmann and
Barnard, 1979), there are relatively few studies that provide
sufficient information with which to test the predictions of this model.
Increases in the frequency and intensity of kleptoparasitism with competitor
density and handling time are commonly observed (reviewed in
Brockmann and Barnard, 1979,
see also Stillman et al.,
1997). These are consistent with the predictions of this model,
which predicts greater use of kleptoparasitism when resource inputs are low
relative to the density of competitors and handling times are high. My model
further predicts that the frequency of kleptoparasitism should change with
changes in the relative abilities of unequal competitors to find resources and
to displace one another from resources.
The frequency of kleptoparasitism often differs between age or sex classes
or with dominance status (reviewed in Barta
and Giraldeau, 1998; Brockmann
and Barnard, 1979). My model predicts how individuals differing in
social status should differ in their use of the kleptoparasitic strategy. When
the differences between classes are in terms of their abilities to find
resources, rather than in their abilities to defend or displace others from
resources, then those individuals that are poor at finding resources should be
more likely to use kleptoparasitism. If, on the other hand, individuals differ
in their abilities to displace one another from resources, kleptoparasites
should exclusively be those individuals that are better at doing so.
When there is a strong dominance hierarchy, with dominants able to displace
subordinates, dominants commonly join and displace subordinates at resource
patches (e.g., Harris's sparrows: Rohwer
and Ewald, 1981). This is consistent with the predictions of the
model. However, in some systems, low-ranked individuals also use
kleptoparasitism. For example, both juvenile and adult kelp gulls will engage
in intraspecific kleptoparasitism (Hockey
and Steele, 1990, Hockey et
al., 1989, Steele and Hockey,
1995). Juvenile gulls are less successful than adults at finding
food (Hockey et al., 1989).
However, kleptoparasites have a high probability of winning fights that they
initiate (i.e., ownership advantage is low), and there is little difference in
the fighting ability of juveniles and adults
(Hockey et al., 1989). Under
these conditions, it would be expected from my model that juveniles would be
more kleptoparasitic than adults. Although both age classes will engage in
kleptoparasitism, juveniles are more likely to do so
(Hockey et al., 1989;
Steele and Hockey, 1995).
My model also predicts that differences in patch use by unequal competitors
should be related to their use of kleptoparasitism. Male dung flies
(Scatophaga stercoraria) engage in kleptoparasitic interactions over
females arriving at dung pats. Borgia
(1980) found that small males
avoid pats with a high density of large males, but if large males are removed,
small males recruit to those pats. In this system, small and large males are
equally likely to be attacked, but large males are more likely to initiate
attacks. There is a very high ownership advantage in dung flies, with <2%
of attempted takeovers successful (Parker,
1970). Under these conditions, my model predicts greater use of
highly productive patches by large, kleptoparasitic males relative to small
males.
Assumptions of the model
The model assumes that, within a patch, there is complete mixing of
competitors and no choice of hosts. This is unlikely to be true in many
circumstances (Ens et al.,
1990). If individuals selectively kleptoparasitize those
individuals that are most easily attacked, this may decrease the advantage of
searching for prey for individuals that are likely to lose contests.
In this model, handlers are assumed to remain where they captured food.
However, if moving among patches entails few costs to handlers, they may move
to patches where kleptoparasitism is less likely. If kleptoparasites can also
easily move and hosts are equally susceptible to kleptoparasitism in all
patches, then this may not affect the predictions of the model, as
kleptoparasites will follow hosts. However, if some habitats are intrinsically
safer from kleptoparasitism than others, or if the distribution of
kleptoparasites is fixed for some reason, then patterns of habitat selection
would be expected to change (as in predator—prey habitat selection
games; Heithaus 2001;
Hugie and Dill, 1994).
Comparison with other models
Several recent models (Broom and Ruxton,
1998; Sirot 2000;
Stillman et al., 1997) have
also modeled interference competition incorporating decision-making by
individuals regarding the form of competition. Broom and Ruxton
(1998) and Sirot
(2000) predicted that
kleptoparasitism and aggressive interactions within groups should increase
with increasing density and handling time. However, these models did not
consider competitive differences among group members, although Sirot's
(2000) model did allow the
targets of kleptoparasitism to not defend their resources. Stillman et al.
(1997) did include competitive
differences and predicted that interference was likely when competitor density
was high, the probability of winning fights was high, and prey encounter rates
were low. The general predictions of these and my model are consistent.
Stillman et al. (1997) also
predicted that only dominant competitors should interfere, while subordinates
should attempt to avoid interactions. In their unequal competitors model,
dominants always won interactions. Because subordinates had no chance of
winning, they did not initiate interactions. In my model, poorer competitors
sometimes use kleptoparasitism, but only when competitive differences were in
terms of abilities to search for prey and hosts, rather than ability to win a
contest that they initiate.
Three previous IFD models incorporated kleptoparasitism among unequal
competitors (Holmgren, 1995;
Korona, 1989;
Parker and Sutherland, 1986).
Parker and Sutherland (1986)
predicted cycling of individuals between patches for either constant or
continuous-input prey dynamics. I never found cycling in my simulations.
Korona (1989) predicted input
matching of all competitor types. Although I found input matching of total
competitive weights, it was only in the absence of kleptoparasitism.
Holmgren (1995) predicted a
semitruncated distribution with all dominant individuals in the more
productive patch and subordinates distributed between patches. My model also
predicted more use of the high-quality patch by better competitors, but this
approached a semitruncated distribution only when ownership advantage,
A, was high, the same conditions under which kleptoparasitism is
rare. In other words, a semitruncated distribution was only predicted when a
handling individual was unlikely to lose resources to a kleptoparasite
(Figure 5). Part of the reason
for this difference in predictions stems from my assumption that searching for
prey and searching for hosts are mutually exclusive. When this is so,
kleptoparasites cannot aggregate together in a patch that contains solely
other kleptoparasites. In Holmgren's
(1995) model, kleptoparasites
could also search for prey and could therefore aggregate with other
kleptoparasites.
These differences suggest that whether kleptoparasites are also able to
search for undefended prey as well as hosts has a major effect on the
predicted distribution of competitors between patches. In intraspecific
kleptoparasitism, individuals typically do not specialize in exclusive
kleptoparasitism (Giraldeau et al.,
1991; Hansen, 1986;
Koops and Giraldeau, 1996).
However, a generalized forager may use a mixed strategy of kleptoparasitism
and searching for prey and still be unable to search for both prey and hosts
simultaneously. To my knowledge, there are no studies on whether animals can
simultaneously search for prey and hosts. However, Lima and Bednekoff
(1999) found that dark-eyed
juncos were able to detect approaching predators when not vigilant, although
with reduced efficiency. The ability to detect both prey and hosts likely
depends on the sensory mechanisms used in searching and the cognitive
trade-offs associated with searching for different items. More research on
these cognitive aspects of foraging is needed to determine the appropriateness
of assuming mutually exclusive versus simultaneous searching for prey and
hosts for any particular system.
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ACKNOWLEDGEMENTS |
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I thank L.M. Dill, M.R. Heithaus, B. Roitberg, and R.C. Ydenberg and anonymous reviewers for comments on earlier versions of this manuscript. Development of the model benefited from discussions with M. Belisle, J. Brown, R. Dukas, L.M. Dill, T. Grand, M.R. Heithaus, N. Hughes, D. Hugie, J. Mitchell, D. Moore, Y. Morbey, F. Sharpe, and P. Willis. This research was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) grant A6869 to L.M. Dill and an NSERC Postgraduate Fellowship and a Simon Fraser University Graduate Fellowship to I.M.H.
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A. Ridley and N. Raihani Facultative response to a kleptoparasite by the cooperatively breeding pied babbler Behav. Ecol., March 1, 2007; 18(2): 324 - 330. [Abstract] [Full Text] [PDF]
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I. M. Smallegange and J. van der Meer Interference from a game theoretical perspective: shore crabs suffer most from equal competitors Behav. Ecol., January 1, 2007; 18(1): 215 - 221. [Abstract] [Full Text] [PDF]
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A. Kun, G. Boza, and I. Scheuring Asynchronous snowdrift game with synergistic effect as a model of cooperation Behav. Ecol., July 1, 2006; 17(4): 633 - 641. [Abstract] [Full Text] [PDF]
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D. A. Shealer, J. A. Spendelow, J. S. Hatfield, and I. C. T. Nisbet The adaptive significance of stealing in a marine bird and its relationship to parental quality Behav. Ecol., March 1, 2005; 16(2): 371 - 376. [Abstract] [Full Text] [PDF]
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I. M. Hamilton and L. M. Dill The use of territorial gardening versus kleptoparasitism by a subtropical reef fish (Kyphosus cornelii) is influenced by territory defendability Behav. Ecol., July 1, 2003; 14(4): 561 - 568. [Abstract] [Full Text] [PDF]
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