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Behavioral Ecology Vol. 13 No. 1: 42-51
© 2002 International Society for Behavioral Ecology
Can information sharing explain recruitment to food from communal roosts?
Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, USA, and Department of Biology, University of Louisville, Louisville, KY 40292, USA
Address correspondence to S.R.X. Dall, who is now at the Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK. E-mail: sashadall{at}iname.com .
Received 29 September 1999; revised 26 October 2000; accepted 4 March 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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The debate over whether communal nests and roosts function primarily as information centers (they facilitate the sharing of foraging information) remains unresolved. Here I use evolutionary game theory to investigate the relative importance of this influential hypothesis and an alternative: that roosts, in particular, function as recruitment centers (they facilitate aggregation at food patches). Basing my model on juvenile common raven (Corvus corax) behavior, I assume there is no net cost to being at food patches in groups, and foragers roost communally. Moreover, one strategic outcome is the observed raven behavior: individuals search independently and recruit from the roost once a patch is found (they play Search-and-Recruit, or SR). I investigate the stability of this in two scenarios that differ in the magnitude of the lost opportunity costs to mutants playing SR in populations of other strategies. When these costs only involve a chance of not being in a group at a located carcass, SR is the only evolutionarily stable strategy under all conditions. However, when these costs also include missing opportunities to be socially dominant, SR no longer enjoys exclusive dominance in the strategy set. Nevertheless, in both cases, there are conditions where group foraging benefits have no effect on the evolutionary stability of SR. Thus, contrary to assertions in the literature, the opportunity to share foraging information can be sufficient to drive the evolution and maintenance of recruitment to food from communal roosts. However, I conclude that both information and grouping benefits are likely to underlie communal roosting behavior in my focal system.
Key words: common ravens, communal roosting, evolutionary game theory, information center hypothesis, recruitment center hypothesis.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Many species of animals gather in groups to rest or raise their offspring. The evolution and maintenance of this communal roosting and nesting behavior is the subject of an ongoing controversy. Early explanations centered on the possible antipredatory benefits of such behavior as the primary selective force responsible for its existence (e.g., Lack, 1968
). However, Ward and
Zahavi (1973), in their now
classic review, concluded in favor of the benefits of sharing information
about patchy and ephemeral food (e.g.,
Barta and Szep, 1992;
Lachmann et al., 2000) as the
ultimate explanation for communal roosts and nests, and the associated complex
behaviors (e.g., aerial displays). This information center hypothesis (ICH,
Ward, 1965;
Zahavi, 1971) has since been
the stimulus for much empirical work (e.g.,
Buckley, 1997; see
Danchin and Wagner, 1997;
Richner and Heeb, 1995, for
reviews), although its explanatory status remains controversial
(Mock et al., 1988;
Richner and Heeb, 1995).
Indeed, Beauchamp (1999), in a
phylogenetic analysis of the functional explanations for communal roosting in
birds, concludes that, although the evidence points to the primacy of foraging
efficiency benefits in driving the origin of this behavior, the precise
mechanisms by which such benefits accrue (including the relative importance of
the ICH) remain unresolved.
In a critical review of the work stimulated by Ward and Zahavi's
(1973) ideas, Richner and Heeb
(1995) conclude that there are
alternative hypotheses that can also account for the evidence, but are rarely
considered in tests of the ICH. Moreover, in a follow-up paper
(Richner and Heeb, 1996), they
argue that one alternative, the recruitment center hypothesis (RCH), can not
only explain many of the findings cited as evidence for the ICH, but it also
avoids flaws in Ward and Zahavi's
(1973) reasoning. Richner and
Heeb (1995,
1996) argue that the ICH can
only explain why successful foragers share their findings with unsuccessful
(unrelated) individuals (what they consider as "the key problem")
by relying on either reciprocal altruism
(Trivers, 1971) or
"naive" group selection
(Williams, 1966). The RCH, on
the other hand, by emphasizing the benefits to the individual of group patch
exploitation (e.g., collective antipredatory vigilance and increased feeding
efficiency), does not require that a successful forager have its
"altruistic" act reciprocated in the future (which is unlikely to
be generally the case due to the largely transitory nature of roost
membership) in order for such behavior to be selected for. However, although
the RCH logic makes broad intuitive sense, simple optimality arguments will
not suffice to assess its importance relative to the ICH. Since the success of
the search-independently-and-recruit strategies, that are the focus of both
the ICH and RCH, depends on their strategic stability against alternative
strategies in an evolutionary arena (their fitness consequences depend on the
strategies played by competitors), an appropriate analysis requires the use of
evolutionary game theory (Maynard-Smith,
1982). Indeed, such analyses can predict outcomes that run counter
to simple optimality intuition; for instance, Clark and Mangel
(1984) show how a simple
flocking strategy can be selected for even if it results in fitness payoffs
that are worse than when foraging alone.
Given that many of the behaviors associated with communal roosts and nests can have both information and recruitment center functions, it is important to be clear on how the two types of function are distinguished. With this in mind, I define any benefits accrued from the sharing of foraging information per se as ICH benefits; referred to as information sharing benefits from now on. On the other hand, I define benefits derived from being in a group at the food patch as RCH benefits; group foraging benefits, hereafter. So, for example, the act of recruiting individuals from a roost or colony to a food patch will confer both information sharing and group foraging benefits to individuals. However, it is only by distinguishing the two formally that we can assess the relative importance of the ICH and RCH in driving the evolution and maintenance of this behavior.
Here I explore formally both the ICH and RCH logic, as defined above, using
evolutionary game theory to assess their relative importance for the evolution
and maintenance of communal roosting behavior in a particular system; I base
my model on the food-sharing and recruitment system of juvenile common ravens
(Corvus corax), studied by Heinrich and coworkers (Heinrich,
1988,
1989;
Heinrich and Marzluff, 1991;
Marzluff and Heinrich, 1992;
Marzluff et al., 1996).
Juvenile common ravens aggregate at communal roosts in the forests of New
England, USA, but roost composition is extremely transient due to the high
mobility of these birds throughout this region (Heinrich,
1988,
1989). The ravens are
specialists on carcasses in the winter, and they search for them singly, or in
pairs. Once a carcass is found, the "finders" will usually
postpone feeding until roost-mates have been actively recruited to the site
(Heinrich, 1988,
1989;
Marzluff et al., 1996). This
can occur as a result of either producing food calls at the patch, or
returning to the communal roost and leading roost-mates after the subsequent
dawn. The data suggest that the latter of the two modes of recruitment is more
important to the ravens (Heinrich,
1989; Heinrich and Marzluff,
1991; Marzluff et al.,
1996). Moreover, in a theoretical treatment of the stability of
immediate (food calls) versus delayed (leading from the roost) recruitment,
Mesterton-Gibbons and Dugatkin
(1999) conclude that immediate
recruitment is unlikely to be an ESS in this system. Therefore, I focus here
on the stability of a delayed recruitment strategy by independent searchers
against other, non-recruiting alternatives. I also include strategies that
involve searching for carcasses as a group in the strategy set. Thus, I am
able to compare the impacts of the benefits to the individual of both sharing
the results of independent search effort (information sharing), and being in a
group at a carcass (group foraging), on the evolutionary stability of the
raven food sharing strategy. The latter benefits include an increase in the
ability to overcome the carcass defense of dominant, territorial adults
(Marzluff and Heinrich, 1992)
and an increase in social status (Heinrich
and Marzluff, 1991), and have formed the basis for functional
accounts of this system (Marzluff and
Heinrich, 1992;
Mesterton-Gibbons and Dugatkin,
1999). Like such work, I also ignore any effects of kinship or
reciprocity due to the high fluidity of roost membership and the subsequent
low levels of relatedness within roosts
(Parker et al., 1994).
The model system
It is relatively easy to imagine that information about food will be
available when foragers gather in groups to rest. Controversy arises over why
this information should be shared among roost members, either passively or
actively, and how this might influence communal roosting behavior (Richner and
Heeb, 1995,
1996). For this reason, I do
not deal here directly with the transition from solitary to communal roosting.
Rather, I assume that communal roosts at least occasionally exist for other,
non-informational or non-recruitment reasons (e.g., for thermoregulation,
predation risk dilution, commodity selection:
Wagner et al., 2000), and
focus on the evolution of behavior that apparently maximizes the efficiency of
these communal roosts for information sharing and/or group foraging:
recruiting to food from the roost.
Following the above reasoning, the players in my model are at a communal
roost. However, each player will rarely find itself at another roost with the
same opponents, unless they all "choose" to return to the same
roost or follow each other around (potential outcomes of the model). This
could be because communal roosts are rare (e.g., they depend on the
availability of suitable roost sites), roost membership is transient, or both.
The birds are specialists on large food patches ("bonanzas") that
are rare, ephemeral, and unpredictable. I assume that their primary goals are
to locate these food bonanzas and gain sufficient access to them to
maintain positive energy budgets; the food patches are large enough that all
of the birds in a roost can potentially achieve such energy budgets at each
one (with free access), but access to them can be restricted suddenly and
unpredictably (e.g., because carcasses can be buried by sudden snowfalls;
Heinrich, 1989; following
Clark and Mangel's [1984]
notation, I assume that the number of birds in the group [n] does not
exceed the number of bird meals available at a patch [m]). For the
sake of simplicity, I assume that a carcass will only last long enough to
allow all players (with free access) to maintain positive energy budgets over
one round of the game (a search period, a feeding period, and two roosting
periods; see below). Thus, this is a purely survival based model and I assume
that a bird's fitness will be maximized if it behaves at a roost so as to
maximize:
 | (1) |
Each bird, if it searches independently, has an equal probability
(
) of finding a food patch in the time available for searching between
roosts (e.g., a day). Thus, if more than one bird searches for food
independently of one another, the probability that at least one such bird
finds a bonanza per search period (day) is an increasing function (S) of the
number of birds searching (k). Moreover, if the birds search together
in a group then the probability that the group finds a food patch is also an
increasing function (G) of the number of birds in the group (k),
since more pairs of eyes will lead to more efficient searching, even if they
are searching together. However, I assume that the rate of increase with
k will be lower for G than S (i.e., 
G/k <
S/k) because group maintenance will require attention
that would otherwise be devoted to searching for food, and, in a group, the
areas searched by each bird will overlap. Specifically:
 | (2) |
 | (3) |
 | (4) |
/
; the smaller this
ratio is, the larger S(k) — G(k) will be, and hence
the better it is to search independently and share carcass encounter
information rather than search together in a group.
The birds will not necessarily get free access to a food bonanza, however,
once it is located. The bonanza may be guarded by non-roost members (e.g.,
con- or heterospecific territory owners)—Scenario 1, and/or dominant
roostmates—Scenario 2 (Heinrich,
1989; Heinrich and Marzluff,
1991; Marzluff and Heinrich,
1992). If it is unguarded (there is free access) then all birds at
the patch will achieve their positive energy budgets with certainty
(q.v.). If the patch is guarded, however, I assume, following
Marzluff and Heinrich (1992),
that the more non-guarding birds there are present, the less able the guards
are to exclude them (guards always achieve their desired budgets with
certainty). Thus, the probability that each non-guarding bird will get
sufficient access to the food to maintain a positive energy budget is an
increasing function (D) of the number of non-guarding birds present
(i). Moreover, I assume that the ability of the guards to exclude
other birds will deteriorate more as i increases, up to the point
where there are so many other birds at the patch that guarding becomes
ineffective (i = icrit). Thus, 0 
D
(i) < 1 is concave up for i <
icrit. Specifically:
 | (5) |
 | (6) |
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The foraging game
I assume that n + 1 unrelated birds find themselves together for
the first time at dawn at a particular roost. Since the roost is made up of
individuals with widely varying histories of foraging success (as roost
membership is transient), there will always be at least one bird that is so
close to starvation that it has to leave the roost to search for food as soon
as possible after dawn. Once the first of such birds (the
"starter" bird: each bird has an equal chance [1/n + 1]
of being the "starter" at a given roost.) has departed, the
remaining n birds can choose one of three actions. They can either:
depart from the roost and search for food independently of any other bird
(play "S"), follow the starter bird and search with it in a group
("F"), or wait at the roost ("W"). Moreover, once a
food patch has been located (or if they have not located food by the end of
the search period), all birds (including the "starter") can choose
between two options: return to the roost and attempt to recruit roost mates
(or be recruited) to a located patch the following dawn (play
"R"); or, do not return to the original roost (roost as near as
possible to the food bonanza) and do not actively recruit (or be recruited by)
other birds to a food patch ("D"). I assume that the energy costs
(i.e., the impact on maintaining a positive energy budget over a round of the
game) of returning to the original roost are equivalent to those of finding
another roost (e.g., finding a suitable roost site costs as much, on average,
as returning to the original roost). If there are multiple independent
searchers playing R, for simplicity, I assume that each has an equal chance of
being the one to recruit the others: their combined probabilities of being the
one to find a food patch and successfully compete for recruits
against any other successful searchers are equal (the players do not differ in
their food finding and recruiting abilities). If a bird is not the recruiter
then it will be recruited to another's patch if it is playing R. I also assume
that a group (>1 birds) of successful searchers will always recruit
solitary searchers, whether or not they are successful (a "sheep"
effect). For the sake of simplicity, I assume that the birds will always play
one of S, F, or W at a roost, and either R or D at a patch (irrespective of
search success). Thus, each individual has six potential strategies, defined
in Table 1.
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By analogy with Mesterton-Gibbons and Milner-Gulland
(1998), I model the strategic
interaction as a symmetric (n + 1)-player game, reduced effectively
to a two-player game by assuming that a focal (mutant) individual interacts
with the n remaining birds, assumed identical. Player 1 is the mutant
individual, and Player 2 is the rest of the group; symmetry implies that the
choice of focal individual is arbitrary.
In terms of the strategy set (Table
1), the state of individuals searching independently for food
patches and pooling this effort by recruiting each other to located patches
(to reap the information sharing benefits of the ICH), corresponds to a
population playing SR. Alternatively, searching in groups (to guarantee
increased access to guarded patches) but returning to a particular roost-site
corresponds to a population playing FR, while searching in groups with mobile
roosts corresponds to a population playing FD. All three such states are
potential outcomes if communal roosts are being used to maximize the group
foraging benefits predicted by the RCH. On the other hand, a population
playing SD would emerge if communal roosts are not used for foraging (e.g.,
they exist solely for thermoregulatory purposes, or they occur randomly
depending on the availability of suitable roosts). Finally, although a
population strategy of playing W at the roost is unlikely to be observed, it
is included in the strategy set to allow for effects of information parasitism
at communal roosts to be explored (e.g., the presence of
"scroungers"; Barnard and
Sibly, 1981; but see Barta and
Giraldeau, 2001 for an explicit treatment of producer-scrounger
games at communal nests).
I analyzed this foraging game in two different scenarios: (1) with food bonanzas only defended by non-roost individuals; and (2) with food bonanzas either defended by non-roost members or within-roost dominants.
Scenario 1: non-roost members defend some bonanzas
In the first instance, I assumed that, once a food patch has been located,
it has a fixed probability (p) of being found in the territory, or
possession, of non-roost individuals (con- or heterospecific) that will defend
it against intruders (e.g., the players in the foraging game). Thus, this
initial scenario includes both the search efficiency (information sharing) and
at-the-defended-patch (group foraging) advantages of the search-and-recruit
strategy employed by juvenile ravens
(Heinrich, 1989;
Marzluff and Heinrich, 1992;
Marzluff et al., 1996). Here,
whether the patch is defended, each player at the patch (recruiter or
recruited) has an equal probability of gaining sufficient access to the patch:
according to D(i) if defended, or with certainty if undefended (with
probability 1 — p). The matrix of rewards per round of play to
a mutant individual, using a given row strategy against a population using a
given column strategy, can be determined for this scenario from (1)-(3), (5),
and (6), and is shown in Table
2.
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I will denote this matrix by A, so that
aIJ is the reward (in terms of (1)) to a mutant
individual playing I against n individuals playing strategy
J. For example, the reward to strategy SR against itself (population
strategy SR) is a11 = S(n + 1) {(1 - p)
+ pD(n + 1)}. This is because there are n + 1 birds
searching independently for food patches (whether or not the focal bird is the
"starter"), and so long as a patch is located (according to
S(n + 1)), all birds (including the focal individual) will end up
gaining sufficient access to it with certainty if it is undefended (with
probability 1 - p), or with probability = D (n + 1) if it is
defended (with probability p). Similarly, the reward to strategy FD
when playing against population strategy SR is a41 =
{n/(n + 1) G(2) {1 - (
x S(n - 1))}}
{(1 - p) + pD(n + 1)} + {{G(2)S(n
- 1) + 1/(n + 1) {S(1) - {G(2)S(n - 1)}} {(1 -
p) + pD(1)}, which is obtained as follows. First, because
the focal individual will not be recruited to any other bird's patch (it is
playing D), it will only ever have a chance of gaining sufficient access to a
patch that is located as a result of its own search effort. If it is the
"starter" (with probability 1/n + 1) then it will always
search alone, finding a carcass with probability = S(1). If the focal bird is
not the "starter" (with probability = n/n + 1),
it will be the only bird to follow the "starter" and search with
it (it played F against a population strategy of S), and thus it will locate a
carcass with probability = G(2). Second, if it is not the
"starter," the "starter" plays R if a patch is found
and returns to the roost to recruit the other n - 1 birds and return,
or be recruited and not return. If the patch is undefended (with probability 1
- p) then the focal bird will gain sufficient access with certainty
regardless of whether its flock mate returns (or if it is the
"starter"). However, if the carcass is defended (with probability
p), then the other birds will join the focal bird (and it will gain
sufficient access according to D(n + 1)) if none of the other birds
found a patch (with probability = 1 - S(n - 1)), or if the
"starter" was able to recruit the others even if a patch was found
by one of them (with probability = S(n - 1)). (If at least
one of the independent searchers finds a patch [with probability S(n
+ 1)], there is an equal chance [] that the successful
"starter" will recruit it/them or be recruited elsewhere
[q.v.].) Alternatively, the focal bird would have to attempt to gain
sufficient access on its own (according to D(1)) if the "starter"
is recruited elsewhere (with probability = S(n - 1)), or if
the focal bird is itself the starter (q.v.). Finally, the reward to
WR playing a population strategy FR is a53 = 1/(n
+ 1){G(n + 1) + nG(n)}{(1 - p) +
pD(n + 1)}. This is because if the focal bird is the
"starter" (with probability 1/n + 1) then all of the
other birds will search with it as a group (population strategy F) and they
will locate a carcass according to G(n + 1). Otherwise, the focal
bird will wait at the roost (playing W) and a carcass will be located with
probability = G(n). In both situations, the focal bird will gain
access to a located carcass with certainty if it is undefended (1 -
p), or according to D(n + 1) otherwise, since it plays R.
The other matrix entries in Table
2 can be obtained similarly.
Scenario 2: roost members can also defend bonanzas
As in Scenario 1, each food patch has a fixed probability (p) of
being defended by a non-roost member. However, if the patch is not defended in
this way (with probability 1 - p), the player that has the most
experience at the patch (spent the most time near it) will be dominant
(achieve its positive energy budget with certainty) and attempt to exclude any
other birds that are present (therefore they will achieve their positive
energy budgets according to D(i)). This dominant bird will not be
able to exclude other roost members from patches that are defended by
non-roost members because all of its effort will be directed at evading this
defense, just like any other player (and thus all birds at defended patches
will achieve their positive energy budgets according to D(i) as
before). I assume that the most experienced bird at a given patch will be the
one that managed to recruit the other R players from the roost
(q.v.). If more than one bird was involved in locating the patch to
be exploited (they searched in a group), but they play different at-the-patch
strategies, the birds that play D (that roost nearer the patch, on average)
are assumed to have the most information about it (and be dominant). If more
than one bird "has the most experience" at a patch, dominant
status is randomly assigned (i.e., the factors, other than relative
experience, that determine dominance at the patch vary randomly with respect
to my formulation); for simplicity, only one bird can be dominant, with all
other birds being subordinate. Thus, this scenario incorporates a potential
finder's advantage at patches that is negated by the presence of non-roost
territorials. This is largely consistent with reports of juvenile raven
behavior (Heinrich, 1994,
1995;
Heinrich and Marzluff, 1991;
Marzluff and Heinrich, 1992).
The reward matrix can be now be determined as before from (1)-(3), (5), and
(6), and is shown in Table
3.
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Following the notation in Scenario 1, I denote this matrix as B so
that bIJ is the reward to the mutant playing
I in a population of J strategists. For example, in contrast
to Scenario 1, the reward to a mutant playing SR against a population also
playing SR is b11 = {S(n + 1)/(n +
1)}{{(1 - p) + pD(n + 1)} + n{(1 -
p)D(n) + pD(n + 1)}}. This is because,
regardless of whether the focal bird is the "starter" or not, if
any of the n + 1 independent searchers discover a food patch
(according to S(n + 1)), each has an equal chance of being the one to
recruit the others to the patch (q.v.), and be dominant. Thus, the
focal individual will gain access to the patch as a dominant (achieving its
positive energy budget with certainty if the patch is undefended (with
probability 1 - p), or according to D(n + 1) otherwise) with
probability 1/n + 1. However, it will be subordinate at the patch
more often (gaining sufficient access, if the patch is undefended, according
to D(n) (one bird is attempting to exclude the other n
birds, including the focal bird), and according to D(n + 1) if it is
defended), with probability n/(n + 1). Similarly, the reward
to an FR mutant in a population of SR strategists is b31 =
1/(n + 1){{S(n + 1)/(n + 1) +
nG(2)}{(1 - p) + pD(n + 1)} +
n{S(n + 1)/(n + 1) + G(2) + S(n -
1) (1 - G(2))}{(1 - p)D(n) + pD(n + 1)}},
which is obtained as follows. If the focal bird is also the
"starter" (with probability 1/(n + 1)), then its pay-off
will be the same as for an SR bird in an SR population (see
b11 above) since all birds will search independently and
play R. Otherwise (with probability n/(n + 1)), the focal
bird will search with the "starter" (k = 2) and all the
other birds will search independently (k = n - 1). Since
groups of successful foragers (
2 individuals) will always recruit solitary
searchers (q.v.), the focal bird will be dominant at a carcass (gain
sufficient access with probability (1 - p) + pD(n +
1)) if its group was successful at finding a carcass and it is dominant in
that group (with probability G(2)). The focal bird will be subordinate
at a carcass (gain sufficient access with probability (1 -
p)D(n) + pD(n + 1)), if it is subordinate
in a successful group or if its group searched unsuccessfully and one of the
solitary searchers found a carcass (i.e., with probability G(2) +
S(n - 1)(1 - G(2))). The other matrix entries can be obtained
similarly (see Table 3).
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RESULTS |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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Conditions for strategic stability
A strong (symmetric) Nash-equilibrium strategy (or strong ESS; Maynard-Smith, 1982
) of such a
game is a population strategy that is also uniquely the focal individual's
best reply to the other n players of it. Thus, a population strategy
is stable if its diagonal element in Tables
2 and
3 is the largest in its column.
In other words, strategy J is stable if
aJJ or bJJ exceeds
aIJ, or bIJ
respectively, for all I 
J. For the results presented
here, I have solved all inequalities that result from such within-column
comparisons for p (the probability that a carcass is defended) to
facilitate assessment of the relative dependence of the stability of strategy
SR on group foraging benefits. Moreover, I explore the influence on these
solutions of /, which determines how much better it is to
search independently than as a group (i.e., the magnitude of S(k) -
G(k)). Thus I illustrate how the magnitude of information sharing
benefits affects strategic stability.
Scenario 1
Where carcasses are only ever defended by non-roost individuals, inspection
of the reward matrix (A; Table
2) reveals that SR is the unique strong ESS: it is the only
strategy for which the payoff to a mutant playing it in a population playing
the same strategy is greater than the payoffs to all other mutant strategies
in similar populations (i.e., aJJ >
aIJ for all I J and
J = 1, but not so for any other J). As a consequence, no
matter which strategy is assumed to be ancestral, a population playing SR
would be predicted to evolve under all of the circumstances covered by this
formulation (for all parameter values, including all possible values
of p). This is despite mutants playing SR not being able to invade
populations playing FD directly (as a14 <
a44), since mutants playing FR can invade such populations
by drift (as a34 = a44) and SR mutants
can invade populations playing FR (a13 >
a33).
Scenario 2
For the situation where carcasses can be defended by both non-roost
individuals and dominant roost mates, the conditions for the
evolutionary stability of SR are less clear-cut. Indeed, the inequalities
resulting from comparing the within-column elements of the reward matrix
(B; Table 3) have few
simple solutions, and for the sake of clarity I will therefore present them
graphically. This is sufficient for the purposes of this analysis since I am
interested primarily in the relative influence of information sharing and
group foraging benefits on the evolutionary stability of SR against its
competitors.
In this scenario, two strategies emerge as strongly evolutionarily stable: SR and FD (following from the roost but not returning again to recruit; Table 1). I will proceed by discussing each strategy's stability separately.
SR as an ESS
A focal individual playing SR in a population also playing SR will always
do better than all other types of focal individual (mutant) in similar
populations, except one: an individual playing FR (following from the roost
and returning to recruit; Table
1). In addition, SR mutants can either always invade populations
playing the other strategies (i.e., those playing SD, WR and WD;
bIJ bJJ for
J = 2, 5, 6; Table 3),
or never (i.e., those playing FD; b44 >
b14; Table
3).
Generally speaking, b11 will not always exceed
b31 (Table
3) because an FR mutant may not experience too much of a reduction
in its probability of getting some access to a carcass from not
searching alone before recruiting (i.e., S(n + 1) - 1/(n +
1){S(n + 1) + n{S(n - 1) + G(2)} is usually not
large), and it can enjoy a higher chance of being a finder at undefended
carcasses (i.e., 1/(n + 1){S(n + 1)/(n + 1) +
nG(2)/2} - 1/(n + 1) can be positive when carcasses are
common and/or roosts are large) than any individual in a population playing
SR. The latter is possible since successful groups (2 individuals) will
always recruit solitary searchers. Therefore, there are three main factors
that influence the stability of SR against FR in my model. First, the
frequency of carcass defense is significant; FR can invade SR populations when
carcass defense is uncommon (at low to medium values of p; SR is an
ESS at high p; Figure
2). This is because the advantage to an FR mutant of having a
relatively high chance of being a finder will be less significant when
carcasses are commonly defended since such benefits are only reaped at
undefended carcasses.
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Another significant factor is the roost size (n), and its
relationship to the critical number of birds required to overcome carcass
defense (icrit). FR can invade when the number of
birds at the roost is either smaller than the number of birds that can
overcome carcass defense, or large (SR is an ESS at intermediate values of
n relative to icrit;
Figure 2). This is because at
small n relative to icrit, carcass
defense will never be totally overcome (and it will be rarely overcome much),
thus putting a premium on being in a position to be a carcass defender (i.e.,
on being a carcass finder). Moreover, when roosts get large, the cost to
following from the roost rather than searching independently becomes less
significant since the impact of losing just two independent searchers and
having them search together, on the roost's probability of actually locating a
carcass, diminishes with the total number of searchers. In other words, at
large n, following another searcher does not result in too great a
"boomerang effect"
(Mesterton-Gibbons and Dugatkin,
1992) of reducing the benefits derived from information sharing to
swamp the at-undefended-carcasses status benefits of recruiting as a pair.
Finally, how much better it is to search independently and share
information than search as a group, is significant for the stability of SR
against FR. This is not too surprising considering the influence of n
above; FR is able to invade for a greater region of parameter space. The less
searching in a group reduces the efficiency of individual search (i.e., as
/ gets larger, the conditions for the stability of SR become
more restrictive; Figure 2).
This is because the aforementioned boomerang effect is reduced as it becomes
less costly to search in a group than search independently.
Figure 2 illustrates the
conditions under which SR is an ESS for a subset of parameter space in this
scenario.
FD as an ESS
Following from the roost and not returning to recruit (FD;
Table 1) cannot invade
populations playing SR directly (b11 >
b41 under all conditions;
Table 3). This is because the
benefits to a mutant FD strategist of always being dominant at undefended
carcasses in a population of SR strategists will never outweigh the costs of
losing out on profiting from the search effort of the majority of the roost
(S(n + 1) >> G(2) for most values of n). Instead, FD
mutants can invade indirectly by invading populations playing FR
(b43 b33 under all conditions;
Table 3), which have invaded SR
populations (q.v.). Once established, a population playing FD will be
stable against all mutants apart from those playing SD (searching
independently but not returning to recruit;
Table 1), or FR, under some
circumstances.
Against a mutant playing SD, a population playing FD can lose out if
carcass defense by non-roost dominants is rare, searching in groups reduces
individual search efficiency dramatically and the roost size is considerably
smaller than the critical number of birds required to overcome carcass defense
(i.e., at small p, when / is small and n <<
icrit; Figure
3). This is because, under such circumstances, the benefit of
always having free access to undefended carcasses (an SD player will always be
by itself) outweighs the costs of having no one to search with you and help to
overcome any carcass defense. In addition, FR can sometimes invade populations
playing FD, but only by drift. This can happen when the roost size is the same
as, or greater than, the critical number of birds required to overcome carcass
defense, or all of the carcasses are defended by non-roost dominants
(n icrit or p = 1;
Figure 3). The reason that the
payoffs are equal under such circumstances (b44 =
b34; Table
3) is that, with no undefended carcasses, or there always being
enough birds to overcome carcass defense, by returning to the original roost
after a carcass is found, an FR mutant suffers no loss in the opportunity to
gain sufficient access to it. Figure
3 illustrates the ESS conditions for FD for a subset of parameter
space.
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Although SR cannot invade populations playing FD directly, where FD is not
a strong ESS (Figure 3; above)
there is still opportunity for SR to spread to fixation. For instance, if an
SD mutant invades a population playing FD (see above), SR can spread to
fixation by drift (since b12 = b22),
because once it invades the emergent SD population (by chance), SD will be
unable to reinvade (since b11 >
b21; Table
3). Under the conditions where FR can spread in an FD population
by drift (q.v.), however, the resultant strategic landscape is less
clearcut. On the one hand, if all of the carcasses are defended by non-roost
territorials (p = 1) and FR starts to spread by drift, SR will always
be able to invade populations of these FR mutants and spread to fixation
(since b13 > b33 and
b11 > b31 when p = 1;
Table 3 and
Figure 2). On the other hand,
if FR is able to spread by drift because n
icrit, the final strategic state will depend on
the magnitude of n. Roughly speaking, at midrange roost sizes, SR
will be able to invade and spread to fixation (b13 >
b33 and b11 >
b31; Table
3 and Figure 2). However, at large n, SR can invade but will be unable to resist
reinvasion by FR (b13 > b33 but
b11 < b31;
Table 3 and
Figure 2), and therefore the
resultant population will switch haphazardly between playing SR, FR and FD
(the latter since b33 = b43 =
b34 = b44 when n
icrit; Table
3), at least in some proportion.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONRESULTSDISCUSSIONREFERENCES |
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In this article, I explore formally the performance of the search-independently-and-recruit foraging strategy employed by juvenile common ravens, Corvus corax, in New England, USA (Heinrich, 1988
,
1989;
Heinrich and Marzluff, 1991;
Marzluff and Heinrich, 1992;
Marzluff et al., 1996),
against a range of other potential strategies that include not recruiting and
searching as a group (Table 1).
This analysis demonstrates that the stability of this strategy in such an
evolutionary environment is influenced strongly by the extremity of the lost
opportunity costs associated with having to return to the original roost to
recruit other birds. On the one hand, where such costs are slight (e.g., are
restricted to missing the opportunity to be in a group in populations that do
not recruit; Scenario 1), searching-independently-and-recruiting (SR) emerges
as the unique strong ESS. Moreover, in this scenario, SR is able to invade
directly populations playing any of the other strategies, apart from the
search-as-a-group-and-move-roosts-daily strategy (FD; i.e.,
aIJ aJJ for
J 4; Table 2).
This is as a result of the benefits, in terms of locating carcasses, accrued
from being one of a number of independent searchers sharing the results of
their search effort (information sharing benefits). Indeed, this evolutionary
dominance emerges regardless of whether there are any benefits from being in a
group at a carcass (at all values of p), and is thus independent of
any group foraging benefits, so long as there are information sharing benefits
to the individual (i.e., S(k) > G(k) for k
2). On the other hand, increasing the lost opportunity costs associated with recruiting by including access-to-undefended-carcass advantages to "finders" (those birds with the most experience of a carcass; Scenario 2), reduces the evolutionary dominance of SR within the strategic environment of my model. Indeed, under such circumstances, SR is no longer the unique, strong ESS (although it can still be a strong ESS under some conditions; Figure 2); FD also emerges as a strong ESS (see below; Figure 3). Generally speaking, SRs strategic stability is weakened in Scenario 2 in two main ways. First, strategies that result in birds following from the roost and searching in groups (F strategies) will be strengthened against SR, since such strategies result in higher probabilities of access to carcasses (regardless of whether they are defended by nonroost territorials) than for independent searchers that recruit. This is because searching in groups always results in the presence of groups at carcasses, and finder status is guaranteed to a member of a successful group of searchers (as groups always recruit individuals at the roost). Thus, a population playing SR can be invaded by an FR mutant (that follows from roost and recruits) where the reduction in the probability of locating a carcass from having two of the n+1 potential independent searchers searching together (i.e., S(n + 1) — {S(n — 1) + G(2)}) is outweighed by the latter of the above benefits to searching in a group (Figure 2).
The other main way that the evolutionary stability of SR is weakened by incorporating at-undefended-carcass finder benefits is against strategies that result in birds not returning to the original roost to recruit, but roosting as close as possible to a located carcass (D strategies). Such strategies again endow their players with an increase in their probabilities of accessing a carcass (relative to SR strategists), but only when it is undefended. This is because birds that play such strategies are guaranteed the highest chance of achieving finder status in my formulation by remaining as close as possible to a located carcass and thus gaining the most experience of it. Both of the above effects combine to allow FD to both invade populations of the other strategies (either directly or indirectly) and resist invasion by any mutant strategies (be a strong ESS) under some conditions (Figure 3). The latter is possible since, by searching in groups and roosting as close as possible to a located carcass after the search day, a population playing this strategy can resist invasion (especially by SR mutants) by maximizing the chance of bestowing finder status to its members and/or guaranteeing its strategists membership of groups at defended carcasses.
With regards to the debate over the explanatory status of the information
center hypothesis (ICH; Ward,
1965; Zahavi,
1971) for communal roosting and nesting behavior (e.g.,
Mock et al., 1988; Richner and
Heeb, 1995,
1996;
Ward and Zahavi, 1973;
Zahavi, 1996), I have also
shown here how information sharing benefits alone can be sufficient
to explain the evolution and maintenance of recruitment behavior from communal
roosts (i.e., that the conditions for SR to be a strong ESS can be independent
of p: any non-information sharing benefits to recruiting). This is
always the case in Scenario 1, but it also emerges in Scenario 2 under some
conditions (e.g., at low to mid-range n;
Figure 2). Such a result runs
counter to Richner and Heeb's
(1995,
1996) assertions that the ICH
can only explain such behavior at communal roosts/nests by relying on
reciprocity or naive group selection arguments, since the results presented
here require no repeated encounters between players and all of the payoffs
that determine evolutionary stability in my formulation are to the individual.
However, under the more realistic conditions modeled in Scenario 2 (i.e., with
substantial costs to recruiting), my results also demonstrate that both the
ICH and a plausible alternative, the recruitment center hypothesis (RCH;
Richner and Heeb, 1995,
1996), have explanatory value
in my focal system. Thus, my analysis follows other functional accounts of
this system (Marzluff and Heinrich,
1992; Mesterton-Gibbons and
Dugatkin, 1999), in leading to the conclusion that both carcass
location (information sharing: ICH) and food access (group foraging:
RCH) benefits are likely to underpin the food-sharing behavior of juvenile
common ravens in the forests of New England, USA.
There are, however, a number of factors that may limit the applicability of
the conclusions that can be drawn from my analysis. On the one hand, I have
focused on a particular system, and therefore my conclusions may not be
relevant to understanding the evolution and maintenance of recruiting from
communal roosts in general. While I concede this point in its strict sense, I
assert that my analysis does have some bearing on the general issues discussed
in the communal roosting and nesting literature (e.g.,
Mock et al., 1988; Richer and
Heeb, 1995, 1996; Ward and Zahavi,
1973; Zahavi,
1996) since I have shown that it is possible for
search-independently-and-recruit behavior to be maintained by information
sharing (ICH) benefits alone. This runs counter to assertions in the
literature (Richner and Heeb,
1995,
1996; q.v.). However,
one aspect of my analysis may limit any damage to Richner and Heeb's
(1995,
1996) thesis: the nature of
the costs to recruiting in the raven system may be too idiosyncratic to
undermine the generality of their argument against the ICH. Lost opportunity
costs were chosen here since the empirical work on the system suggests that
the ravens are maximizing the probability of access to carcasses, rather than
their rates of energy intake (Heinrich,
1989; Marzluff and Heinrich,
1992). However, it may be that a reformulation with rate
maximization as the currency and energetic costs to recruitment could change
the results significantly, and may be more generally applicable (relevant
beyond wide-ranging scavengers).
On the other hand, there are limitations to my formulation that highlight
the need for further work on the juvenile common raven system. For instance, I
have assumed that each bird can only ever play one type of strategy. This is
unlikely to be the case in reality since a raven will probably change its
searching/recruiting behavior according to circumstance and its state.
Therefore, an obvious extension to my current analysis would be to allow the
players to use strategies that are conditional on such factors (e.g., only
recruit if the carcass is being defended). Indeed, such an extension would
allow "cheating" (waiting at the roost to be recruited) to be
modeled more like the scrounger strategy in a producer-scrounger game
(Barnard and Sibly, 1981;
Giraldeau, 1997); for instance,
whether an individual waits can be made dependent on the frequency of
searchers in the group. This is likely to result in a more realistic
assessment of the conditions under which sharing search effort at a roost can
be stable against information parasitism, than is possible from my current
formulation (see Barta and Giraldeau
[2001] for such an analysis at
communal nests).
So, to conclude, I hope that my analysis of the food sharing behavior of juvenile common ravens helps to clarify the debate over which hypothesis can explain recruitment to food from communal roosts. By formalizing the logic of both the information center hypothesis and an alternative (the recruitment center hypothesis) in an evolutionary game, I show that the benefits of sharing information can be sufficient to allow recruitment to food patches to evolve and be maintained. However, upon final examination, this work also demonstrates how a complete explanation of such behavior at communal roosts, at least, can ultimately rest with both hypotheses. As in many polarized debates, both sides are probably right.
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ACKNOWLEDGEMENTS |
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This work was supported by a National Science Foundation award (# 9626637) to L.A. Dugatkin. Thanks especially to Michael Mesterton-Gibbons and Lee Dugatkin for extensive help in developing the model and for useful discussions that greatly improved the manuscript. I would also like to thank Zoltan Barta and Heinz Richner for helpful discussions of this and their own work, and three anonymous referees for helpful comments on previous versions of the manuscript.
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