Behavioral Ecology Vol. 7 No. 1: 43-48
Productivity in a social wasp: per capita output
increases with swarm size
Robert L. Jeanne* and Erik V. Nordheimb
"Departments of Entomology and Zoology, and bDepartment of Statistics, University of Wisconsin,
Madison, WI 53706
We measured the productivity of newly-founded colonies of Polybia ocddentalis, a Neotropical swarm-founding social wasp, over
their first 25 days. By both of the measures we used, number of nest cells built by the swarm and dry weight of brood produced,
colony-level productivity was a significant positive quadratic function of the number of adults in the swarm, indicating that per
capita output increased with swarm size. Subdividing adults into queens and workers did not improve significantly on these
models, but the proportion of queens was a significant factor explaining brood production in one of two sampling years. Earlier
work on P. ocddentalis suggests that the mechanism behind the pattern is that workers transferring materials to one another
experience increasing queuing delays as group size decreases. The largest colony in each of the two years produced unusually
low outputs of brood. One interpretation is that the curve of group-size related brood productivity peaks at intermediate group
size and that these colonies are on the downward part of the curve. That these same two colonies also had the lowest proportions
of queens suggests a second interpretation: these colonies were constrained to low brood production by a low colony-level
oviposition rate. A third possibility is diat these were mature colonies, and mature colonies may allocate a smaller fraction of
resources to brood rearing than do younger colonies. Our result contradicts earlier findings for a variety of social and subsocial
Hymenoptera that per capita productivity declines as group size increases. We suspect that Michener's result for swarm-founding
wasps is an artifact of his having to lump colonies of different species and different stages of development to obtain adequate
sample sizes to plot. If our result for P. ocddentalis can be generalized to other swarm-founders, then these wasps have evolved
a mode of colony organization fundamentally different from that of other wasps. Thus, our result places new significance on
the role of group dynamics as a factor affecting group size in different taxa. Key words: colony size, Polistinae, productivity,
social wasps, swarms, Vespidae. [Behav Ecol 7:43-48 (1996)]
"T A That determines the size of a social group? Group size
V V varies tremendously across species, from just a few individuals in loosely cooperative groups of vertebrates and insects to millions in some of the ants and termites (Wilson,
1971, 1975), yet we have only a rudimentary understanding
of the causes of the variability. For example, the question of
why colonies of honey bees typically contain tens of thousands
of workers instead of just hundreds, or millions, has no satisfactory answer.
The forces acting on social group size undoubtedly include
factors both intrinsic and extrinsic to the group. In a frequently cited paper, Michener (1964) investigated intrinsic
factors influencing group size in the social Hymenoptera. Using published data to examine patterns of group productivity
for a range of species, he found for most species that colonylevel productivity increases with colony size but that productivity per female decreases. With the caveat that sampling bias
may be responsible for the pattern, Michener concluded that
this "indicates the existence of social patterns causing higher
efficiency per female the smaller the group" (Michener, 1964:
334).
Michener noted that this was a paradoxical result because
it suggested that natural selection acting on productivity alone
would drive group size down, eventually eliminating sociality.
The implication is that social cooperation must therefore be
maintained by countervailing extrinsic forces that confer
greater fitness benefits on being in larger groups despite their
lowered per-female productivity. Candidates include greater
effectiveness of defensive, competitive, or homeostatic mechanisms, leading to increasing survivorship with increasing
Received 26 September 1994; revised 14 March 1995; accepted 21
March 1995.
1045-2249/96/$5.00 O 1996 International Society for Behavioral Ecology
group size (Holldobler and Wilson, 1990; Michener, 1964;
Strassmann et al., 1988).
Results of a study of work efficiency in the social wasp Polybia ocddentalis are seemingly at odds with Michener's findings (Jeanne, 1986). In this polistine wasp, workers in large
colonies (mean: 512 females) accomplished a given amount
of nest repair in 43% fewer worker-minutes than workers in
small colonies (mean: 40 females). The gain in work rate in
larger colonies appeared to come from a reduction in delays
incurred in queuing for transfers of materials from worker to
worker.
Can this result be reconciled with Michener's paradox? One
possibility is that the higher work rates of larger colonies apply
to specialized tasks, such as nest repair, but do not translate
into greater overall per capita output of brood. Perhaps, for
example, workers in large colonies spend a greater proportion
of their time waiting idly to meet contingencies than do workers in small colonies. If this were so, then productivity measured in terms of brood output per female, as in Michener's
survey, may decrease with increasing colony size.
The purpose of the present study is to resolve this issue for
P. ocddentalis by measuring per capita productivity for a range
of colony sizes, while controlling the variables that confounded Michener's study: species, season, and stage of colony development Our results clearly show that per capita productivity increases with group size over a wide range of group size,
contradicting Michener's pattern.
METHODS
Polybia is one of 24 genera of tropical wasps (Vespidae: Polistinae) that found colonies through swarms of workers and
queens. During subsequent colony development, the initially
high number of queens reduces to one or a few, a pattern
called cyclical oligogyny (Queller et al., 1993; West-Eberhard,
Behavioral Ecology Vol. 7 No. 1
44
1978). In the remaining five genera of the subfamily, one or
a few inseminated queens initiate colonies independently of
workers. Swarm-founders have larger colony sizes (10s—10* individuals) than do independent founders (lO'-lO2 individuals) and overwhelmingly dominate them in terms of abundance in most habitats (Jeanne, 1991).
We conducted field studies on P. ocddenlalisul Centro Ecologico 'La Pacifica,' near Canas, Guanacaste, Costa Rica
(10°25' N, 85°7' W). Canas is within the Tropical Dry Forest
(moist province transition) Life Zone (Tosi, 1969), which is
marked by strong wet-dry seasonality, the wet season extending from May through October. Mean annual rainfall (19781987) for Caiias is 1369 mm. Rainfall in 1982 and 1984, the
years of the study, was 1123 mm and 1415 mm, respectively
(W. Hagnauer, personal communication). Native vegetation of
the region is tropical dry forest, but this has been broken up
at our site by pasture and cropland. Colonies were located in
shrubs and trees in pastures, hedgerows, forest edges, and on
and around buildings. We collected data on the population
at La Pacifica in September-October 1982 and June-July
1984.
We induced active colonies to form absconding swarms by
dismanding dieir nests. A few adults in each colony were
marked with a distinctive color so die swarm could be recognized when found later. Swarms emigrated to new sites and
began building their new nests widiin 12-36 h. We used departure time of each swarm from the old site as the time of
initiation of the new nest.
Each swarm was allowed to construct a nest at die new site
and rear brood undisturbed for 25 days. Swarms of diis species
construct die nest in the first week or so, dien switch to feeding die larvae that begin to hatch at about diat time (Forsyth,
1978; Jeanne, 1986; Jeanne, personal observation). The nest
is not normally enlarged until after die production of new
worker offspring. Twenty-five days is just short of the egg-adult
development time of approximately 30 days (Machado, 1977).
By not allowing die recruitment of adult offspring into die
founding population, we maintained a clear distinction between producers (adults) and the results of dieir efforts
(brood).
On die evening of die 25di day, we collected each colony
widi its nest. Escapees, along with any foragers diat spent die
night away from die nest, clustered at die nest site die following morning and were added to die collection.
We dissected die nest and adult population die day after
collection. The combs and cells in each comb were counted
and die immature stages (eggs, larvae, and pupae) were removed from each cell and preserved in Kahle's fixative. We
dien separated die nest into its cellular and noncellular components by carefully scraping die cells from dieir underlying
basement envelope widi a razor blade and sealing die material
in a plastic bag. The remaining noncellular material was freed
of any adhering meconia (larval feces) and saved in a second
bag. We weighed each of die two components of the nest
separately on a Sartorius analytic balance.
We removed brood collections from dieir fixative by vacuum filtering on preweighed, oven-dried filter paper over a
Buchner funnel to remove excess liquid. We dien dessicated
brood and filter paper to uniform dryness in a vacuum oven
at 60°C and weighed to die nearest 0.1 mg. Net weight of die
brood was calculated by subtracting die tare weight of die
paper.
Aldiough queens are slighdy larger dian workers in some
dimensions, the castes are not reliably recognized by inspection. Therefore, we dissected females while still fresh to determine reproductive condition. Queens were defined as inseminated females having at least one opaque egg (egg widi
yolk) per ovary. We counted workers and queens and preserved diem separately in Kahle's fixative.
Analysis
The number of brood cells built by die swarm was used as a
measure of nest size, while die dry weight of brood was used
as a measure of brood productivity. We used regression analysis to assess die effect of die number of females on nest size
and brood productivity. For each of die two response variables
(cell number and brood weight), we used two approaches to
regression. In die first approach, we used die response variable as is and considered a polynomial model of total adult
numbers as die primary portion of die prediction equation.
In die second approach, we divided each response variable by
die total number of adults, resulting in per capita measures
of nest size and brood productivity. We discuss bodi approaches in our results.
For bodi approaches, we considered models widi and widiout a constant. For models widiout a constant, we define "effective /?" = 1 - SSErr/SSTot^ where SSErr is calculated
for die given model and SSTot^, is die total sum of squares
for any model diat includes die mean. We conservatively considered terms significant if dieir p value was less dian .10.
We allowed for different intercept and slope terms for all
variables for 1982 and 1984. If die coefficients for any variable
were not significandy different between die two years, we combined die data for die two years for diat variable. Thus die
resultant models for die two years are linked widi one anodier
and a modification in die sample for one year might affect
bodi.
We considered two mediods for determining if die numbers
of workers and queens affect die response variables differently. For our primary analysis, we considered the proportion of
queens (and diis proportion squared) as predictor variables.
We also considered polynomial models using die numbers of
workers and queens separately. Since diese latter models were
more complicated and never improved our fit in a significant
way, we do not report diese results.
Finally, we considered die possible influence of some colonies as oudiers. To assess die significance of oudiers, we created a new independent variable for each potential oudier
(Weisberg, 1985). The variable takes die value of 1 for die
potential oudier colony and die value of 0 for all odier colonies. This results in a "1 value" for die oudier test, which is
distributed as a Student's t distribution. Since die potential
oudier colonies were selected after looking at die data, we
must account for a "selection bias." This requires an adjustment of the resulting p value wherein diis value is multiplied
by die number of observations in die data set. We note diat
die use of indicator variables as suggested by Weisberg (1985)
results in die identical model for die remaining colonies
(diose not diought to be oudiers) as would occur if die potential oudiers were removed from die data set.
We assume diroughout diat all colonies experienced die
same rates of adult attrition during die 25 days. We performed
our analyses using Systat for Windows v. 5.1 and Minitab release 8.2.
RESULTS
Data on collected colonies are summarized in Table 1. Note
diat data for some colonies are incomplete. We found no evidence of correlation of colony size widi type of local foraging
habitat. None of die colonies had males, despite die presence
of males in some of die parent colonies from which die
swarms were derived.
Jeanne and Nordheim • Productivity in a social wasp
Table 1
Size and output of Potybta octidentalU swanns at the end of 25 days of growth
Colony
Date
16
49
76
85
92
93
103
113
114
120
109
113
124
127
129
132
133
138
139
140
154
6Oct82
7Oct82
29 Oct82
16 Oct 82
14 Oct 82
14 Oct 82
16 Oct 82
27 Oct 82
30 Oct 82
30 Oct 82
17Jul84
18Jul84
30Jul84
17Jul84
6Jul 84
31 Jul 84
30Jul 84
15 Jul 84
15 Jul 84
15 Jul 84
22 Jul 84
Adults
Workers
Queens
598
24
567
371
279
44
42
126
108
79
355
355
691
278
310
218
719
152
156
597
21
557
325
260
35
41
107
101
64
339
—
673
252
—
—
669
129
140
1
3
10
46
19
9
1
19
1562
1547
41
35
7
15
16
18
26
—
—
50
23
16
15
6
Prop.
queens
Cell
Non-cell
WL
Wt.
Total
nest WL
—
—
3.771
0.377
5.760
1.902
1.495
0.256
0.229
0.653
0.303
1.277
2.480
2.780
7.010
2.110
3.076
9.089
0.847
14.753
4.988
3.728
0.996
0.880
1.536
0.689
2.270
7.050
7.660
17.510
6.430
7.231
12.860
1.225
20.513
6.890
5.223
1.252
1.109
2.189
0.992
3.547
9.530
10.440
24.520
8.540
10.308
—
—
—
—
0.0695
0.1513
0.1026
0.0096
0.1463
7.790
1.010
0.930
6.960
0.570
19.420
3.200
2.920
16.530
0.840
27.210
4.210
3.850
23.490
1.410
13.947
1.958
1.406
7.931
0.551
0.0017
0.1250
0.0176
0.1240
0.0681
0.2045
0.0238
0.1508
0.0648
0.1899
0.0451
0.0260
0.0935
Brood
wt.
0.419
0.031
5.257
1.738
1.042
0.165
0.047
0.416
0.005
—
3.951
4.747
11.084
2.897
3.221
Cells
2496
195
2806
1083
891
144
109
425
194
504
1594
1644
4526
995
—
588
4542
949
548
—
293
All weights in grams. Date gives date of collection.
Nest size
Regressing the number of cells (Q in the nest on total adults
(A) in the swarm gave a statistically significant, interpretable
model with a high i? (/? = .984):
CI9S2 = 202.9 + 0.36/1 + 0.0065A2
(1)
and
5000
C/flM = 202.9 + 1.54A + 0.0065A2.
(2)
Since colony #16 appeared to be an oudier with respect to
brood weight (see below), we assessed its impact on cell number by considering it as a possible oudier using die oudier test
described above. This gave us a direct indication of die extent
to which die cell number for diis colony departed from the
model. Fitting #16 as an oudier improved die model somewhat and showed diat #16 was significandy inconsistent widi
die model {t ratio = -3.08, p = .008). Widi colony #16 removed, /? improved to .987, and die equations for the two
years become
= 182.4 + 0.0082A*
g 4000
and
c
= 449.5 + 0.0082A2.
0
200
400
600
800
Number of adults
figure l
Cell number as a function of swarm size, by year. Colonies #129 and
#140 (1984) lacked cell number data and are omitted. Colony #16,
an outlier, is not included in the regression for 1982. Regression
line for 1982 (dashed) is given by Equation 3, for 1984 (solid) by
Equation 4.
(4)
These equations are plotted along widi die data in Figure 1.
To estimate die importance of the A2 term we used a model
with both linear and quadratic terms (A and A1) to test the
null hypodiesis diat die coefficient of A2 is 0. The null hypodiesis was rejected widi a t value of 6.08 (df = 13, p <
.0001). Thus, models containing a positive coefficient for A2
are significandy better dian linear models.
Computing die number of cells/adult and regressing diis
on adult number yielded a model diat was less explanatory
(/<? = .446). Colonies with low numbers of adults exhibited
significant scatter, indicating unaccountable variability.
Bodi models for cell numbers show diat die number of cells
produced per adult increases widi swarm size, as indicated by
die positive coefficient of the A2 term. This increase in per
capita productivity could be due eidier to increased work output by die members of the swarm or to a more efficient architectural configuration in larger nests; i.e., perhaps as nest
size increases, die proportion of total nest material allocated
to cells also increases.
To test die latter possibility, we regressed die weight of cellular material (MJ on the weight of noncellular material
(MJ) in die nests and found a linear relationship, suggesting
Behavioral Ecology Vol. 7 No. 1
5000
(0 4000 -
o
3000 -
O 2000
0)
n
0
5
10
15
20
1000 -
0
that the proportion of total nest material allocated to cells is
constant The regression equation is
Mc = O.SMM^
(5)
with an effective / ? of .992 (N = 20) (Figure 2). Alternatively,
but logically equivalently, cells comprised on average 28.4%
of the weight of the nest, regardless of nest size (Figure 3).
Cell number also highly correlated with overall nest weight,
C = 166.96M,
10
15
20
25
Weight of nest (g)
Weight of non-cellular material (g)
Figure 2
Weight of cellular as a function of noncellular material, 1982 and
1984 combined. N = 20. Regression line is given by Equation 5.
5
Figure 4
Cell number as a function of total nest weight, 1982 and 1984
combined. Af = 18. Regression line given by Equation 6.
(effective i ? = .975), supporting the assumption that cell
number is a reliable measure of overall nest size (Figure 4).
Brood weight
Two colonies (#16 in 1982; #140 in 1984) appeared extreme
outliers with respect to brood weight (Figure 5). Applying the
O
•
(6)
1982
1984
0140 I
O #76
400
800
1200
1600
Number of adults
0
5
10
15
20
25
30
Weight of nest (g)
Figure 3
Proportion of total nest weight allocated to brood cells as a
function of total nest weight, 1982 and 1984 combined. N = 20.
Figure 5
Brood dry weight as a function of swarm size (number of adults),
by year. Colonies #16 and #140 are not included in the models.
Colonies #120 (1982) and #132 (1984) are omitted for lack of data.
Regression line for 1982 (dashed) given by Equation 7. lines for
1984 (solid) given by Equation 8 with three values for p(Q) (from
left to right in the figure ): .2, .0896 (die mean value for both
years), and .002.
47
Jeanne and Nordheim • Productivity in a social wasp
outlier test to these resulted in t ratios of —10.88 and -30.44,
respectively, for #16 and #140. These are sufficiently extreme
to mitigate against any "selection bias" inherent in selecting
these two colonies. The constant term for 1982 was not significant, so we omitted it from our models. The best model
for dry weight of brood in grams (Wj was (Figure 5)
W19S2 = 0.0000155A*
and
(7)
Wi9S4 = -2.554 + 0.00926A + 0.0000155A*
(8)
+ 19.211,&(Q)
(effective/? = .995).
As we did for cell number, we estimated die importance of
die A2 term by using a model widi bodi linear and quadratic
terms (A and A1) to test die null hypodiesis diat die coefficient of A! is 0. The null hypodiesis was rejected widi a t value
of 6.27 (df = 10, p < .0001). Thus, models containing a positive coefficient for A1 are significandy better dian linear models.
Using diis model to calculate prediction intervals for brood
weights for die two omitted colonies, we obtain (4.244, 6.977
g) and (43.580, 56.682 g) for #16 and #140, respectively. The
observed brood weights of 0.419 g and 7.931 g are far outside
of diese intervals, suggesting that diey are extreme oudiers
widi respect to diis model. In odier words, diese two colonies
were not at all consistent widi die model. We note diat for
1984 die brood weight increases widi die proportion of
queens. Colony #140 had a very low proportion of queens.
Thus, aldiough Equation 8 is inadequate as a model for diis
colony, it suggests diat a lower queen proportion predicts a
lower brood weight
An alternative approach is to analyze brood weight per capita (W/A) as a new variable, HL Brood weight per capita
(eliminating colonies #16 and #140) bore a positive linear
relationship widi adult number (A) and proportion of queens
[p(Q)] (-fl? = 934), rejecting the null hypodiesis diat die coefficient of A is 0:
= 0.0O00182A
and
= 0.0000182A + 0.074/>(Q).
(9)
(10)
We also considered an alternative model diat does not treat
colonies #16 and #140 as oudiers. Such a model describes die
relationship between brood weight and adults as rising toward
a peak and dien declining as colony size increases. We use a
diird degree polynomial regression model for diis description.
However, such a model cannot incorporate colony #16 well
because diis colony is only slighdy larger dian colony #76.
Viewing colony #16—but not colony #140—as an oudier, we
get a good cubic fit (effective F? = .996) (Figure 6):
WI9S2 = -0.00462A + 0.000O371A* - 0.000000023A3 (11)
and
= -4.347 + 0.00626A + 0.0000S71A*
- 0.000000023A3 + 53.475/>(Q)
- 154.374 [p(Q)Y.
(12)
DISCUSSION
Our conclusion is diat for bodi cell number (nest size) and
brood weight, die per capita productivity of swarms of Polybia
ocadenlaiis during dieir first 25 days of growdi increases widi
die number of adults in die swarm, at least for swarm sizes of
up to 700 adults. Alternative explanations diat assumed linear
effects only, diat separated adults into queens and workers, or
3
•o
20 -
I
18 -
o
•
;
1
1
1982
1984
16 -
o
o
.Q
14 -
•5
10 -
/
m
\
/
12 -
\
/
/
/
/
/
8 -
o>
"55
1
6 -
#140 m^
-
5
4 -
-
Q
2-
-
0-
-
0
400
800
1200
1600
Number of adults
Figure 6
Brood dry weight as a function of swarm size, by year. Curves are
third order polynomials fitted to data for each year, given by
Equation 11 for 1982 (dashed line; colony #16 omitted) and
Equation 12 for 1984 (solid line).
diat assumed nest configuration changes with size did not improve significandy on die models we presented, and none
challenged the conclusion diat die effect we found is real.
Colonies #16 and #140 were oudiers not consistent with our
models. Three possible explanations occur to us: (1) oviposition rate constraint; die extremely low proportions of queens
in diese colonies (Table 1) could mean diat productivity was
constrained by die rate at which queens produced immatures
(eggs) radier dian by die rate at which die workers could rear
diem; such an effect has been shown for die wasp Melapolybia
azleca (Forsydi, 1978); (2) group dynamics constraint per
capita productivity may peak at some value of swarm size and
decline diereafter (Figure 6); or (3) colony ontogeny constraint: dieir large size and low proportion of queens suggest
that diese two colonies may have been mature when we induced diem to swarm (Forsyth, 1978; Queller et al. 1993).
Mature colonies may have a reduced per capita brood-rearing
capacity in comparison widi younger colonies, e.g., by virtue
of allocating relatively less to brood rearing and more to defense and homeostasis.
Earlier work on P. occidentalis (Jeanne, 1986) supports our
interpretation diat per capita productivity increases widi
swarm size and provides a mechanism to account for die pattern. That study, done on some of die same colonies included
in die present work, showed diat die amount of nest construction accomplished per unit time averaged 1.76 times greater
in diree large colonies dian in four small ones. The study
supported die hypodiesis diat at least some of die loss of per
capita productivity in small swarms was due to greater queuing
delays. The present result supports die hypodiesis diat die
higher average individual work rate of workers in larger colonies (Jeanne, 1986) translates direcdy into greater per capita
cell and brood output and is a mechanism behind diat increase. Anodier possible mechanism, not addressed here, is
diat conflict over reproductive rights increases widi decreasing swarm size and results in reduced productivity (P. Nonacs,
personal communication).
We found productivity of bodi cell number and brood
Behavioral Ecology Vol. 7 No. 1
48
weight for 1982 consistently and significantly lower than for
1984. If this difference is biologically significant, at least three
differences between the two data sets could account for it (1)
1982 was drier than 1984, and less rainfall could mean fewer
arthropod prey, which could translate into reduced productivity across all swarm sizes; (2) data for 1982 were collected
in September-October, while the 1984 data were taken in
June-July; P. ocadentaUs relies heavily on lepidopterous larvae
and other soft-bodied insects (Gobbi et al., 1984; Jeanne, unpublished data), which initiate their growth with the onset of
wet season in April or May (Forsyth, 1978); by SeptemberOctober there could be fewer lepidopterous larvae still within
the size range acceptable to P. ocadentalis foragers, which
could translate into lower productivity rates; or (3) although
the correlation between season and colony cycle in P. ocadentalis is not fully understood, some evidence suggests that most
colonies mature and reproduce toward the end of the wet
season (Forsyth, 1978; Jeanne, personal observation). If so,
this may mean that swarms induced during those months
(1982) may have been more likely to have come from mature
colonies than would be the case in June and July (1984). If,
as suggested above, swarms derived from mature colonies have
lower productivity rates, this could account for the difference
between the two years. Further research is required to tease
apart the roles played by these factors.
Our result is at odds with Michener's (1964) finding that
per female productivity for a variety of social and subsocial
Hymenoptera declines as group size increases. Michener's result for these wasps may be an artifact of his having to lump
colonies of different species and different stages of development to obtain adequate sample sizes to plot. In fact, we predict that the pattern we find in Polybia occidenlalis can be
generalized to other swarm-founding polistines. In any event,
our results overturn, for these wasps, the current paradigm
that the reproductivity effect exerts a downward force on
group size in the social insects and that large groups are maintained solely by extrinsic selective factors.
Thus it appears that taxa differ with respect to whether they
show an increasing or decreasing per capita productivity with
group size. The independent-founding wasps, with much
smaller colony size than the swarm founders, do seem to adhere to the Michener pattern (Hoshikawa, 1979; Ito, 1985;
Litte, 1977, 1981; West-Eberhard, 1969), suggesting that the
swarm-founding wasps have evolved a form of colony organization that is qualitatively different from that of the independent-founders. More importantly, this places new significance
on group dynamics as a factor affecting group size in different
taxa.
David Post and Holly Downing provided help in the field. Eric Espe
provided programming assistance. We thank J. Baylu, K. London, P.
Nonacs, S. O'Donnell, S. Overmyer, J. Wenzel, and an anonymous
reviewer for their helpful comments on earlier drafts of the manuscript. Research was supported by National Science Foundation grants
BNS-8112744 and IBN-9222108 to R.L.J. and by the College of Agricultural and life Sciences, University of Wisconsin, Madison.
REFERENCES
Forsyth AB, 1978. Studies on the behavioral ecology of polygynous
social wasps (PhD dissertation). Cambridge, Massachusetts: Harvard
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