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Behavioral Ecology Vol. 12 No. 1: 111-119
© 2001 International Society for Behavioral Ecology
The adaptive value of inactive foragers and the scout-recruit system in honey bee (Apis mellifera) colonies
Department of Genetics and Ecology, University of Aarhus, DK-8000 Aarhus C, Denmark, and Department of Biology, Duke University, Durham, NC 27708-0338, USA
Address correspondence to C. Anderson, LS Biologie I, Universität Regensburg, Universitätsstrasse 31, D-93040 Regensburg, Germany. E-mail: carl.anderson{at}biologie.uni-regensburg.de .
Received 29 November 1999; revised 28 June 2000; accepted 11 July 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE MODELSRESULTSDISCUSSIONREFERENCES |
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In honey bee (Apis mellifera) colonies, scouts search for productive forage sites and then recruit other workers to those locations using a waggle dance. A simple and tractable mathematical model of the honey bee scout-recruit system was developed to study the relationship between nectar availability, the efficiency of the honey bee's recruitment system, and the optimal proportion of scouts that maximizes net gain (benefit - cost), or, energetic efficiency (benefit/cost - 1). The models consider both the energetic costs and benefits of active scouts and recruits as well as the cost of an inactive forager reserve. They predict conditions when individual foraging is favored over the honey bee's recruitment system, when the colony should abandon foraging altogether, and the optimal proportion of scouts (when the scout-recruit system is favored). The models' predictions qualitatively match empirical data. Surprisingly, previous empirical data from the honey bee suggest that recruits' costs are greater than scouts'—recruits spend significantly longer searching for a forage patch than do scouts—thereby causing researchers to rethink how the scout-recruit system might be adaptive. Using average returns, the models demonstrate how the scout-recruit system is adaptive despite these apparent higher recruit costs relative to the scouts'. A sensitivity analysis demonstrates that the results are robust to a broad range of relative costs of active workers, inactive workers, and the energetic benefits of the forage. Consequently, the model is demonstrated to be relevant to many insect societies that employ a scout-recruit system.
Key words: foraging, honey bee, inactives, recruits, reserve foragers, scouts.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE MODELSRESULTSDISCUSSIONREFERENCES |
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Charles Elton once remarked that "All cold-blooded animals spend an unexpectedly large proportion of their time doing nothing at all, or at any rate, nothing in particular." This is confirmed by comparative studies of vertebrates (Herbers, 1981
)
and, surprisingly, also appears true of social insects
(Schmid-Hempel, 1990),
individuals that are commonly associated with a high rate of activity.
Contrary to popular belief, the simile "as busy as a bee" is
misleading; Lindauer (1961)
and colleagues followed a single honey bee throughout its life and showed that
the bee "loafed" 40% of the time (70/177 h). More detailed studies
(Seeley, 1995) confirm an
unexpectedly high rate of inactivity in honey bees, especially for the younger
non-foraging bees, with about 30% of all bees resting at any given moment
(Seeley TD, personal communication;
Winston, 1987).
Honey bees will forage as far as 11 km from their nest
(Seeley, 1995;
Visscher and Seeley, 1982) and
so these resources are clearly very valuable to the colony. Why then aren't
any workers who are not involved in intranidal tasks contributing to the
foraging process? Some evidence (reviewed in
Schmid-Hempel, 1991; but see
Visscher and Dukas, 1997)
suggests that honey bees have a limited lifetime energy budget, equivalent to
around 800 km of flying (Gould and Gould,
1988). Because flying is so energetic
(Schmid-Hempel et al., 1985;
Wolf and Schmid-Hempel, 1990;
Wolf et al., 1989), by
conserving their efforts and only flying to known productive patches—the
good sites found by scouts—recruits can lead longer and more productive
lives maximizing their lifetime work contribution to the colony (Jeanne's
[1986] "demographic
advantage"). This idea is supported by Sekiguchi and Sakagami's
(1966) findings that a
considerable number of bees do not forage, or only rarely so, and that their
stimulation threshold for dances and food odors is high. Thus, these bees may
serve as a backup foraging force in times of "great field mortality or
opportunity" (Michener,
1974).
Honey bee foragers face an additional problem to the high energetic expense
of collecting nectar: the volatile nature of nectar availability and
dispersion. For instance, in the space of a few days, conditions may change
from nectar dearth to nectar flow (e.g.,
Seeley, 1995: Figure 2.15).
Seasonal changes, climate, and competition can all play their part to make
nectar collection, and importantly, any planning on the part of the colony,
difficult. Clearly, a colony shouldn't have its foragers sitting idle in the
nest when forage is available. However, because flying is so energetic there
is also little point in having a large active forager force expending lots of
energy flying to different potential forage sites when there is little or no
forage at hand. A colony requires sufficient scouts to monitor nectar
availability and ensure that quality sites are found but that scouting force
should not be so large that collectors are limiting when good sites have been
found. The question considered in this study is what proportion of the
foraging force should scout for food, and thus how many should remain in the
nest both conserving energy and acting as a recruitment pool?
In this study I present a simple and tractable model of active (scouts) and
inactive (reserve) foragers in an insect society. The model is used to study
the relationships between nectar availability, the efficiency of the
recruitment system, and the optimal proportion of scouts. The model considers
maximization of two currencies that honey bees may use: net gain and energetic
efficiency (Schmid-Hempel et al.,
1993; Seeley,
1994,
1995). For clarity the model
refers to a population of honey bee foragers but it should be stressed this is
used solely as an illustrative example; the model's assumptions and
conclusions should apply equally well to many other insect societies that
employ a scout-recruit system. Finally, empirical data show, contrary to
expectations, that time spent searching for a forage patch is higher for
recruits than scouts (138 versus 85 min respectively,
Seeley, 1983; 121 versus 82
min, Seeley and Visscher,
1988). These counter-intuitive results have caused researchers to
reconsider how the bees' scout-recruit system is adaptive. Seeley
(1983) suggested that
consideration of average returns may clarify these perplexing findings. This
is the approach adopted in this study and one of its main objectives.
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THE MODELS |
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TOPABSTRACTINTRODUCTIONTHE MODELSRESULTSDISCUSSIONREFERENCES |
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Introduction
The model considers the energetics of honey bee scouts, recruits, and unemployed foragers during a single foraging bout. Initially, a "bout" is taken to be sufficiently long so that a scout can find a site, recruit others to it, and that those recruits locate the patch. Later, longer timescales are considered. Notation is summarized in Appendix A.
I consider a population of N honey bee nectar foragers. Some
proportion of these, s 
(0,1], are scouts that leave the nest
at the start of the bout while the remainder are unemployed foragers that
remain in the nest and serve as potential recruits. Each scout searches
independently for forage, and it is assumed that each can check one
"forage site," such as an area of clover or heather, which may
contain sufficient nectar for several foragers to exploit simultaneously. That
is, each forage site may contain several "forage patches" where
each patch contains sufficient forage for only a single forager to exploit.
There is some probability, p, that the site contains forage, and if
so, then its quality (the number of patches) is <q>, the mean
of some distribution q(·).
It is assumed that a "successful" scout, that is, one that
finds a productive site, makes some heuristic judgement of the site quality
and returns to the nest to recruit the appropriate number of foragers
(<q> - 1). This is akin to assuming that the scout's dance
duration is proportional to site quality (with appropriate limits) which is
roughly true of honey bees (Seeley,
1995). Unsuccessful scouts continue to search their site in vain
for the rest of the foraging bout. Unemployed foragers respond to recruiting
scouts and attempt to locate the advertised site. However, recruitment is not
perfect. I assume that, on average, a recruit returns with a reduced
load of nectar defined by a parameter 
(0,1]. The justification
is that honey bee recruits take several trips to find the advertised forage
patches (Seeley, 1983,
1995;
Seeley and Visscher, 1988; see
parameterization section). That is, each recruit makes several unsuccessful
trips, each time returning to the nest unladen, before she finds the
advertised site and returns with a single full nectar load.
At the end of the bout, four categories of workers are recognized:
- Successful scout—a scout that found a productive site and
returned with a load (1 unit) of nectar;
- Unsuccessful scout—a scout that failed to find a productive
site and returned without nectar;
- Recruited worker—a worker that was recruited to a productive
site and returned with some ( units of) nectar;
- Inactive worker—an unemployed forager that remained in the
nest throughout the foraging bout.
(Unsuccessful recruits that failed to find the advertised patch are taken
into account through the parameter .) The proportions of these four
worker types are denoted fs, fu,
fr, and fi respectively and sum to
1.
Energetic payoff
Model I: maximization of net gain
At the end of the bout the colony's energetic gains and losses (in Watts)
are calculated for the four worker groups. Because I use an average-return
approach and only consider the average nest-forage site distance it is
convenient to work in Watts rather than absolute return (Joules). Model I
assumes that the colony's maximand is net gain (benefit - cost). I assume that
inactive workers cost the colony Ei Watts through
metabolic costs. Foraging is a more costly activity because of the high
energetic costs of flying, and so an unsuccessful scout costs the colony
Ea Watts, where Ea >
Ei. A successful scout however, returns with a full load
of nectar worth F Watts (where F > Ea
and F takes into account the duration of the foraging trip) but also
incurs the metabolic costs of flying (Ea) and so its net
gain is F - Ea Watts. A recruited worker incurs
the costs of flying but requires several unsuccessful trips (on average; see
parameterization section) each costing Ea Watts, before
she finds the advertised site and gains F Watts from a nectar load.
Thus, at the end of an average trip, she returns with a smaller reward,
F, and so her net gain is F —
Ea Watts.
The colony's net gain (payoff) per second per capita (r(s)) for
some proportion of scouts is:
 | (1) |
The parameter p and the distribution q(·), which
has mean <q>, define the environment. Thus, for a given
environment {p, q(·)} we can determine the following average
proportions of each of the four workers:
 | (2) |
Model II: maximization of energetic efficiency
There is some evidence (Seeley,
1994,
1995) that honey bees may not
always maximize net gain but a different currency, net energetic efficiency,
the maximand in model II. Energetic efficiency is the marginal benefit
(benefit - cost) divided by the cost, or, alternatively (benefit/cost) -1. In
both models I and II, the average benefit is F(fs
+ fr) and the cost is Ea(1 -
fi) + Eifi. Thus, with this
new currency the colony's payoff, now denoted r' (s),
is:
 | (3) |
The average proportions fs, fu, fr, and fi are unchanged from Equation 2 and so can be substituted into Equation 3 to obtain the final payoff (Appendix B).
Parameterization
The model was parametized as follows:
- Ei = 0.42 x 10-2 Watts and
Ea = 3.36 x 10-2 Watts
(Schmid-Hempel et al.,
1985:63).
- F = 0.196 Watts, resulting from a crude assumption that a load of
nectar, upon arrival at the nest, has an energetic value of 552J (55 flowers
x 10.05J / flower; Schmid-Hempel et
al., 1985), and that an average foraging trip takes 47 min
(Anderson, 1998). This gives an
energetic return of 0.196J for each second of the foraging trip.
- = 0.25. Seeley
(1995:126) reports that
"on average, a bee will need to make approximately four tries, that is,
conduct some four dance-guided searches, to locate a flower patch advertised
by a dancer." Earlier studies reported 4.8 ± 3.2 trips (range
1-12, n = 20; Seeley,
1983) and 4.1 ± 2.8 trips (range 1-12, n = 44;
Seeley and Visscher, 1988). In
the results section, is varied from 0.1 to 1.
No values for p and <q> were estimated but they are both explored over a broad range. Because analysis of these models is in the form of a per capita payoff, the payoffs are independent of the size of the foraging population size, N.
Limitations of the models
I assume an unchanging resource distribution (constant p) and make
no attempt to model daily or seasonal variations in the forage distribution,
any renewal processes, or competition from other colonies. Although honey bees
do face these factors, they are not relevant on the timescale of these models,
a single foraging bout, because the probability of encountering a profitable
site is unlikely to change.
In these models the probability of locating a patch, p, is
independent of the mean quality of the patch, <q>, which is not
always the case in nature. However, as Jaffe and Deneubourg
(1992) highlight in a similar
model, it does stress the fact that the size of the forage sites is much
smaller than the total forage area. For instance, Visscher and Seeley
(1982) calculated that the
circle encompassing 95% of their bees' foraging sites had a radius of 6 km
(Area 113 km2), and so each patch of flowers represents a tiny
proportion of this range.
I assume that all bees are equal in terms of weight, crop size, searching ability, and so on, and that each patch is equidistant from the nest. As this model is analyzed only in terms of average payoffs, these results are not affected by these assumptions. These assumptions do, however, prevent analysis of a third possible currency that bees may use: rate of food collection (net gain/time).
Last, the models consider the optimal way to employ N foragers as
scouts or potential recruits to maximize one of two currencies. Under natural
conditions, N is expected to vary in response to colony needs and
conditions, such as the amount of stored nectar
(Schmid-Hempel et al., 1993;
Seeley, 1995), and colonies
may switch between different maximizing currencies during the year (Seeley,
1994,
1995). These other factors
were not incorporated into the model.
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RESULTS |
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TOPABSTRACTINTRODUCTIONTHE MODELSRESULTSDISCUSSIONREFERENCES |
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Model I: maximization of net gain
Figure 1 shows per capita payoff (r), in the form of net gain, against proportion of recruits (s) and recruitment efficiency (
) for four environments. The
thick black line in each figure represents the optimal strategy—the
proportion of scouts, s*, that maximizes
payoff—against recruitment efficiency.
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Clumped food dispersion
When food is clumped (p =.05, <q> = 10;
Figure 1a) two distinct optimal
regimes are observed. First, the sparseness of patches (low p)
combined with low recruitment efficiency mean that net gain is negative, for
all s, and the colony's best strategy is to minimize its losses and
remain in the colony (i.e., s* = 0). However, there
appears to be a threshold at = 0.4 above which the scout-recruit
system is favored—the few good sites found by scouts can be exploited
well by recruits—and s* remains fairly constant at
around 0.7.
Nectar flow
During nectar flow (high p, large <q>;
Figure 1b) two optimal regimes
are also observed. When recruitment efficiency is low, all foragers
should scout: most scouts will find productive sites, a return of F -
Ea, which will cover the costs (-Ea)
of the few unsuccessful scouts. However, with high recruitment efficiency only
about 15% of the colony should scout because the recruits will exploit these
large and profitable sites well.
Nectar dearth
During nectar dearth (low p; small <q>;
Figure 1c) sites are both
scarce and poor. The colony can at best minimize its costs by remaining in the
nest—thus, s* = 0 for all —and drawing
off its honey reserves as would occur during overwintering.
Many small flower-patches
Figure 1d shows net gain
when productive sites are abundant (p =.8) but small
(<q> = 3). As in nectar flow when recruitment efficiency is low
(Figure 1b), the colony should
send out many scouts, but as recruitment efficiency increases the colony
should keep some workers as inactive workers ready for recruitment. In
general, the quality of the environment can be roughly summarized by the
product p<q>, the total amount of food in all the
patches, and different environments with similar values of
p<q> tend to exhibit similar payoff surfaces.
Model II: Maximization of energetic efficiency
Figure 2 repeats the results
from Figure 1 using the new
currency, energetic efficiency. The results are surprisingly similar,
particularly when a broad variety of environments are considered
(Figure 3). For many
environments the predictions of the two models, the proportion of scouts that
maximizes payoff, for either currency, are virtually identical
(Figure 3).
Figure 2 highlights two
environments in which this is not the case. With a clumped food dispersion and
low recruitment efficiency (Figure
1a versus Figure
2a) energetic efficiency favors some scouting while this is not so
when net gain is considered—the cause of this difference is not clear.
During nectar dearth (Figure 1c
versus Figure 2c) there is a
large difference in the models' predictions—net gain favors abandonment
of foraging while energetic efficiency favors scouting
(Figure 3). The cause of this
difference is discussed later.
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Multiple trips to a patch
So far, the models consider payoff for single foraging bouts. But, once a
recruit has located a profitable patch it will most likely make multiple trips
to that patch (e.g., Seeley and Visscher,
1988: Figure 1). A
honey bee recruit takes four dance-guided trips, on average, to initially find
the advertised patch ( = 1/4) and so its average net gain for those
four trips is F - Ea = F / 4 -
Ea. However, once she has located the patch, on subsequent
trips she will fly directly to that patch, collect a full load of nectar and
so receive a net gain of F - Ea for the trip.
Therefore, subsequent successful trips increase a recruit's effective
recruitment efficiency, denoted '. Effective recruitment
efficiency reflects the average nectar gain for all the trips that a
recruit makes to a particular patch. It is a weighted average of recruitment
efficiency (for the first 1/ trips), and a recruitment
efficiency of one for the full nectar loads for all (m) subsequent
trips:
 | (4) |
Provided < 1, multiple trips to a profitable patch will always
increase a forager's effective recruitment efficiency and thus her average
payoff. But by how much? Rearranging Equation 4 gives the number of subsequent
trips which gives rise to a particular value of ':
 | (5) |
Table 1 shows values of
m for ' {0.5, 0.75, 0.9, 0.95}. The third column
illustrates the number of subsequent trips needed to produce the effective
recruitment efficiencies in column 1 with = 
. Only
two subsequent trips doubles effective recruitment efficiency from
to 
. Only eight subsequent trips increase the payoff from
F/4 - Ea to 3F/4 -
Ea, that is, from 0.013 W to 0.111 W, more than an
eight-fold increase. In good conditions, foraging trips can be short, so it is
not unreasonable for a single bee to make many trips to the same foraging site
during a day. For instance, Park
(1928) reports a mean of 13.5
(maximum of 24) trips per day during heavy nectar flow. Thus, under the right
conditions, honey bees can readily achieve an effective recruitment efficiency
of 0.9, or higher.
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In themselves these results are not particularly surprising: recruits that
miss the advertised patch on their first few attempts will increase their
average return by making multiple trips to the patch. The significance of the
results can be appreciated if we return to the payoff surfaces in
Figure 1. Except where the
colony's payoff is negative (Figure
1c), the proportion of scouts at which the maximum payoff is
reaped is generally lower with higher recruitment efficiency, at least for the
conditions pertinent to the honey bee, that is, = 0.25 vs.
' 
0.9. (These results have been explored over a wider range
of conditions than shown in Figure
1.) In short, multiple return trips to a forage site favor a
smaller proportion of scouts and so greater forager inactivity. Not only will
this increase net gain or energetic efficiency but there are additional
adaptive benefits which are discussed later.
Environment-dependent optimal strategies
Figure 3a shows the optimal
proportion of scouts (s*) that maximizes net gain against
p and <q>. (Effective recruitment efficiency is fixed
at 0.8, a value reflecting the honey bee's low recruitment efficiency (
= ) but with multiple return trips.) The surface is partitioned into
three sections. The smallest and lowest (rightmost) section in
Figure 3a shows that during
nectar dearth, (p and <q> both low), the colony can
only lose energy and so at best minimize its losses by abandoning foraging.
With more productive environments, the central section, colonies should use
their recruitment system and send out scouts. Importantly, the curvature of
this central subsurface indicates that as forage quality increases, whether in
terms of site quality (y-axis) or proportion of productive sites (x-axis),
then the colony should sent out a smaller proportion of scouts. Finally, when
the probability of finding a productive forage site is greater than
recruitment efficiency (p > '; highest and leftmost
section of Figure 3a) then the
colony should abandon its recruitment system and forage individually.
Figure 3b is as for
Figure 3a but with energetic
efficiency. Results are similar to those for net gain except that the decision
to abandon foraging is absent. Here the colony should always forage if a
chance exists of finding food (at least for these particular values of F,
Ea, Ei, and '). The difference between
these currencies can be explained by considering payoffs under high costs.
With net gain (benefit - cost), the payoff decreases with increasing cost.
However, with energetic efficiency (benefit / cost - 1), as costs increase,
the first term tends to zero and so payoff tends to a constant, -1.
Sensitivity analysis
It was anticipated that the results of the previous sections would depend
strongly on the fact that flying is so much more energetic than inactivity,
that is, Ea >> Ei. However, a
sensitivity analysis demonstrates that this is not so. The above results are
robust for a broad range of values of F and Ea
relative to Ei. As an example I show results for two
different environments: (1) center of the recruitment section of
Figure 3 (p = 0.5,
<q> = 10), and (2) rightmost section of
Figure 3 (p =.05,
<q> = 10). Table
2 shows, for both currencies, how the optimal proportion of scouts
changes when either Ea or F is varied as some
integer multiple, c, of Ei.
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When Ea is varied (with fixed F) there is some
threshold value above which flying is so costly that the colony should abandon
foraging (e.g., when Ea 36Ei for
net gain, Table 2).
Importantly, there is a very broad range, c = 1-35, at which
s* is unaltered. Similarly, when F is varied
there is some threshold value below which the benefit of the nectar load is so
low, relative to the costs of collecting it, that the colony should also
abandon foraging. However, any value of c above this means that the
colony should collect the nectar, and s* does not vary at
all, especially for energetic efficiency in which results are particularly
robust.
This robustness is due to the fact that s* occurs when the number of productive patches found by scouts (minus the number of scouts) matches the number of inactive workers (i.e., ps[<q> - 1] = 1 - s), and, crucially, this is essentially independent of F, Ea, and Ei. An important implication is that many of the models' results hold when the costs of collecting the material are not that much greater than inactives. Thus, this model should apply equally well to the scout-recruit system in other groups, such as ants, that do not fly and in which Ea is likely only marginally greater than Ei.
Inactive foragers
Thus far, apart from when there is so little food that the colony should
abandoning foraging (Figure 3),
inactive workers are always recruited (fi = 0) as part of
the optimal strategy. However, there are two situations in nature where this
is unlikely to be the case: (1) where the productivity of the environment
fluctuates, and (2) where the amount of nectar in the environment is
limited.
Fluctuating environment
Suppose that the environment is productive (some positive p and
<q>, as before) with probability ß, and unproductive
(p = 0), with probability 1 - ß. In this fluctuating
environment, for some fixed strategy {s} a colony expects a net gain
payoff as in equation 1 with probability ß and payoff -
Eas - Ei(1 - s) (Appendix B
with p = 0) with probability 1 - ß. Thus,
 | (6) |
Some s, s*, maximizes colony payoff and will be
associated with some optimal fraction of inactives
(fi*, from Equation 2):
 | (7) |
But, at s* the number of patches the scouts need to
recruit for (ps([q] - 1)) equals the number of recruits (1 -
s) and so
 | (8) |
With the following parameters values: F = 0.196;
Ea = 0.0336; Ei = 0.0042; =
0.8; p =.01; <q> = 10, and ß = 0.5, it was found
that s* = 0.52 (with a per capita net gain of 0.015).
Substituting these latter values into Equation 8 gives
fi* = 0.24. Importantly, this demonstrates that
an inactive forager force is adaptive when the environment fluctuates. The
reasoning is as follows: for constant environments, when there is not food the
optimal strategy is inactivity, that is, when p = 0 then
s* = 0. When the environment is productive then there is
some positive s*; in short, if p > 0 then
s* > 0. Thus, in a fluctuating environment the colony
must come to some compromise, an intermediate and positive value of
s* and so there will be inactives. Interestingly, in very
rich environments (high <q>), s* will be
low in any case (see earlier) and so there is less conflict between
s* in unproductive vs. rich environments.
Limited resources
If resources are limited with less productive patches than foragers
(N), the forager excess should remain inactive. They are essentially
a burden during poor forage: a set of workers consuming resources but who do
not make a foraging contribution. Optimal behavior might be to reassign these
inactive workers to other tasks, that is, adjust the size of the forager
population. However, these reserve foragers come into their own when there is
a sudden burst of nectar productivity (e.g.,
Seeley, 1995: Figure 2.15) and
the nectar they can bring in during these times outweighs their energetic
costs during leaner times. That is, these workers are adaptive as part of an
optimal strategy for the whole set of foragers on a longer timescale.
Based on the estimates of F, Ea, and Ei, the net gain of a successful foraging trip is roughly 40 times that of the costs of an inactive worker. Even allowing for a recruitment efficiency of 0.8, a worker only needs to bring in nectar for about 3% of her time to "pay her way." However, because the foragers in a colony are not just bringing nectar in for themselves but for the rest of the colony and they need to produce a stockpile for the winter, the actual "break even" work proportion will be higher than 3%.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHE MODELSRESULTSDISCUSSIONREFERENCES |
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I have presented a model of a scout-recruit system that predicts the optimal proportion of foragers that should act as scouts thus leaving the remainder as energy-saving inactives, but who are available as potential recruits. To the best of my knowledge this model is unique in that it considers the energetic return for an insect society from the whole group of foragers, both active and inactive. Results show that the optimal proportion of scouts, based on maximizing either net gain or energetic efficiency, depends strongly on the quality of the environment (p<q>) and the ability of recruits to locate a patch advertised through a recruitment dance (
)—the "waggle
dance" in the case of honey bees (von
Frisch, 1967). In an empirical study, Seeley
(1983) found that the
proportion of honey bee foragers which found their next forage site through
scouting, as opposed to recruitment, was low (5%) in times of rich forage and
high (36%) during poor forage. Also, Waddington et al.
(1994) found a reduced role of
recruitment as part of the overall colony foraging strategy in habitats with
abundant small patches of flowers. Both these data qualitatively match the
predictions of the current models (Figure
3).
Seeley (1983) and Seeley
and Visscher (1988) measured
the time that scouts and recruits took to find a forage site. Surprisingly,
recruits took significantly longer (60% longer,
Seeley, 1983; 47% longer,
Seeley and Visscher, 1988)
than scouts. This has caused researchers to consider other ways in which the
scout-recruit system may be adaptive. Seeley
(1983) suggested that an
analysis based on average return per forager might clarify this perplexing
result. This study adopts such an approach and sheds some light on the matter.
On the basis of a single foraging trip, a scout's energetic costs may well be
lower than a recruit's costs. Crucially, this is because a recruit that acts
upon a waggle dance rarely finds the advertised patch on its first attempt. On
average, they require four (but up to 12) energetically expensive trips before
they find the patch and receive a payoff, a nectar load. Thus, these fruitless
and expensive trips can cause the search time for a recruit to exceed that of
a scout. However, what must be taken into consideration is that once the
recruit has located the site she may make many profitable return trips to that
site. Considering average returns, multiple trips to a forage patch can then
increase a recruit's profitability above that of a scout. Also, waggle dancers
can recruit not just one but many recruits to the same site. This will further
increase the recruit's return relative to the scout's. Last, scouts are
selective in the sites they dance for and they tend to advertise quality
sites. These benefits are then passed onto recruits: scouts may encounter both
poor and quality sites but recruits are directed to quality forage. All these
factors will increase the adaptive value of recruits.
The model predicts that for a variety of environmental conditions an
inactive reserve forager force is favored. By increasing demand for
comb-building, Kolmes
(1985a,b)
demonstrated that honey bee colonies do have reserve forces that can be called
on without detrimentally affecting performance of other tasks. Thus, honey bee
colonies do not fit Oster and Wilson's
(1978) idealized
"ergonomically efficient" colony organization in which all members
are actively tackling tasks. The presence of a reserve forager force in the
nest is adaptive at the colony-level
(Seeley, 1997) for a variety
of reasons. A reserve force acts as a buffer for the fluctuating and
unpredictable demand for work because inactive workers in the nest can be
recruited to other tasks while scouts out in the field cannot. Inactivity for
non-foragers may be important as the workers may spend their energy producing
brood food or wax (Lindauer,
1952). Last, a forager uses her own information and experience to
decide to abandon a patch when the patch's profitability declines
(Anderson and Ratnieks, 1999).
Paradoxically, active workers only have knowledge about their current patch
whereas inactive workers in the nest are exposed to many workers dancing for
their respective patches. Inactive workers therefore have access to better
information about forage conditions than the active workers
(Seeley, 1995) and so the
dance area and inactive workers may serve as information center.
As I, and others (Jaffe and Deneubourg,
1992; Johnson et al.,
1987), have shown, there is a unique proportion of scouts that
maximizes net gain—and also in this study, energetic efficiency—to
the colony. However, there are other issues involved. There is some evidence
that honey bee colonies use different currencies at different times of the
year (Schmid-Hempel et al.,
1993; Seeley,
1994). Small colonies or those with few nectar reserves to draw on
may be better to maximize rate of nectar delivery to the nest whereas larger
colonies may do better able to maximize energetic efficiency, especially when
the demographic advantage is taken into account
(Seeley, 1994). When forage
conditions are poor the colony should sit tight in the nest and await better
conditions. Unfortunately though, the colony can only monitor when forage is
available by sending out scouts to check, thus incurring some energetic and
unprofitable trips (Visscher and Seeley,
1982). In this sense, the colony will always be acting
suboptimally. This "error" can be regarded in the same adaptive
sense as ant foragers who lose a foraging trail (Deneubourg et al.,
1983,
1987) or honey bee recruits
that miss the advertised flower patch
(Weidenmüller
and Seeley, 1999) but who then explore new areas and find other
new high quality sites.
The model presented here predicts an optimal proportion of scouts that
maximizes some energetic currency, but how such a colony-level response is
mediated is unknown. There is some evidence that honey bee scouts have a
higher tempo and exhibit more consistent foraging rates than recruits, and
that a bee's scouting rate correlates with her previous foraging rate
(Seeley, 1983). If this is so,
then it is highly likely that there is some regulatory mechanism that adjusts
the relative proportions of scouts and recruits in the forager population.
However, a concerted research effort will be needed to elucidate this
mechanism.
APPENDIX A
Notation
|
APPENDIX B
Payoffs
From Equations 1 and 2, model I is defined by:
 |
[0,1], (0,1], Ea
> Ei (0,
], and <q>
{1,2,..., } are constants and s [0,1] is the
variable under colony control.
From Equations 2 and 3, model II is defined by:
 |
(Note that in model II when ps([q] - 1) 1 -
s, the payoff function is a linear function in which the sign of the
gradient simply depends on the sign of p - . That is, reserves
are favored when > p implying a good recruitment system,
and/or, few productive sites.)
|
ACKNOWLEDGEMENTS |
|---|
I thank Koos (J. J.) Boomsma, Jennifer L. V. Jadin, Francis L. W. Ratnieks, and Stanley S. Schneider for commenting on earlier versions of this manuscript. Members of the Centre for Mathematical Biology at the University of Bath (U.K.) also provided valuable feedback. The author was supported by a postdoctoral fellowship from the research network "Social Evolution" of the Universities of Aarhus, Firenze, Keele, Sheffield, Uppsala, Würzburg and the ETH Zürich, financed by the European Commission via the Training and Mobility of Researchers (TMR) programme. The Department of Biology at Duke University provided additional support.
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