Behavioral Ecology VoL 8 No. 1: 75-S2
Within-group aggression and the value of
group members: theory and a field test with
social wasps
Hudson Kern Reeve1 and Peter Nonacsb
•Section of Neurobiology and Behavior, Seeley G. Mudd Hall, Cornell University, Ithaca, NY 14853,
USA, and b Department of Biology, University of California at Los Angeles, Los Angeles, CA 90095,
USA
We present a simple, general model of how the optimal level of intra-group aggression should vary in different social contexts.
A key component of this model is the value of the recipient of aggression to a potential aggressor (i.e., the ratio of expected
long-term group productivity with the recipient present to the expected group productivity with the recipient absent). The
recipient's value measures its contribution to group reproductive success. "We demonstrate theoretically that if aggression increases the aggressor's share of the group's expected total reproductive output, but at the same time decreases the magnitude
of this overall reproductive output, then the optimal level of aggression toward a recipient will decrease with increasing recipient's value. This proof establishes a rigorous theoretical connection between the level of aggression within a group and the
benefits of belonging to such a group and can be tested by experimentally manipulating the values of group members to each
other. We test, and thus illustrate the utility of, this model by examining aggression within experimentally-manipulated foundress
associations of social wasps. We show that the value of co-foundresses to each other in the social wasp Poiistes fuscatus lies in
their ability to provide insurance against colony failure caused by die loss of all tending foundresses. Removals of worker-destined
eggs and pupae, which increase the value of co-foundresses, both lead to significant reductions in aggression by the dominant
foundress, despite die fact that the immediate, selfish benefits of competitive aggression should increase when empty brood
cells are present Removal of reproductive-destined eggs, which does not affect co-foundress value, but increases the benefits of
selfish aggression, causes a significant increase in aggression by beta foundresses. Finally, wing reduction of subordinate co-foundresses significantly increases aggression by dominant foundresses, as expected since the subordinate's value is reduced.
Our results indicate that foundress aggression is sensitive to the value of future cooperation, as predicted by die optimal
aggression model. The model may apply widely to both invertebrate and vertebrate societies. Kty words: aggression, animal
societies, conflict, cooperation, eusodality, punishment, social contracts, social wasps, Potistts. [Bthav Ecol 8:75-82 (1997)]
T
he evolution of aggression within social groups has been
receiving increased theoretical attention in recent years
(Archer, 1988; Clutton-Brock and Parker, 1994; Enquist and
Leimar, 1990; Reeve and Sherman, 1991; West-Eberhard,
1981). However, we are still a long way from understanding
the function and modulation of aggression in most animal
societies. Most investigators have a general notion that aggression somehow promotes selfish reproductive interests
widiin groups and that it should be restrained when it sufficiendy compromises reproductive gains achieved by intragroup cooperation. However, precisely how intra-group aggression is expected to vary in different social contexts remains largely unexplored.
A dieory of adaptive plasticity in intra-group aggression can-
of aggression toward odier group members should influence
the probability that die aggressor will obtain reproductive contributions from die recipients of aggression and that die magnitude of die latter contributions will depend on die costs and
benefio of belonging to a group. Far from being an unwanted
complication, die linkage between aggression and advantages
or costs of group-living presents an opportunity to develop an
ecological dieory of intra-group aggression, ultimately permining us to predict and explain patterns of aggression in
differerH social, genetic, and ecological settings.
Received 22 Auguit 1995; accepted 20 March 1996.
1M5-2249/97/J5.00 o 1997 Intenutioiul Society for Beh*vtor»] Ecology
We first present a simple yet general model of how the optimal level of intra-group aggression should vary in different
social contexts. The connection between aggression and
group-membership advantages (and thus between aggression
and ecological theories of group evolution) is mediated by
what we define as the vahu of the recipient of aggression to
a potential aggressor The value of a recipient is the ratio of
expected (present+future) group productivity with die reciplent present to die expected group productivity widi the recipient absent. We dien test diis model by manipulating die
value of co-nesting social wasp queens (PoUstts fuscatus) to
each other and examining die resulting changes, if any, in die
levels of aggression among these queens.
We begin by assuming that die two interactants in a social
group have a symmetrical genetic relatedness, r. The two interactants occupy and recognize distinct roles (e.g., dominance positions). The latter assumption allows us to use die
additive version of Hamilton's rule to model die evolution of
die interactants' aggressive interactions (Parker 1989; Reeve,
in press). The pair has an expected total productivity Pt if the
recipient cooperates completely widi die actor and an expetted total productivity Px if die recipient completely fails to
cooperate widi die actor ( L c dies or leaves). The realized or
actual expected productivity E(a) is intermediate between die
laoer &«> values and is represented by e{a)Pt + [1 - «(a)]P,,
where t(a) varies from 0 to 1 and represents die degree to
Behavioral Ecology Vol. 8 No. 1
76
OQ0
E(a)
- sia)])(t(a)Pt
(1)
2
We define the recipient's value v as the ratio i t / P , !• Maximizing Expression 1 with respect to a is then equivalent to
maximizing the expression
/ = [r+ (1 -r)s{am<a)(v -1) + 1]
(2)
And thus the optimal level of aggression a* will satisfy dl/da
=» 0 at a = a*, Le.,
( v - 1)
+ (1 - r)
ds(o)*(a)
da
+ (1 - i)S{a) - 0 at a ** a*
(3)
where S(a) = dt(a)/da and s'(o) = ds(a)/da. Thus, Equation S implicitly gives a*(v).
What we seek are the conditions under which the optimal
level of aggression increases with declining recipient value
(i.e., the conditions under which da*/dv < 0). By the implicit
function theorem (Marsden and Tromba, 1981),
level of aggression, a
figure 1
Relationship between aggression, a, and both the group's total
reproduction [E(a): areas of circle* at top] and the aggrestor't
fraction of the total reproduction [s(a): proportionate areas of
shaded portions of circles].
which the actual group productivity approaches the productivity under complete cooperation. The quantity t(a) is a function of the level of aggression a directed by the actor toward
the recipient The fraction of the pair's total reproductive output achieved by the actor is s(a) (where the "s" stands for
the skew in reproduction), which also depends on the level
of aggression a (Figure 1).
We note that the two functions «(a) and s(a) include the
effects of any responses of the recipient to the level of aggression, a, by the actor. To see this, let the optimal level of
the recipient's aggression a' be given by some function, h(a),
which depends on the level of aggression a by the actor. Since
the actor's and the recipient's level of aggression should jointly affect both the realized group productivity and the actor's
fraction of reproduction, we should
represent the former as
t(a, a") and the latter as s(a, a1). By substitution, the latter
functions are the same as e[a, A(a)] and i[(a, h(a)], respectively, which are functions only of a and thus can be written
simply as «(a) and s(a), respectively. To solve for the optimal
joint aggression levels (a*, a'*), we would use a game-theoretic approach. However, we are asking a different question,
i.e., how the optimal levels of aggression should change as
other factors (such as recipient's' value) change. The latter
question can be answered without explicitly calculating the
optimal levels of aggression, as long as it is realized that e(a)
and j(a) implicitly include the consequences of aggressioninduced changes in the recipient's behavior. These two functions could be inferred empirically by measuring how group
output and fraction of reproduction change as a varies (e.g.,
by hormonally altering aggression levels).
By Hamilton's rule (Hamilton, 1962a,b; see also Grafen,
1984), a level a, of an actor's aggression will be favored over
a level a, of its aggression if
>0.
-(1 The lauer condition implies that the optimal level of aggression by an actor will be that maximizing the inclusive fitness
measure
3*7
da* ^ dvda
dv " ~~d*T
at a ;
(4)
da*
Since the denominator is negative (because the level of aggression maximizes I), the sign of da*/dv is the same as the
sign of the numerator of the right-hand side of Equation 4,
Le.,
ds(a)e(a)
(5)
at a ~ a*
da
The right-hand side of Equation 5 occurs as a term in the lefthand side of Equation 3. Substituting into Equation 3, we obtain
dvda
+ (1 - r)
0.
(6)
Equation 6 can be satisfied only if s (a) and Pl/dvdo are of
opposite sign. In particular, if / ( a ) is positive, then 3*1/dvda
must be negative. Thus, if aggression increases the actor's
share of reproduction (/(a) > 0), which also necessitates that
it. deereases the total amount of reproduction (i.e., /(a) < 0,
if Equation 3 is to be satisfied), then 3*1/dvda < 0, and thus
the optimal level of aggression will increase with declining
recipient value (da*/dv < 0).
The central result (henceforth referred to as the Value-Aggression Theorem) is appealingty straightforward: If aggression increases the actor's share of the group's expected total
reproductive output, but at the same time decreases the magnitude of this overall reproductive ouq>ut (as in Figure 1),
then the optimal level of aggression toward a recipient will
decrease with increasing recipient's value. This is merely a
precise way of saying that aggression toward a recipient should
vary inversely with the recipient's value, if the aggression functions to achieve "selfish" reproductive gains. The optimal aggression model applies to groups of larger than size two if
such groups can be viewed as composed of dyads, such that
the interactions within each dyad have negligible effects on
the reproduction of group members outside the dyad. The
Vahie-Aggression Theorem thus opens a line of investigation
into the connection between the costs and benefits of group
living and the level of aggressien within a social group. The .
basic test, whether applied to invertebrate or vertebrate •
groups, involves (1) an ecological analysis of the benefits of
group living, (2) manipulation of the magnitude of the benefit conferred by a group member, and (3) examination of
Reeve and Nonacs * Aggression in animal societies
die resultant amount of aggression among group members.
Manipulations that increase a group member's value should
reduce aggression toward that group member, if the effect of
the manipulation on value v exceeds any opposing effects on
selfish reproductive opportunities / ( a ) .
A field test of the role of value in aggression among
co-founding social wasp qneena
We tested the Vahie-Aggresrion Theorem of die optimal aggression model by a«*^t«ing its ability to explain and predict
patterns of aggression in manipulated and undisturbed associations of co-nesting queens (co-foundresses) of die eusocial
paper wasp PoUsUs fuscatus. In this species, die colony cycle
begins when inseminated, overwintered females initiate aerial,
paper nests in die spring. Sometimes two or more foundresses
cooperate in die construction of nests and rearing of brood,
with die behaviorally dominant foundress typically laying most
of die eggs. This "founding phase" ends when die first brood
eclose as adult workers in early summer. The workers care for
die second cohort of brood, which will develop into males
and next year's foundresses during late summer and early Ml
(Noonan, 1981; West-Eberhard 1969).
Our manipulations consisted of removing brood at various
times in die founding phase and altering die foraging efficiency of subordinate foundresses. The predictions of die optimal aggression model depend on both (1) die value v of a
given wasp as perceived by her nestmates and (2) die potential gain in die share of reproduction s'(a) achievable by selfish aggression. The removal of brood creates empty brood
cells in which new eggs can be laid by any foundress (Reeve
and Nonacs, 1992), so brood removal potentially increases die
benefits of competitive aggression [i.e., consideration of die
second factor alone would lead to die prediction that brood
removal should increase foundress aggression (a* increases as
s'(a) increases) ] . However, if brood removal somehow increases foundress value, and this effect outweighs die effect of increased return for selfish aggression, then die optimal aggression model predicts die opposite result (Le., brood removal should decrease foundress aggression). To evaluate die
latter possibility, it is first necessary to quantify die value of
co-nesting wasp foundresses to each other.
Vahu of co-foundressa m social wasps
Reeve (1991) reviewed evidence on die benefits of co-founding in wasps of die genus PoUsUs and concluded thai die main
benefit is "survivorship insurance" [Le., when two or more
foundresses associate, there is a reduction in die probability
that die entire colony will fail because of chance loss of all
adults (e.g., because of foraging-related mortality) before die
first workers emerge (Strassmann and Queller, 1989)]. Recent
demographic data also strongly indicate a survivorship insurance benefit for co-nesting of foundresses in a North American population of die introduced species, PoUsUs dommuhu
(Nonacs and Reeve, 1995).
Following Reeve (1991), we assume that the amount of time
remaining in die founding period (Le., until die first workers
eclose) is T and that lifetimes of foraging foundresses are independently exponentially distributed with a mean equal to
\/m (m is the mortality rate). If both foundresses in a colony
die in die founding period, die colony fails. When a female
joins another foundress, die joined foundress stops foraging
and has negligible mortality, an assumption motivated by die
finding that die dominant foundress forages substantially less
than do subordinate or solitary foundresses (review in Reeve,
1991; P. Juscatus: Noonan, 1981; West Eberhard, 1969). If a
subordinate joiner subsequently dies (as die result of foraging) , die joined foundress resumes foraging. Let Nx and N,
77
be die mean number of offspring produced by surxrixring one
and two foundress nests, respectively. The expected future reproduction of a single foundress colony is; JVK*""7). The expected total direct reproduction of a two-foundress colony is:
AT, I mr-r+T-t
Jo
dt
(7)
The first term of Expression 7 encompasses die case in which
die subordinate foundress dies before worker emergence, and
die dominant foundress assumes die foraging role. If die
dominant survives until worker emergence, die colony produces die same number of offspring as a surviving single-foundress colony (Af,). The second term of Expression 7 encompasses die case in which die subordinate foundress survives
until worker emergence (which occurs widi probability 5 "
e~mT), with die result diat die dominant survives (since it never
has to assume foraging) and die colony produces N2 offspring. Expression 7 simplifies to
According to die survivorship insurance model, die overall
probability diat a two-foundress colony survives, given diat a
single foundress colony survives with probability S, should be
r
"r^T-t> dt
S[\ -
(Nonacs and Reeve, 1995).
An important simplifying feature of die model above is that
if die subordinate dies at any point before worker emergence
(even late in die founding phase), its contribution to colony
productivity is effectively lost. Thus, die survivorship insurance model differs from "head start" models for die evolution
of sodality (Queller, 1989, 1994), which depend on die preservation of such contributions. To die extent that die contribution of an ill-fated subordinate can be preserved by die
remaining foundress, die survivorship insurance model yields
a conservative estimate of die total productivity of a foundress
association.
The value of one foundress to die other can be measured
as die ratio of die expected productivity of a two-foundress
colony to diat of a one-foundress colony at die same stage in
die colony cycle, Le., as
which reduces to:
k+ mT
(9)
where *
From this expression, we deduce diat die value of a foundress increases linearly widi (1) die time T until workers
emerge, (2) die foraging-related mortality rate m, and (3) die
proportionate gain in productivity (* — 1) of a surviving nest
caused by die presence of die odier foundress.
Removal of late-stage, worker-destined brood from a nest
will obviously increase T. Likewise, k increases, because die
loss of workers will increase die proportional contribution of
die subordinate relative to those of workers. For example, if
diere are diree workers, each contributing die same amount
as a subordinate, * would be equal to ( 3 + l ) / 3 = 1.33, whereas ft in die case of just two workers would equal die greater
value ( 2 + l ) / 2 » 1JH). In sum, removal of worker-destined
brood should increase die value of foundresses to each other.
Thus, our experimental brood-removal manipulations allow
us to determine whedier aggression varies facultatively with
die social environment in accordance with die optimal level
of aggression model, and in particular whether aggression is
sensitive only to changes in immediate selfish opportunities
Behavioral Ecology VoL 8 No. 1
78
Table 1
Predictions of tbe *»p**w<p* affcreMiofl wwiH^ (wtth tbe iwiuiiififTTitt tttmt \
apond primarily to
gain or to d i a u y m long-term value of nestmata), a null model, and the observed bdutlun of the foundresses m rejponic to four
experimental numpoladon*
.Experiment
Null model
Potential selfish gains
Foundren value
Observed
Removal of
worker eggs
No effect
Decreased aggression caused
by increase in k
Decrease in alpha*
Decrease in beta
Removal of
worker pupae
Removal of lezual
No effect
Increased aggression caused by
egg-laying competition or
punishment for reproductive cheating
Increased aggression due to egglaying competition
Increased aggression caused by
egg-laying competition or
punishment for reproductive
rh^lring
Effect unclear
Decreased aggression caused by
increases in k and T
No change in aggression because
no change in foundress value
Decrease in alpha*
Decrease in beta
Increase in alpha
Increase in beta*
Increased aggression by alpha
caused by reduced k of the
forager; reduced aggression by
forager
Increase in alpha*
Decrease in forager
Wing-dipping
subordinates
No effect
of No effect
> Significant changes in behavior.
or perhaps also to changes in the long-term value of co-foundreses (Table 1).
To verify the applicability of the survivorship insurance
model to our study species, Potistes fuscatus, we censused 65
P. fuscatus colonies at the Cornell University Liddell Reid Station and in rural areas around Ithaca, New York, USA from
27 May 1994 to 7 September 1994. Forty-five colonies had
solitary foundresses and 18 colonies had multiple-foundresses
(of the latter, 15 colonies had two foundresses, one had three
foundresses, and two had four foundresses). All foundresses
were given individual enamel paint marks on their when their
colonies were discovered (27 May—3 June for 61 colonies; 5
and 12 June for two late-starting single foundress colonies).
Colonies had a mean of 10.3 (single-foundress nests) and 16.4
(multiple-foundress nests) egg-bearing cells at first discovery.
Colonies were censused 50 times at the Liddell Field Station
(28 colonies) and 5-16 times at the remaining sites (35 colonies) throughout the founding phase, the worker phase, and
the reproductive phase [(i.e., the period during which males
and gynes ("future foundresses) eclose from the nest)].
Wasps that usurped or adopted nests of disappeared foundresses (N ™ 3) were included in subsequent censuses and
were treated as new foundresses. The mean emergence date
(±SE) for the first workers was strikingly consistent across colonies (8 Juhr±0.9 days; N « 20 Liddell colonies). The mean
emergence date for the first males, which occurs near the
beginning of the reproductive phase, was 10 August±1.4 days
(N ™ 17). These dates are very similar to those for P. fuscatus
populations studied in Michigan (Noonan, 1981). We inferred
that beginning of the reproductive phase was approximately
1 August (the earliest date of first male emergence), which is
also similar to Michigan populations (Noonan, 1981). We recorded which colonies failed before emergence of reproduclivcj and which colonies survived to produce at least some
reproductives (Le., males and females emerging during the
reproductive phase beginning 1 August).
A significantly greater fraction of multiple-foundress colonies (78%) than single-foundress colonies (47%) survived to
produce reproductives, in accordance with the survivorship
insurance model (/> <.O5, chi-square test). Of the 24 singlefoundress failures, 21 (87.5%) failed because the foundress
disappeared; three (123%) flailed because the entire worker
force disappeared (before the foundress) during the worker
phase. Of the four multiple-foundress colony failures, three
failed because of disappearance of all foundresses before die
first workers eclosed and one failed because of infestation by
parasitic wasps. If disappearance of foundresses before worker
emergence is considered as the sole cause of colony failure,
the probability of multiple-foundress success (.82) still significantly exceeds the probability of single-foundress success (.50;
p <.O5, Chi-square test). Overall, 92% of nest failures caused
by foundress disappearance occurred in the founding phase,
in accordance with the survivorship insurance model.
Since 5 = 0.50±0.08 SE, the survivorship insurance model
(see above) predicts a multiple-foundress survival probability
equal to .85, closely matching the observed probability of
.82±0.09 SE. Thus, the available evidence strongly supports
the hypothesis diat die benefit of nest co-founding in P. fuscatus is survivorship insurance and thus that the value of cofoundresses to each other is given by Expression 9.
Testing iht Vahu-Aggrtssion Thtortm: effects of brood
removal and wing-dipping on P. fuscatus foundress
aggression rates
All brood-removal and wing-dipping experiments were performed at the Harvard University Concord Field Station and
the Carlisle Great Brooks Farm in eastern Massachusetts in
the summers of 1991 and 1992.
For all colonies in brood removal experiments, we recorded
all interactions among foundress queens between 1000-1130
h and 1500-1600 h for two successive days. Interactions included nutrient exchange, antennadon, aggressive threats
(darting, chasing), and aggressive contacts (mounting with
forced crouching, lunging, grappling, and biting) (Reeve and
Nonacs, 1992). Alpha and beta queens were identified informally before observation by their dominance-subordinance
behaviors. Dominant queens were easily recognized by their
ritual mounting of subordinates, abdominal wagging, high
percentage of time on the nest, relatively frequent egg-laying
behavior, and monopolization of incoming prey, as documented in many other studies (review in Reeve, 1991). Dominance hierarchies were confirmed during first-day observations. Dominance never reversed after manipulation (e.g.,
dominants continued to meuat subordinates and subordinates never mounted dominants).
Before second-day observations (about 0830 h), the comb
and all queens were collected. The queens were cooled in a
4°C refrigerator while brood (eggs or pupae) were removed
Reeve and Nonacs • Aggression in animal tocieties
ALPHA
control worker eggs
removed
N-5
N-5
79
BETA
control
N-5
r—r "•
worker eggs
removed
N-5
•P<«JM4
Figure 2
Results of worker-egg removal experiment- Asterisked changes in
aggression rate were significantly different from zero (WOcoxon
one-ample tests). The decline in alpha's aggression rite in
treatment colonies alto was significantly greater than that observed
in controls (p <.O21, Mann-Whitney (/test). Bars represent
standard errors.
BETA
ALPHA
N-5
uu
removals
N-<
N-ll
r"r'
N-5
•
uu
removals
N-6
N-ll
*P<&028
Flgure 3
Results of worker-pupae and reproductive-egg icuiuval experiments.
Asterisked changes in aggreaion rate were ngnificantly different
from zero (WHcoxon one-«ample tests). Bars represent standard
errors.
nificant decline in aggression rates of alphas (mean change
° -74%) and a non-significant decline in the aggression rates
of betas (mean change « -12%) (Figure 2). Alpha and beta
with forceps. (Control combs were merely touched with foraggression rates in control colonies did not significantly
ceps.) The comb was then gtued to its initial location, and die
change (mean change =» +29% and +1%, respectively; Figure
beta queen was replaced. The alpha queen and other subor2), and the decline in alpha's aggression rate in egg-removal
dinates were subsequently released from their holding concolonies significantly differed from the corresponding change
tainers. Observations resumed after the alpha queen returned
in controls (p <.021; Mann-Whitney t/test).
to the nest (1-2 h within release). Observations of nests with
eggs removed were blind with respect to treatment (Le., since
2. Pupal removal experiment Removal of worker-destined
the deeply recessed eggs were not visible from several feet,
pupae from late foundress colonies creates empty cells that
observers could not distinguish between nests with eggs reare increasingly likely to be filled with reproductive-destined
moved and control nests). However, observations of nests with
eggs (Reeve and Nonacs, 1992), leading to the expectation
pupae removed could not be blind with respect to treatment.
that competitive aggression should increase. However, such
Observations were audio-taped or video-oped. Aggression
removal Increases both T (by increasing die time before the
rate is calculated as the number of aggressive threats and confirst cohort of adult workers emerges) and k (by increasing
tacts directed by one queen toward the other, per hour bodi
die contribution of a foundress relative to workers, as in Exwere on the nest (Reeve and Nonacs, 1992). For all experiperiment 1). Thus, removal of worker-destined pupae should
ments we calculated die difference in aggression rate (agincrease a foundress's long-term value (Table 1).
gressive acts/ h) between the second and first day of obserWe observed six colonies, containing x = 2.14 foundress
vations.
queens, from 20-27 June 1992, 2-3 weeks before worker
emergence, probably bracketing die beginning of the period
In the wing-dipping experiments, the above procedures
of reproductive-egg production. A mean of 6.2 pupae were
were followed, except that brood were not removed and
removed from six field colonies. Since removal of pupae was
combs were not detached from the nesting substrate.
1. Worker-egg removal experiment. Our first manipulation was performed after removal of worker-destined eggs (10-18
June) and prior to die later removal of reproductive-desdned
to remove worker-destined eggs in early foundress associaeggs (16-18 July), die five controls for the worker-egg removal
tions, which potentially creates the opportunity for selfish gain
experiment and die five controls for the reproductive-egg rethrough competitive aggression (Potistts workers sometimes
moval experiment also were regarded as controls for the pureproduce and therefore can be reproductivery valuable to
pal removal experiment One of the colonies used for the
foundresses; review in Reeve, 1991). However, egg removal in
pupal removal experiment had been used 8 days before as a
effect also increases a foundress's long-term value by increascontrol for the worker-egg removal experiment
ing A [i.e., the proportionate reproductive contribution of the
subordinate] since worker production u reduced (Table 1).
Removal of worker-destined pupae caused a marked and
significant decline in aggression rates of alphas (mean change
A mean of 15.4 worker-destined eggs were removed from
= -65%) and a non-significant decline in the aggression rates
five treatment colonies and and no eggs were removed from
of betas (mean change = -29%) (Figure 3). Alpha and beta
five control colonies (x = 2.5 foundresses for all 10 colonies)
aggression rates in late stage control colonies, like those of
from 10-18 June 1992. Because of a prolonged (> 2-week)
carry stage control colonies, did not significantly change
period of lower than normal spring temperatures, nests at this
(mean change = - 2 % and -11%, respectively; Figure 3), and
time were much less developed than eastern Massachusetts
the change in alpha's aggression rate in pupa-removal colonests at the same time in the summer of 1991 (when removal
nies was significantly different from that in controls (p <.013;
of reproductive eggs was performed for some colonies; see
Mann-Whitney t/test).
below). Retarded nest development was indicated by relatively
small comb sizes and absence of pupae. These nests were ob3. Reproductive-egg removal experiment. To facilitate comparserved ^ 3 weeks before worker emergence, when predomiisons with results of die other brood removal experiments, we
nantly worker-destined eggs were still being laid (e.g., Noonpresent data on removal of reproductive-destined eggs, taken
an, 1981).
from Reeve and Nonacs (1992). Unlike removal of workerdestined eggs or pupae, removal of reproductive-destined
Removal of worker-destined eggs caused a marked and sig-
80
Behavioral Ecology Vol. 8 No. 1
BETA
wing-dipping (mean change = —45%), but there was no significant correlation between the wing-dipped subodinate's
change in proportion of time foraging and the change in alpha's rate of aggression toward that subordinate (r = +0.36;
p >.10).
Condusaons of field test of the \Une-Aggresskm Theorem
N-7
N-7
Figure*
Reculu of wing-dipping experiment Asterisked changet in
aggression rate were significantly different from zero (Wilcoxon
one-cample tests). Ban represent standard errors.
eggs should not affect either A or T, and thus the value of
co-foundresses should be unaffected. Therefore, wasps should
act to increase their selfish gains by becoming more aggressive.
We observed sixteen colonies, each containing 2-4 (x = 2.4)
foundress queens, from 10-27 June 1991 and from 16-18 July
1992. The 1992 removals were conducted in the cool summer
when colony initiation was delayed. All colonies were observed
1-14 days before the emergence of workers, when the first
batch of reproductive-destined eggs u laid (Noonan, 1981). A
mean of 14.0 reproductive-destined eggs were removed from
11 treatment colonies and no reproductive-destined eggs were
removed from five control colonies.
As reported in Reeve and Nonacs (1992), removal of reproductive-destined eggs caused a marked and significant increase in the aggression rate of betas (mean change =
+ 149%) and a non-significant increase in the aggression rates
of alpha (mean change = +75%). There were no significant
changes in controls (Figure 3).
4. Wing-clipping experiment Impairment of a subordinate
foundress's ability to contribute to colony productivity in effect lowers her long-term value by causing a reduction in k.
Thus a dominant responding to only to selfish opportunities
would not necessarily exhibit an increase in aggression, but a
dominant responding to reduced value of the subordinate
should increase her rate of aggression (Table 1).
We clipped distal portions of the wings of subordinate foundresses to increase their difficulty of flying. We observed seven
colonies, containing x = 2.7 foundress queens, from 20-24
June 1992. In all colonies, a subordinate foundress's forewings
were clipped H of their length from the wingtip on the morning before the second day's observations (subsequent data
analysis indicated that five wing-dipped subordinates were
beta foundresses and two were gamma foundresses). Preliminary observations of wing-dipped foundresses indicated that
25% shortening of the wings still permitted long-distance
flight by foundresses but increased the difficulty of such
flights. Four of the colonies in the wing-clipping experiment
had been used as controls 1-2 weeks previously for the workeregg removal experiment.
Wing dipping of subordinates caused a marked and significant increase in the aggression rates of alphas (mean change
** +189%) and a non-significant decrease in the aggression
rates of the wing-dipped wasps (mean change » -36%) (Figure 4). Alpha's increase in aggression was greater, but not
quite significantly so, than that in controls (p = .097; MannWhitney U test). Wing-clipped subordinates reduced their
proportion of time spent foraging from 0.54 to 0.19 after
The four results from our manipulations (Table 1) strongly
suggest that (1) foundresses behave in accordance with the
framework of the optimal aggression model, and (2) changes
in foundress aggression often are more sensitive to changes
in the long-term value of cooperation than to changes in immediate, selfish reproductive opportunities:
1. Removal of worker-destined eggs caused a dramatic, significant decrease in the rate of aggression of the alpha toward
the beta foundress (Figure 2). The removal of worker-destined eggs likely increases k (and thus the value of the subordinate to the dominant) by delaying the production of the
affected cohort of workers and consequently increasing the
potential contribution of the subordinate relative to those of
workers.
The aggression of the beta foundress toward the alpha
foundress dropped only slightly (and not significantly) in response to worker-egg removal (Figure 2). Interestingly, the
value of the alpha, to beta should be less affected by workeregg removal than will the value of beta to alpha, because the
alpha's "contribution" in the worker phase is probably less
than the contributions of individual workers and subordinates
[the dominant forages relatively little in the worker phase
(Reeve and Gamboa, 1983)]. For example, let the queen's
contribution to productivity be 1—* and that of a worker or
subordinate be 1. A reduction from three to two workers increases the value of the alpha to the beta from (5 —x)/4 to
(4 — x)/3 as compared to the bigger gain of [(4— x)/(3— x)
- [ ( 5 - x ) / ( 4 - x ) ] in the value of the beta to the alpha. The
smaller increase in the alpha's value to the beta should, according to the optimal aggression model, lead to a smaller
decrease in aggression by the beta toward the alpha than in
aggression by the alpha toward the beta, as was observed.
2. Worker-pupa removal caused a dramatic and significant
reduction in alpha's rate of aggression toward beta (Figure
3). Removal of worker-destined pupae increases foundress value by increasing both k (as for removal of worker-destined
eggs) and also T, by effectively lengthening the time until the
first workers emerge. Since pupal removal affects both variables it might seem surprising that the drop in alpha's aggression was comparable to that in the worker-egg removal
experiment, in which only * could have been increased. However, nearly three times as many worker eggs were removed
as were worker pupae, which may mean that the overall increases in beta's value were similar in these two experiments.
Beta's aggression again dropped (more so than in any other
treatment and control), but the decrease was not significant.
Again, the lesser response by beta is consistent with the prediction of a lesser change in alpha's value to beta than in
beta's value to alpha.
The overriding effect of long-term foundress value is particularly evident in the pupal-removal experiments, which
were performed probably dose to the beginning of reproductive-egg production. Pupal removal caused reductions in aggression, even though eggs laid in the empty cells created by
the removal had a relatively high probability of developing
into reproductive*. The suppression of conflict in this eoatoxt
supports the general notion that foundresses have a "social
contract" over reproduction [i.e., to capitalize on the benefits
of cooperation, foundresses in effect agree to divide up the
reproduction without escalated aggression as long as severe
81
Reeve and Nonacs • Aggression in animal societies
reproductive cheating is not detected (Reeve and Nonacs
1992, 1993)].
3. When reproductive-destined eggs instead of worker-destined eggs are removed, there should be no change in the
value of either foundress to the other (T is unaffected and
egg removal will reduce N, and Nt to the same degree such
that their ratio k is unaffected). However, both the sudden
availability of empty brood cells and the perception of cheating on the reproductive contract means that the perceived
rate of increase of selfish gain via aggression [s'(a)] is expected to increase. Indeed, beta foundresses dramatically and
significantly increased their aggression toward alphas when
reproductive-destined eggs were removed (Reeve and Nonacs
1992, 1993; Figure 3). Although alphas increased their aggression toward betas, the increase was inconsistent and not
figpifirant (Reeve and Nonacs, 1992; Figure 3). Reeve and
Nonacs (1992) suggested that alphas are less willing to escalate aggression than are betas under these circumstances: An
aggressive dominant would risk both her own death and that
of her subordinate through injury and thus jeopardize her
long period of reproduction in the weeks ahead. By contrast,
betas will, with high likelihood, disappear shortly after the
workers emerge and thus are expected to become more aggressive to protect their short-term reproductive interests. In
the optimal aggression model, the change in alpha's aggression may be less because the increase in the gain rate for
aggression [s'(a)] is lower for her.
4. In the wing-dipping experiment, the subordinate's ability
to contribute to colony productivity was impaired, which leads
to a decrease in its value from the perspective of the alpha
(by decreasing k). Alpha strongly and significantly increased
its rate of aggression toward wing-dipped subordinates. However, wing-clipped subordinates slightly decreased their aggression toward dominants (not significantly), which also accords with the model because the wing-dipping should have
(if anything) increased the value of the alpha to the wingdipped subordinate. From the subordinate's point of view, T
would not have been affected but k would be increased if, for
example, a wing-dipped subordinate were less fecund as a
replacement queen than were a normal subordinate. It is also
conceivable that wing-dipping increases the mortality rate m
per unit time foraging for the subordinate (but not for the
dominant, should the dominant be forced to take on the foraging role). Increased morality rate for the subordinate
would reinforce the effect of A in causing different responses
by the alpha and the beta: The value of the subordinate to
the dominant would be decreased, and the value of the dominant to the subordinate would be increased.
In sum, our results are in general agreement with the ValueAggression Theorem obtained from the optimal aggression
model. Indeed, foundress behavior would be puzzling without
the concept of a long-term cofoundress value that can override the effect of selfish, immediate reproductive opportunities on the optimal level of aggression. The Value-Aggression
Theorem also illuminates other patterns of aggression in Potistts wasps. For example, the aggression model, in combination with survivorship insurance advantages of foundress associations, predicts that the aggression of alpha and beta
should increase as the period of reproductive-egg production
approaches (i.e., as Tdecreases). The appropriate design for
detection of colony stage effects would be to measure aggression within the same colonies over a single colony cycle. Indeed, Gamboa and Stump (in press) recently employed this
design and discovered, as predicted, that alpha and beta foundresses become more intensely aggressive toward each other
later in the founding period.
Implication of the Value-Aggression Theorem for future
rtndiei of «njiti»1 aggression
Our first test of the Value-Aggression Theorem suggests that
it will be profitable to explicitly investigate the relationship
between level of mtra-group aggression and the value of
group members to each other in other animal sodeties. Few
studies have examined the modulation of within-group aggression, perhaps because of a lack of a dear theoretical
framework relating aggression to the benefits of group-living
and because of our still-rudimentary empirical understanding
of the latter benefits. However, some data do suggest a link
between value and aggression in other social taxa. For example, group-living brown jays in Costa Rica exhibit higher
levels on intra-group aggression at higher population densities, when groups are larger and the reproductive benefit of
having a group member is lessened (Williams et al., 1994).
Perhaps the most informative tests of the optimal aggression model, including the Value-Aggression Theorem, will involve comparison of levels of aggression among group members varying in either their value to the group or in their
selfish opportunities for increasing their fraction of reproduction. For example, relatively "lazy" animals are predicted to
receive higher levels of aggression, as the naked mole-rat
(Reeve, 1992; Reeve and Sherman, 1991). Group members
that have the highest rate of return [/(a)]on their level of
aggression [Le., doTninant members with relatively high fighting ability] should display the highest levels of aggression, as
is widely observed in vertebrates and invertebrates (Archer,
1988). Indeed, in our current study of undisturbed Massachusetts colonies {N = 39), alpha P. fuscatus queens were consistently and significantly more frequently aggressive than beta
queens (mean alpha aggression rate across all colonies •=• 18.2
acts/h; mean beta aggression rate = 9.1 acts/h; p ** 0.0001;
Wilcoxon paired-sample test).
In addition to explaining and predicting levels of aggression within animal sodeties, die Value-Aggression Theorem
can be turned around to illuminate the benefits of grouping
when the latter are unknown. In particular, manipulations of
factors that decrease intragroup aggression despite increasing
(or not affecting) selfish reproductive opportunities within
the group will suggest that these factors closely relate to the
benefits of cooperation.
We thank the stafB of Levine research laboratory and the New York
State Gamefarm Eacility (Ithaca, New York, USA) and the Carlisle
Great Brooks Farm (Carlisle, Massachusetts, USA) for access to colonies on their building!. We also thank S. Emlen, M. Mangel, J. Shellman-Reeve, P. Sherman, and D.S. Wilson and two anonymous reviewe n for helpful comments on the manuscript. HJCJL was supported
by a New York State Hatch Grant and an NSF grant (IBN-9408024)
with P.N. P.N. was additionally supported by an NSF grant to Marc
Mangel, UC Davis.
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