Behavioral Ecology Vol. 12 No. 2: 121-127
© 2001 International Society for Behavioral Ecology
Breeding colonies as information centers: a reappraisal of information-based hypotheses using the producer—scrounger game
a Behavioural Ecology Research Group, Department of Evolutionary Zoology, University of Debrecen (formerly Kossuth University), Debrecen, H-4010, Hungary b Department of Biology, Concordia University, 1455 ouest Boulevard de Maisonneuve, Montréal, Quebec H3G 1M8 Canada
Address correspondence to Z. Barta, who is now at the Centre for Behavioural Biology, School of Mathematics, University of Bristol, Bristol, UK. E-mail: z.barta{at}bristol.ac.uk . L.-A. Giraldeau is now at the Department of Biological Sciences, University of Québec at Montréal.
Received 16 September 1999; revised 12 January 2000; accepted 14 April 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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One of the most cited hypotheses for the evolutionary advantages of colonial breeding proposes that colonies serve as a place of information exchange about the location of food—the information center hypothesis. Despite its popularity, the hypothesis generated considerable controversy over its predictions and role in the evolution of colonial breeding. As a consequence, the hypothesis still lingers on, despite numerous apparent falsifications from both observational and experimental approaches. The controversy has three roots: the unclear causal direction between coloniality and information center, the unrecognized distinction between colonial breeding and colonial roosting, and the use of an implicit group selectionist argument. Here we try to clarify this controversy by applying an entirely individual selection-based approach, the producer-scrounger game, to the information center hypothesis. Furthermore, we show how other information-based alternatives of the original information center hypothesis (e.g., local enhancement and recruitment center hypotheses) can be included in a common framework. Our model predicts that individuals relying on information transfer at the colony should be rather common in nature. This prediction is essentially unaltered by the inclusion of either local enhancement or recruitment center. On the other hand, the frequency of leading unknowledgeable individuals (the most accepted sign of information center) is expected to be very low. The model indicates that tests of information-based hypotheses should focus on the expected relative frequency of food-searching flights rather than the frequency of leading.
Key words: information center, local enhancement, producer-scrounger games, recruitment center.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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The evolution of avian colonial breeding poses somewhat of a paradox. An estimated 13% of living bird species breed in densely packed colonies (Lack, 1968
) and do so despite
extensive apparent disadvantages to the individual colony members. Colonial
breeding may increase ectoparasite infection
(Brown and Brown, 1996),
increase competition for food, nesting sites, nesting material, and mates, and
even lead to kleptogamy (for a review, see
Wittenberger and Hunt, 1985).
The advantages required to offset such important costs must be numerous and
obvious. Yet, to date, little evidence of any strong advantage for colonial
nesting has accumulated (Brown and Brown,
1996).
One of the most cited hypotheses for the evolutionary advantages of
colonial breeding proposes that colonies serve as a place of information
exchange—the information center hypothesis
(Ward and Zahavi, 1973). The
hypothesis is based on the observation that many colonially breeding birds
feed on highly aggregated and abundant food patches whose locations are
unpredictable both in space and time
(Lack, 1968;
Ward and Zahavi 1973;
Wittenberger and Hunt, 1985),
precisely the conditions that make it onerous to find food
(Barta, 1992). Colonies provide
the opportunity to reduce these search costs by allowing individuals to obtain
information on food location simply by watching the behavior of successful
foragers rather than searching for food themselves.
The hypothesis spawned a flurry of tests that generally tend to refute the
hypothesis (for a recent review, see
Richner and Heeb, 1995).
Despite numerous apparent falsifications from both observational and
experimental approaches, the hypothesis lingers on, possibly as a result of
disagreement over its predictions and role in the evolution of colonial
breeding (e.g., Bayer, 1982;
Mock et al., 1988; Richner and
Heeb, 1995,
1996;
Wittenberger and Hunt, 1985;
Zahavi, 1996).
The controversy concerning the role of the information center hypothesis in the evolution of avian colonial breeding has three sources. One concerns the causal direction between coloniality and information center, the other an unrecognized distinction between colonial breeding and colonial roosting, and the third the use of an implicit group selectionist argument.
Causal direction
The information center hypothesis (Ward
and Zahavi, 1973), as originally presented, claimed that (1) both
colonies and roosts serve as places of information transfer about food
location, increasing the colony members' individual foraging success
(Beauchamp, 1999), and (2)
information transfer was the main selective advantage for the evolution of
coloniality (Mock et al.,
1988; Richner and Heeb,
1995). The problem with this formulation is that support for the
first statement does not constitute backing for the second; information
transfer could be the consequence of colony formation; colonies could have
evolved as a result of advantages that do not concern information transfer
(Bayer, 1982;
Mock et al., 1988;
Richner and Heeb, 1995). In
the current study we assume explicitly that the colonies already exist, i.e.
we deal with conditions maintaining an information center and not the center's
role in the origin of colonial breeding.
The difference between breeding colonies and communal roosts
The information center hypothesis was formulated to account for both the
evolution of colonial breeding and communal roosting. However, there are
important differences between the two systems that could have a significant
bearing on the formulation of evolutionary arguments. A roosting bird that
locates a food patch could benefit by not returning to the roost by saving the
travel time and energy needed to commute between the feeding area and the
roost and by avoiding parasitism by previously unsuccessful roost mates
(Richner and Heeb, 1995). A
breeding bird that encounters a food patch, on the other hand, has little
choice but to return to its breeding colony regularly if it is to feed its
nestlings successfully. So, for a breeding bird the decision is not whether to
return to the colony but whether to breed in the colony in the first place.
Choosing to breed alone, away from a colony, could avoid the costs of food
parasitism resulting from the information center, but not the time and energy
costs of commuting between the foraging site and its nest. Consequently,
although it is entirely appropriate to ask why a successful forager should
return to the colony (the key problem sensu
Richner and Heeb, 1995) in the
case of communal roosts, it is not an appropriate question for colonial
breeders (Dugatkin, 1997;
Wittenberger, 1981). In the
current study we deal specifically with information-based advantages that
follow from colonial breeding. For recent treatments of information based
advantages of communal roosts, see Mesterton-Gibbons and Dugatkin
(1999), Dall (submitted).
Hidden group-selectionist view
In its original formulation, the information center hypothesis does not
explain how evolution could favor birds that go out to search for new food
patches when following food finders, as a result of information transfer, is
more rewarding than searching under the patch distributions hypothesized to
promote information centers. The hypothesis overlooks the individual's search
cost by emphasizing the collective advantage of the colony as a place of
information transfer—a group selectionist view that has led some to
abandon the information center completely, replacing it with more realistic
evolutionary hypotheses for the origin of colonial breeding (e.g.,
Buckley, 1997; Richner and
Heeb, 1995,
1996;
Weatherhead, 1983). Others
have failed to recognize that the information center hypothesis must be cast
as a game theory problem (e.g., Dugatkin,
1997: 79).
Two information-based alternative hypotheses for colonial
breeding
The confusion highlighted above concerning the information center
hypothesis has had two important consequences. First, it has prevented the
development of quantitative models based on individual selection that could
generate widely acceptable and openly testable predictions and hence has
hampered our ability to reject the hypothesis more firmly. Second, in the wake
of the lack of success of the information center, alternative hypotheses, some
harboring the same hidden problems have arisen, confusing the issue even
further. We review two of these hypotheses briefly here because as we show,
they constitute mere variants of a general information-center hypothesis.
The local enhancement hypothesis
(Buckley, 1997;
Mock et al., 1988) assumes
that birds breed in colonies because colonies increase the local density of
foraging birds, which in turn leads to increased probability of patch
discovery through cuing on a feeding conspecific's location (local
enhancement; Mock et al.,
1988;
Pöysa,
1992; Thorpe,
1956). In an elegant simulation study, Buckley
(1997) showed that the
possibility of local enhancement could lead to the evolution of colonial
breeding when food distribution is clumped and ephemeral. Showing the effect
of local enhancement, however, does not automatically rule out the information
center hypothesis as a factor in the evolution of colonial breeding. In the
case of Buckley's model, this is especially true because Buckley
(1997) did not allow
individuals to use the information center.
The recruitment center hypothesis assumes that animals gain from exploiting
a patch in groups (Evans,
1982; Richner and Heeb,
1995). Therefore, upon finding a patch an individual gains by
recruiting companions to it. The colony then is useful as a means to provide
increased certainty that recruits will be found (Richner and Heeb,
1995,
1996). This hypothesis,
however, also suffers from a group selectionist view; it does not explain why
birds go out to search alone if waiting behind to be a recruit is more
profitable.
Toward a unified view of information-based hypotheses for colonial
breeding
Breeding colonies provide many documented instances of selfish exploitation
of others' efforts: taking of nest materials from unattended nests
(Hoogland and Sherman, 1976),
extrapair copulations (Møller and
Birkhead, 1993), intraspecific brood parasitism
(Brown and Brown, 1996), and
food kleptoparasitism (Wittenberger and
Hunt, 1985). The exploitation of food-finding efforts, therefore
appears a reasonable expectation, and so we apply a game-theoretic model of
selfish exploitation to the problem of information transfer at the breeding
colony, recognizing that the process of information exchange likely
corresponds to a producer-scrounger game
(Barnard and Sibly, 1981;
Giraldeau, 1997).
The producer-scrounger game was first proposed to investigate the
exploitation of others' food-finding efforts in foraging flocks
(Barnard and Sibly, 1981). The
model assumes that individuals can use two alternative foraging tactics:
producer and scrounger. Producer is a tactic that actively searches for new
food patches. Scrounger waits (or searches) for successful producers and moves
in to exploit the food (Barnard and Sibly,
1981; Giraldeau and Beauchamp,
1999). The game assumes that the scrounger tactic does better than
the producer tactic when few individuals use scrounger because abundant
exploitable food patches are made available by the many individuals playing
the producer tactic. The scrounger tactic does worse than the producer tactic
when it is common. The reason is twofold: first, many fewer food patches are
available as a result of the lower number of individuals engaged in playing
producer, and second, the number of individuals competing within the scrounger
tactic is larger. This strong negative frequency dependence of payoffs leads
to a mixed evolutionarily stable strategy (ESS;
Maynard Smith 1982), where
both tactics obtain equal pay-offs if players are phenotypically equal. Formal
theoretical models have shown that the evolutionarily stable proportion of
scrounger in foraging groups depends on (1) the proportion of a food patch
consumed by the producer individual before the arrival of the scroungers, the
finder's share (Caraco and Giraldeau,
1991; Vickery et al.,
1991); (2) the dominance structure of the flocks
(Barta and Giraldeau, 1998);
and (3) the energy reserves of the foragers
(Barta and Giraldeau, 2000;
Caraco and Giraldeau, 1991).
Some empirical results support the models' predictions (see
Giraldeau and Beauchamp, 1999,
for a review).
An information center can function as a producer-scrounger game. Assume
that a bird finds food patches according to a Poisson process with rate
. Under this assumption the average time needed to find a patch is
1/ (Clark and Mangel,
1986). If Ns birds look for food independently
and each finds patches with rate then the average time needed to find
at least one patch by them is 1/(Ns), which is
much less than 1/ (assuming Ns > 1)
(Clark and Mangel, 1986).
Therefore, a bird that is able to detect its companions' food patches will
exploit patches more often. For a colonial breeder, one possible way to locate
others' food patches is to wait at the colony and follow successful returnees
on their next trips to their previously discovered foraging patch—that
is, use the colony as an information center. This wait-and-follow tactic, much
like scrounger, prospers for two reasons: it can locate food patches more
frequently than birds searching themselves, and it saves the time and energy
spent on searching. Therefore, the wait-and-follow strategy can spread in the
colony, so long as the patch has enough food after it is discovered and it
exists long enough to allow its finder to return at least once. Of course, as
is true of scrounger, the wait-and-follow tactic cannot be stable alone; if no
one goes out to find novel food locations, then none will be available to be
exploited. This is precisely why the producer-scrounger game theoretical
approach is appropriate for all three information-based hypotheses
(Table 1).
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The information center as a producer-scrounger game
We assume that birds breed in a colony of size N. The individuals
feed, by returning n times, on ephemeral food patches that disappear
before birds can completely exploit them. As a consequence, n is
independent of the number of birds foraging on the same patch (i.e., no
competition for food). On each trip the birds consume a meal of A and
then depart to feed their nestlings. A round trip between the patch and the
nest, including the time needed to consume a meal and to feed the nestlings,
requires t time units. After the disappearance of a known food patch,
the individuals can choose between two exclusive food-finding
tactics—search or wait-and-follow. Searchers start a new food-finding
trip without returning to the colony ("peripheral switching" sensu
Waltz, 1982). They find food
patches as a Poisson process with rate . Let the time needed for a
round trip be equivalent to one time unit (i.e., t = 1) so that
gives the number of food patches found during the time of a round
trip. We assume quite reasonably that finding a patch takes longer than the
commute between it and the nest, so that < 1 in all cases.
Individuals using wait-and-follow, in contrast, return to the colony and wait
there for a bird returning successfully (i.e., with food) and follow it on its
next foraging trip to its previously discovered foraging patch ("central
place switching" sensu Waltz,
1982). Note that both searchers and wait-and-follow individuals
can lead others to the food patch, but searchers always return successfully
(i.e., with food) according to our definition, while wait-and-follow
individuals can be both successful or unsuccessful returnees, and only
wait-and-follow individuals can follow leaders.
Under the above assumptions, the food intake rate for an individual playing
searcher is
 | (1) |
 | (2) |
Np
gives their combined food finding rate
(Clark and Mangel, 1986). This
is based on the assumption that wait-and-follow strategists get to know all of
the patch discoveries of searchers. The searchers' gains do not depend on
their proportion, while the gains of wait-and-follow strategists decline
steadily with increasing proportions of that strategy (1 - p; i.e.,
it is negatively frequency dependent). It can be shown that the information
center game as outlined here fulfils all of the conditions of the
producer-scrounger game (Table
1).
At equilibrium, if all players have equal phenotypes, both searchers and
wait-and-follow strategists should have the same food intake rate
(Caraco and Giraldeau, 1991;
Maynard Smith, 1982;
Vickery et al., 1991). This
gives the equilibrium proportion of searchers as
 | (3) |
According to Equation 3, the wait-and-follow strategy can spread in the
population (i.e., 
< 1) if
< 1 - 1/N - 1/n; that is, if it is difficult to
find new patches (i.e., large searching cost can be saved), the colony is
large (many opportunities to follow someone), and the patches can be visited
several times (it is worth returning to a discovered patch). This prediction
concords with previous considerations (e.g.,
Allchin, 1992; Barta and
Szép,
1992,
1995;
Erwin, 1977;
Waltz, 1982).
Comparing the energy intake of searchers (Equation 1) and wait-and-follow
strategists (Equation 2) in a colony of Ns searcher and
one wait-and-follow strategist (i.e., N = Ns + 1)
reveals that an individual should always join a colony of
Ns searchers and play as a wait-and-follow strategist if 1
- 1/Ns > + 1/n. This means that an
originally small aggregation of only a few searchers (as few as two) will grow
quickly into a much larger colony containing mostly wait-and-follow
strategists so long as the foraging patches can be visited several times
(i.e., n > 2) and they are hard to find (i.e., < 1/6
for n = 3). Another prediction of this model is that the number of
searchers in breeding colonies should always be kept very low (as low as two,
independently of colony size) given that conditions for the growth of the
originally small aggregation continue to hold.
Let us express the frequency of information transfer as the proportion of
departures involving leading wait-and-follow strategists to all departures
from the colony during time T. During T time units,
s searchers find
sT food
patches. Information about the location of these patches is passed on to the
N - s
wait-and-follow strategists. The searcher and the wait-and-follow strategists
exploit a patch for n(1 + N -
s) departures. Therefore
sTn(1 +
N - s) departures
occur during T. From these departures leadings can occur either
sT times
when the food discoverer leads all wait-and-follow strategists to the patch on
a single departure, or
sT(N
- s) times when all
wait-and-follow strategists are led to the patch one at a time (note that
individuals playing the wait-and-follow tactic can also act as leaders). Any
other frequency between these minimum and maximum estimates, depending on the
details of the information transfer process, is possible. It follows, after
some calculus, from the above that the minimum proportion of information
transfer to all departures is
 | (4) |
 | (5) |
decreases. These equations predict, however,
that the frequency of information transfer can be low in a colony of
individuals playing the information center game.
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A more useful sign of the operation of an information center can be derived
if one can distinguish food-searching flights from transit flights directed to
known patches. The distinction between these two types of flights could
perhaps be based on the analysis of the whole flight path. One can expect that
individuals going to a patch of known location fly to it using a less
circuitous route than individuals who encounter a patch after having searched
for it. It is also possible that transit and search flights are characterized
by distinct altitudes. If transit and search flight types can be
distinguished, then our game makes a unique prediction that could help
experimentalists test the information-center hypothesis more effectively. The
searchers find
sT food
patches on the same number of food-searching flights. These patches are
exploited by
sTn(1 +
N - s)
departures, all of which except
sT are
transit flights to known patches, either because individuals know the location
of the patches or because they are led to them. It follows that the proportion
of food-searching flights to all flights is
 | (6) |
, implying that one can expect to detect
food searching flights only very rarely if the information center operates,
especially in large colonies feeding on rare patches visitable several times.
Increasing N and decreasing reduces the proportion of
searchers and so decreases the proportion of search flights. Raising
n, in contrast, increases the number of visits to a discovered patch,
which naturally also leads to decreasing proportion of search flights.
Comparing Equation 4 to Equation 6 reveals that the frequency of
food-searching flights never exceeds the frequency of departures involving the
leading of wait-and-follow strategists (i.e., the frequency of information
transfer at the colony).
Local enhancement and recruitment center hypotheses as variants of
the producer-scrounger information center game
In the following sections we show how the local enhancement and recruitment
center hypotheses for the evolution of colonial breeding can be included in
the information center game and how predictions of the information center
hypothesis are changed by doing this. First we consider the local enhancement
hypothesis. We keep all of the assumptions of the information center game but
add one—namely, that searchers can also be informed of the food
discoveries of other searchers. This increases the searchers' foraging rate
from to + a(Np - 1) (given
Np > 1), where 0 
a 1 is the efficiency of the
local enhancement (LE). If a = 0 there is no local
enhancement while a = 1 means that a searcher gets information about
all of the food patches discovered by the other Np - 1 searchers.
While the food-finding rate of individual searchers increases, we also assume
that their combined corporate feeding rate does not change; the patch
exploitation time is negligible compared to search time. So all searchers look
for food during almost all the available foraging time. Based on this
assumption, the food intake rate for a searcher using local enhancement (given
NpLE > 1) is
 | (7) |
 | (8) |
LE, by making Equations 7 and 8
equal, can be calculated by solving the following equation
 | (9) |
LE, is always greater than
the equilibrium proportion of searchers without local enhancement,
, given that a > 0.
Making the determinant of Equation 9 equal to zero and solving this equation
for a gives the critical value of a above which no
wait-and-follow strategist can persist in the colony
(Figure 2a).
 | (10) |
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From Equation 10 it can be seen that local enhancement should be effective
in preventing wait-and-follow strategists from spreading
(Figure 2b) when it is hard to
find food (low ) and patches can be visited several times (n
> 2)—precisely the conditions under which one can expect the spread
of wait-and-follow strategists (see above). This very effective local
enhancement, however, can be an unreasonable assumption because most colonial
species search for food in a vast space, making it unlikely that a searcher
would ever get to know about all others' food discoveries (consider, for
instance, the case when they are searching in opposite directions from the
colony). Therefore, one may expect to encounter wait-and-follow strategists in
almost every colony despite local enhancement.
One can model the recruitment center (RC) hypothesis (Richner and
Heeb, 1995,
1996) keeping the same
assumptions as the information center game by allowing meal size (A)
to be larger when the wait-and-follow strategists reach the patch (the group
foraging advantage). Note that we do not consider here the case of active
recruitment—that is, successful patch finders do not advertise their
findings actively. The often complex displays that are assumed to be signs of
active recruitment (Richner and Heeb,
1996) may not be as relevant for colonies as they are for communal
roosts. Under these conditions the food intake rate for a searcher in the
recruitment center is
 | (11) |
,
1996, for possible
mechanisms). In a recruitment center the wait-and-follow strategist's gain is
 | (12) |
 | (13) |
,
(given b > 1), that is, wait-and-follow strategists spread more in
recruitment centers than they do in information centers. This prediction holds
when the group foraging benefits can depend on the group size so long as these
benefits are non-zero. |
DISCUSSION |
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In this article we clarified three sources of confusion concerning the information center hypothesis that have also affected to some extent two alternative information-based hypotheses. We proposed a cogent answer to the key question of why any individuals actively search for food when following food finders is hypothesized to be more beneficial. We modeled the information center as a producer-scrounger game with specific tactics of search and wait-and-follow. By doing so we provided an entirely individual selection-based interpretation for the operation of information centers. The game shows how the benefits of a wait-and-follow strategy can be negatively frequency dependent. As a consequence, the game predicts a mixed ESS solution where searchers are never completely excluded from the breeding colony. This means that, even in the absence of any mutual benefits, there will always be individuals who leave the colony to find new food patches and hence provide exploitation opportunities to other colony members. Basically, searchers are kept by virtue of the extra meal they obtain from the discovered patch—an advantage that is similar to the finder's share in foraging flocks (Caraco and Giraldeau, 1991
; Vickery et al.,
1991).
It is important that the model does not require individuals to specialize
in a given role and either search or wait and follow exclusively. What is
required is that the proportion of strategies be kept at the equilibrium
value. Individuals can achieve this either by specializing or by randomly
alternating between strategies or by any mixture in the population that yields
the stable proportion (Giraldeau and
Livoreil, 1998).
The detailed investigation of the equilibrium proportion of searchers shows
that only a few individuals should leave the colony to search for novel
locations of food. As a consequence, a large part of the colony is expected to
be playing wait-and-follow and rely on the patch location information provided
by the returning searchers. This picture is not significantly modified by
allowing local enhancement (Buckley,
1997; Thorpe,
1956) or recruitment centers
(Evans, 1982;
Richner and Heeb, 1995) to
operate. In fact, our analysis reveals that the recruitment center increases
the proportion of colony members relying on information transfer at the colony
beyond expectations of the simpler information center hypothesis. It is true
that local enhancement can lead to the elimination of the wait-and-follow
strategy but does so only if local enhancement is extremely, and perhaps
unreasonably, efficient, allowing all birds to monitor the success of all
others concurrently. At moderate efficiencies of information transfer by local
enhancement the equilibrium proportion of searchers is affected only
negligibly. As a consequence, one may expect information transfer on food
location at the colony to be rather common in nature, independently of whether
local enhancement or recruitment center mechanisms operate.
Predicting that information centers should be common may appear paradoxical
given that only a small number of published studies clearly support the
operation of information centers at breeding colonies
(Brown, 1986;
Greene, 1987; but see
Fleming, 1990;
Gori, 1988;
Waltz, 1987). This paucity of
support is especially daunting given the considerable research effort invested
in testing the hypothesis (for a review, see
Richner and Heeb, 1995). Our
game theoretic model, however, suggests that the empirical basis used to
reject the occurrence of information centers may not have been entirely
appropriate. Our model predicts, for instance, that frequent cases of leading
(the most commonly assumed sign of the operation of an information center)
should only be expected when the colony members exploit extremely ephemeral
food patches where n is very close to 2. Therefore, it may not be so
surprising that one of the few instances of support for the information center
based on such evidence comes from a study of cliff swallows
(Brown, 1986) that fed on
highly ephemeral food patches that usually existed no longer than 20-30 min
(Brown and Brown, 1996). Our
model also predicts that information transfer events can be rare, and
therefore difficult to observe, if individuals can visit a patch several
times. The consequences of the possibility of low frequency of leading are
twofold. First, this may explain why only a handful of studies support the
operation of information centers. Second, the information center game still
cannot be convincingly falsified simply by documenting the absence of leading.
Our game theoretic model, however, offers an alternative means to falsify the
information center hypothesis.
The information center game predicts that the proportion of food searching
flights to all departures should never exceed the proportion of leading when
the information center is at work. One way to get such evidence would be to
use remote-sensing techniques to trace the whole flight paths of individuals
leaving the colony (e.g., Benevenuti et al., 1998;
Kenward, 1987;
Priede and Swift, 1994). One
could convincingly reject the information center hypothesis by showing that
the frequency of food-searching flights from the colony exceeds the frequency
of information transfer as measured by instances of leading.
Both local enhancement and recruitment center hypotheses are consistent
with an increased foraging efficiency and so may be more promising candidate
hypotheses for the evolutionary origin of avian colonial breeding
(Beauchamp, 1999). Because the
gain obtained by the searcher strategy does not depend on its frequency and
the two strategies' gains are expected to be equal at equilibrium, the
information center hypothesis is not consistent with an increase in the
foraging efficiency of colonial individuals. As a consequence, its role in the
origin of colonial breeding can be questionable. But if more than two
searchers aggregate initially, for whatever reason, it would always be
profitable for subsequent individuals to join them to play the wait-and-follow
strategy rather than to attempt breeding alone. So even if the information
center is not involved in the original aggregation of the first two
individuals, it could play a role in inflating the initially small aggregation
into a large breeding colony. Thus the information center cannot be ruled out
completely as a factor in the evolution of breeding colonies. An
individual-based simulation to investigate this aspect of information center
is under way.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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The solution of the following equation gives the equilibrium proportion of searchers in baseline condition:
 | (\mathrm|<|A|>|1) |
 | (\mathrm|<|A|>|2) |
 | (\mathrm|<|A|>|3) |
 | (\mathrm|<|A|>|4) |
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ACKNOWLEDGEMENTS |
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This study was supported by an OTKA (Hungarian Scientific Research Fund) grant (T030434) to Z.B. and a Natural Sciences and Engineering Research Council (Canada) research grant to L.-A.G. Z.B. was supported by a János Bolyai Research Fellowship (Hungary). We are grateful to S. X. R. Dall and an anonymous referee for helpful comments.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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