Demographic predisposition to the evolut
Proc. Nati. Acad. Sci. USA
Vol. 88, pp. 10993-10997, December 1991
Evolution
Demographic predisposition to the evolution of eusociality:
A hierarchy of models
(altruism/Ropalidia/demography/assured fitness returns/delayed reproductive maturation)
RAGHAVENDRA GADAGKAR
Centre for Ecological Sciences and Centre for Theoretical Studies, Indian Institute of Science, Bangalore, 560012 India
Communicated by Charles D. Michener, July 22, 1991
I present a hierarchy of models that illustrate,
ABSTRACT
within the framework of inclusive fitness theory, how demographic factors can predispose a species to the evolution of
eusociality. Delayed reproductive maturation lowers the inclusive fitness of a solitary foundress relative to that of a worker.
Variation in age at reproductive maturity makes the worker
strategy more profitable to some individuals than to others and
thus predicts the coexistence of single-foundress and multiplefoundress nesting associations. Delayed reproductive maturation and variation in age at reproductive maturity also select for
mixed reproductive strategies so that some individuals whose
reproductive maturation is expected to be delayed can first act
as workers and later switch over to the role of a queen or
foundress. Assured fitness returns shows how identical mortality rates can have different consequences for workers and
solitary nest foundresses because a solitary foundress will have
to necessarily survive for the entire duration of development of
her brood, whereas a worker can hope to get proportional
fitness returns for short periods of work. In concert with
assured fitness returns, delayed reproductive maturation and
variation in age at reproductive maturity become more powerful in selecting for worker behavior, and mixed reproductive
strategies become available to a wider range of individuals.
These phenomena provide a consistently more powerful selective advantage for the worker strategy than do genetic asymmetries created by haplodiploidy.
When members of a species live in groups comprising individuals of more than one generation, cooperate in brood care,
and relegate reproduction to one or a small number of
individuals in the group, they are thought to represent the
most highly evolved stage in social evolution in the animal
kingdom and are appropriately termed eusocial (1, 2). All ants
and termites, many species of bees and wasps, and the naked
mole rat Heterocephalus glaber are eusocial (1-4). The most
striking feature of eusociality is the presence of a sterile
worker caste.
In the highly eusocial termites, ants, and honey bees, the
workers are often morphologically differentiated, have lost
most or all ability to mate and reproduce, and may have
reached an evolutionary cul-de-sac from which a return to
fertile or solitary life may be difficult, if not impossible. In
many species of primitively eusocial wasps and bees on the
other hand, social nest foundation is facultative; a nest may
be founded either by a single female or by a group of females,
only one of whom assumes the role of the queen and the rest
remain sterile and work to rear the queen's brood. A newly
eclosed female in a primitively eusocial species appears to
have several options: she may leave her natal nest to found
a new single- or multiple-foundress nest, she may leave to
usurp another foundress's nest, she may stay back on her
natal nest and work for her mother, or she may stay back and
eventually inherit the role of the queen in the nest of her birth.
Thus, given that they have the choice of reproducing, explaining worker behavior is even more challenging in primitively eusocial insects.
Predisposition to the Evolution of Eusociality
Hamilton (5, 6) argued that the sterile worker castes in
eusocial species are explained if we can show that the
inclusive fitness of a sterile worker is greater than that of a
solitary nest foundress and thus provided a powerful theoretical framework for the study of social evolution. The
inclusive fitness of a solitary nest foundress or a worker can
be conveniently represented as the product of three components (7, 8): (i) an intrinsic productivity component that
represents the number of individuals that she can rear provided she survives for their entire developmental period, (ii)
the coefficient of genetic relatedness, representing the probability that genes present in the solitary foundress or worker
are also present in the brood she cares for, and (iii) a
demographic correction factor that should be used to devalue
the intrinsic productivity factor because of the fact that the
solitary foundress or worker may not survive for the entire
developmental period of the brood under her care. Thus a
nonreproducing worker will get more inclusive fitness than a
solitary foundress, and natural selection will favor the evolution of a worker caste if
3p
a> b rs,
[1]
where f3 is the intrinsic productivity of a worker, p is the
coefficient of genetic relatedness of a worker to the brood
under her care, a is the demographic correction factor for a
worker, and b, r, and s are the corresponding parameters for
a solitary foundress. ClearlyI three kinds of factors can
contribute to Inequality 1.
Ecological or physiological predisposition: f3> b. Workers
are able to rear more brood per capita than a solitary
foundress. This may happen because of better protection
from parasites, predators, and conspecific usurpers in a
group nesting situation compared to a single foundress nest
(9-16) or because those who opt for worker roles may be
subfertile individuals whose b would be relatively small if
they became solitary foundresses but whose (3 as workers
would be relatively high (17-21).
Genetic predisposition: p > r. Workers have access to
brood that are more closely related genetically to themselves
than a solitary foundress is to her offspring. The male haploid
genetic system in the Hymenoptera coupled with an ability to
bias investment in favor of female brood can make this
possible (5, 6, 22-24).
Demographic predisposition: a > s. This has seldom been
considered explicitly for social insects (but see refs. 7, 8, and
25-27) and will form the subject of the rest of this paper. The
inequality a > s may imply that workers have a lower rate of
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10993
10994
Evolution:
Gadagkar
mortality compared to solitary foundresses. This is probably
true, but quantitative data on survivorship of solitary
foundresses are hard to obtain (7, 8). Besides, I wish to show
that even if workers and solitary foundresses have identical
mortality rates, the consequences of such mortality for the
magnitude of the demographic correction factors and thus for
inclusive fitness can be quite different for workers and
solitary foundresses. To do so I shall use survivorship data
obtained from workers in field colonies of Ropalidia marginata (see below) (8) throughout this paper. By using survivorship data from workers to estimate the demographic
correction factor for solitary foundresses, I will perhaps
overestimate the inclusive fitness of solitary foundresses but,
to the extent that I do so, my estimate of the advantage of the
worker strategy will be conservative.
In what follows I shall contrast the inclusive fitness of a
solitary foundress on the one hand and a worker in a
multifemale nest on the other and assume for simplicity that
each nest produces a single batch of synchronous brood. I
shall use field and laboratory data on the primitively eusocial
tropical wasp R. marginata (Lep.) (Hymenoptera: Vespidae)
throughout, to illustrate the models (28). R. marginata, like
most primitively eusocial wasps, is a progressive provisioner
where the brood is entirely dependent on the adults for food
and protection. This makes my models particularly applicable to them and, by the same token, somewhat less applicable, although not entirely inapplicable (see ref. 24), to mass
provisioners such as the many species of primitively eusocial
Halictines (29).
Delayed Reproductive Maturation
Experiments involving isolation of freshly eclosed virgin R.
marginata females into individual laboratory cages have
revealed two forms of preimaginal caste bias. First, about
50%o of the females tested died without building a nest and
laying eggs; second, even those that did build a nest and lay
eggs took a long and variable amount of time to start doing so
(19, 20). Both these forms of preimaginal caste bias appear to
be mediated by the quantity of larval nutrition, such that
individuals fed relatively well as larvae have a high probability of developing into egg layers and early reproducers.
Conversely, those fed relatively poorly as larvae have a high
probability of developing into non-egg-layers or late reproducers (21). The time required to attain reproductive maturity
ranged from 14 to 191 days (mean ± SD = 48 + 31 days) (30)
(Fig. 1). Such delayed reproductive maturation will differentially affect the inclusive fitnesses of solitary foundresses and
workers (7, 8, 17). This is because, to successfully rear brood
to the age of independence, solitary foundresses will have to
survive for the sum of the period required for reproductive
maturation and the brood developmental period. Workers
are, however, unaffected by any delay in their reproductive
maturation as their work (and fitness) depends on the queen
supplying them with brood. It will thus be sufficient for them
to survive for the duration of the brood developmental
period.
By using the mean delay in reproductive maturation of 48
days (Fig. 1), an estimate of the brood developmental period
of 62 days for R. marginata (8), and survivorship data from
field colonies of R. marginata (8), I compute the asymmetrical fitness consequences of such delayed reproduction
maturation for the inclusive fitnesses of solitary foundresses
and workers. The demographic correction factor s for solitary
foundresses is the probability of survival for 48 + 62 = 110
days, which is 0.015 (8). The demographic correction factor
afor workers on the other hand is the probability of survival
for the duration of the brood developmental period of 62
days, which is 0.12 (8). These rather different values for the
demographic correction factors obtained for a solitary nest-
Proc. Natl. Acad. Sci. USA 88 (1991)
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AGE (DAYS) AT THE TIME OF LAYING THEIR FIRST EGG
FIG. 1. Frequency distribution of wasps in different age classes
at the time of laying their first eggs. Two hundred ninety-nine freshly
eclosed female R. marginata were isolated in individual laboratory
cages (19, 20, 30). Of these, 147 died without laying eggs. Of the
remaining 152 that built a nest and laid eggs, 73 were "caught" in
winter, which is unfavorable for the initiation of egg laying by
isolated females in the laboratory (30). The remaining 79 individuals
that initiated egg laying before getting caught in winter were used to
construct this frequency distribution, which has a mean SD of 48
31 days and a range of 14-191 days.
±
±
ing female on the one hand, and a worker on the other hand,
illustrate the disadvantage of delayed reproduction maturation for a solitary foundress compared to a worker. Assuming
that b = A, the threshold p value required for satisfying
Inequality 1 is given by the equation
threshold p = s/2o, = 0.06.
12]
Alternatively, assuming that p = r = 0.5, the threshold b/,
value required for satisfying Inequality 1 is given by the
equation
threshold b/,
=
a/s
=
8.0.
[3]
This means that, other things being equal, workers would
break even with solitary foundresses in spite of rearing brood
related to them by a mere 0.06, or if p = r, then they would
do so in spite of solitary foundresses being capable of
performing 8 times more work per unit time. Compared to the
maximum threshold of 1.5 obtained under haplodiploidy
(when the brood consists entirely of full sisters), delayed
reproductive maturation is thus 5.3 times more effective than
haplodiploidy in promoting the evolution of a worker caste.
Variation in Age at Reproductive Maturity
Thus delayed reproductive maturation appears to be capable
of providing a substantial advantage for workers over their
solitary nesting counterparts (Table 1). Indeed, the advantage
for workers is so great that one begins to wonder why the
solitary founding strategy persists at all. However, a mixture
of single-foundress and multiple-foundress nests is common
in a variety of primitively eusocial species (26, 29). Any
reasonable theory should therefore not only explain the
existence of multiple-foundress associations with their sterile
worker castes but should also explain why single-foundress
and multiple-foundress associations coexist. The variation in
age at reproductive maturity with a range of 14-191 days (Fig.
1) may provide just such an expectation. With increasing
delay in reproductive maturation, the threshold p required for
satisfying Inequality 1 decreases while the threshold b/B
Evolution:
Proc. Natl. Acad. Sci. USA 88 (1991)
Gadagkar
Table 1. The advantage of assured fitness returns, delayed
reproduction, and both acting in concert in the primitively
eusocial wasp R. marginata
Assured
fitness
Both acting
Delayed
in concert
returns
reproduction
Parameter
Demographic
correction
factor for
solitary nest
0.015
0.12
foundresses s
0.015
Demographic
correction
factor for
0.43
0.43
0.12
workers a
0.017
0.14
Threshold p
0.06
28.7
3.6
8.0
Threshold b/l
Relative strength
compared to
2.4
19.1
5.3
haplodiploidy
increases (Fig. 2, dashed line). Since the advantage of the
worker strategy is small for early reproducers and large for
late producers, a polymorphism with single-foundress and
multiple-foundress associations will be favored by natural
selection.
Mixed Reproductive Strategies
The models and data considered above also suggest the
possibility of selection for an individual to adopt a mixture of
worker and queen strategies. If there is likely to be a delay in
attaining reproductive maturity, then such an individual
would maximize her inclusive fitness by first being a worker
and then, approximately at the time of attaining reproductive
maturity, changing over to the role of a foundress or queen.
The data in Fig. 1 on the time required for R. marginata
females to start laying eggs show that 28% of the wasps could
0.5-
LLJ
have completed rearing one entire brood (by working for 62
days) before they became reproductively mature (Fig. 3). R.
marginata follows a perennial indeterminate colony cycle
where queen supersedure leading to serial polygyny is common (28, 31, 32). Thus, many females first act as workers and
later become queens in their natal colonies. Since there is
always a substantial advantage of becoming the queen of a
large well-established colony, there should always be selection for any individual to take over the role of the queen.
However, if there is a delay in attaining reproductive maturity, individuals should be selected to first work for their
colonies before becoming queens. This explains why social
organization in R. marginata colonies does not appear to be
wrecked by potential queens who instead appear to behave
like all other nonqueens until they become queens. Indeed,
we are not able to predict the identity of the potential queen
or the timing of occurrence of a queen supersedure (33). In
addition, we also occasionally witness wasps working for
some time in their natal colonies and later leaving to found
single- or multiple-foundress colonies away from their natal
nests (R.G. and K. Chandrashekara, unpublished observations).
It should be mentioned however that if the adoption of a
worker role results in a significant drain on the physiology of
an individual, this may further -delay its reproductive maturation. In the course of our studies of R. marginata, we have
often been struck by what seem to be adaptations for reducing, if not overcoming, the negative consequence of assuming
worker duties for the possibility of future reproduction. Not
all individuals take on equally energetic or risky tasks, and
opportunities for future reproduction are not evenly distributed. Indeed, female wasps in R. marginata can be classified,
by a statistical analysis of their time-activity budgets, into
three behavior castes that we have labeled sitters, fighters,
and foragers (34). Sitters and fighters perform the less energetic and less risky intranidal tasks of feeding larvae and
building the nest and have relatively better developed ovaries, whereas foragers perform the bulk of the energetic and
risky extranidal tasks of leaving the nest in search of food and
have poorly developed ovaries (35).
Assured Fitness Returns
0.4
-J
10995
The asymmetry in the demographic correction factors for
solitary foundresses and workers seen so far was due to the
requirement that solitary foundresses have to survive longer
0.3
0 2-
i
100AFR
401
~ % Wasps that have
not yet begun to lay
eggs by 62 days 28
a
Ui
_
60
z
c]j
60-
403 0 -/
I)
AFR VARM 0
20
o--0
4
iO
IO 40-
VARM
3
---
20
Mean egg to adult
brood developmental
time =62 days
|
<
0
20-
--
40
60
80
100
AGE (DAYS) AT REPRODUCTIVE MATURITY
FIG. 2. The advantage of variation in age at reproductive maturity and assured fitness returns. Threshold p (A) and threshold b/(8
(B) required to satisfy Inequality as a function of age at reproductive
maturity for the individual action of variation in age at reproductive
maturity (VARM; dashed line) and for assured fitness returns (AFR)
and variation in age at reproductive maturity acting in concert (solid
line) are shown.
0
20
60
AGE IN DAYS
40
80
100
FIG. 3. Scope for mixed reproductive strategies. The data in Fig.
1 are rearranged to show that 28% of the wasps had not yet begun to
lay eggs by 62 days, which is the egg to adult brood developmental
period for the species. These wasps could thus have reared one entire
brood as workers before switching over to the role of queen or
foundress.
109%
Evolution:
Gadagkar
Proc. Natl. Acad. Sci. USA 88 (1991)
than workers to rear the same number of brood. I will now
consider a factor that will cause differences in the magnitudes
of the demographic correction factors for solitary
foundresses and workers, even when they survive for the
same period of time (7, 8, 25, 27).
While solitary foundresses have to necessarily survive
until the end of the developmental period of their brood,
failing which they will lose all their investment in it, workers
have a special advantage. If a worker cares for some brood
for a part of its developmental period and dies before bringing
it to independence, there is a good chance that another
worker from that colony will continue to care for the same
brood. Thus workers in multifemale nests are assured of
some fitness returns for their labor even if they work only for
a fraction of the brood developmental period (8). The demographic correction factor for solitary foundresses, s, is once
again the probability of surviving up to the end of the brood
developmental period (62 days); which is 0.12 (8). To allow
for the fact that workers can get fitness returns in proportion
to the fraction of the brood developmental period for which
they survive, the demographic correction factor for a worker,
a, was computed as
r=
I
i=l
pi(i/n)
+
E Pi= 0.43,
In the absence of assured fitness returns, the advantage of
mixed reproductive strategies can only be exploited by
individuals who have a delay of 62 or more days in attaining
reproductive maturity. When assured fitness returns and
mixed reproductive strategies act in concert, however, the
advantage of mixed reproductive strategies becomes available to individuals with a variety of values of age at reprodqctive maturity. Their labor as workers is not wasted even
if they leave their natal nests to become solitary foundresses
or queens of other multiple-foundress nests, because assured
fitness returns will give them fitness returns in proportion to
the fraction of the brood developmental period thatthey have
worked for. By making the advantage of mixed ieproductive
strategies available to a wide range of individuals, assured
fitness returns and mixed reproductive strategies'acting in
concert facilitate selection for the worker strategy because
suitable conditions for'an individual to shift -over 'from a
worker role to that of a queen can hardly be expected to
appear predictably after 62 days or its multiples!
Discussion
x0
n-I
Assured Fitness Returns and Mixed Reproductive Strategies
Acting in Concert
[41
i=n
where Pi is the proportion of workers who have a life span of
i days. Using Eqs. 2 and 3, the threshold p and b/l required
for satisfying Inequality 1 are0.14 and 3.6, respectively. Thus
the relative strength of assured fitness returns compared to
haplodiploidy is 2.4.
I will now show how assured fitness returns can act in
concert with the three other factors we have considered so
far-namely, delayed reproductive maturation, variation in
age at reproductive maturity, and mixed reproductive strategies-to provide an even more powerful force in selecting
for worker behavior.
Assured Fitness Returns and Delayed Reproductive
Maturation Acting in Concert
Assured fitness returns and delayed reproductive maturation
in concert because delayed reproductive maturation
can lower the fitness of a solitary foundress and assured
fitness returns can simultaneously boost the fitness of workers. To quantify the consequences of such action of assured
fitness returns and delayed reproductive maturation in concert, I simply need to' use the value of the ,Iemographic
correction factor s for solitary foundresses of 0.015 from the
section on delayed reproductive maturation and the value of
the demographic correction factor orfor workers of0.43 given
by Eq. 4, from thie section on assured fitness returns. Now,
Eqs.'2 and 3 yield values of 0.015 and 28.7 for the threshold
p and by/, respeptively, required for satisfying Inequality 1.
Thus assured fitness returns and delayed reproductive maturation acting in concert have a relative strength of 19.1
compared to haplodiploidy (Table 1).
can act
Assured Fitness Returns and Variation in Age at
Reproductive Maturity Acting in Concert
Just as assured fitness returns and delayed reproductive
maturation can act in concert and provide a more powerful
advantage for workers, assured fitness returns and variation
in age at reproductive maturity can also act in concert and
provide, for any given delay in attaining reproductive maturity, a more powerful advantage for the worker strategy (Fig.
2, solid line).
The models presented here show how several factors acting
either singly or in concert with one of them (namely, assured
fitness returns) can differentially affect the demographic
correction factor in the inclusive fitness equation and make
the worker strategy more advantageous thana solitary nestfounding strategy. A particularly satisfying feature of these
models is that such an advantage of the worker strategy over
the solitary nest-founding strategy can be more pronounced
for some individuals than for others, thereby suggesting ways
by which a coexistence of both strategies in a population can
be selected.
Three kinds of data pertaining to the primitively eusocial
tropical wasp R. marginata have been used to illustrate these
models. The first concerns field data on the survivorship of
marked females in natural nests. The sepond concerns brood
developmental time calculated from natural nests. The
third-namely, the time taken to build nests and start laying
eggs by freshly eclosed virgin females, isolated into individual laboratory cages-needs some justification. Solitary nest
founding is quite common in this and many similar species
(26, 28, 36); isolating the females is therefore not particularly
unnatural. There is good reason to believe that mating is not
essential for a female to develop her ovaries and lay eggs and
even to establish herself as the sole egg layer of a colony (in
spite of the presence of other mated females in that colony),
to prevent all her-nestmates from developing their ovaries,
and to maintain apparently normal social organization (37).
The behavior of virgin females isolated in laboratory cages is
therefore unlikely to' be so artificial as to tell'us nothing about
natural situations. Although the distribution of the time taken
for reproductive maturation under natural conditions may not
be identical to that in Fig. 1, some extent of delayed reproductive maturation and some variation in age at reproductive
maturity are certain to exist in nature. In natural colonies of
R. marginata that exhibit perennial indeterminate colony
cycles (32) with frequent natural queen successions (31), the
age at the time of takeover for 17 queens from four colonies
ranged from 7 to 78 days (mean ± SD 38 23) (31). My goal
in using the data in Figs. 1 and 3 has therefore been to
illustrate the models, indicate expected trends,' and draw
attention to the need to, obtain good data'on demographic
parameters under natural conditions..
The models presented here provide a consistently more
powerful selective advantage for worker behavior when
compared to the advantage of haplodiploidy (Table 1). But
Evolution:
Gadagkar
Proc. Natl. Acad. Sci. USA 88 (1991)
10997
they do not explain why eusociality has arisen 11 times
independently in the Hymenoptera but only twice in the rest
ofthe animal kingdom (2). Stated in this form, the distribution
of eusociality certainly suggests an obvious role for haplodiploidy (which is nearly universal in the Hymenoptera) in
the evolution of eusociality. The paradox of the taxonomic
distribution of eusociality is unlikely. to be solved unless we
begin to ask why, for example, is eusociality restricted to the
Aculeata within the Hymenoptera (38). One way to do so
would be to look for other kinds of predispositions for social
life in those groups that do show eusociality. The models
presented here point to some factors that should be examined
in this context. But a word of caution may be in order here.
Delayed reproductive maturation and variation in age at
reproductive maturity seen in today's eusocial species may
not necessarily reflect the situation that may have prevailed
in their solitary ancestors. This is because delayed reproductive maturation and variation in age at reproductive maturity
can also coevolve with eusociality. For instance, late reproducers will be at a relatively smaller selective disadvantage in
a eusocial species compared to a solitary species because of
the possibility of gaining indirect (inclusive) fitness in the
former: Nevertheless, any delayed reproductive maturation
and variation in age at reproductive maturity that may have
accidentally existed in the solitary ancestors of today's
eusocial species would have predisposed them to the evolution of eusociality. One pleasing consequence of this argument however is the realization that delayed reproductive
maturation and variation in age at reproductive maturity can
play a role both in the origin as well as in the maintenance of
eusociality!
I suspect that the models and ideas developed here will
have wider applications beyond the evolution of eusociality
in the Hymenoptera. Two obvious examples come to mind.
(i) In many species of birds, some individuals postpone
breeding and remain as "helpers" in their natal nests, assisting their parents in foraging and defense. The helpers
may, in later years, establish their lwn nests and breed
(39-42). (ii) An interaction between cooperation and conflict
is being increasingly recognized as a central paradigm in
understanding a whole range of phenomena, including aggregation in cellular molds (43), the evolution of development in
multicellular organisms, and indeed the evolution of multicellularity itself (44, 45).
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I thank Madhav Gadgil, V. Nanjundiah, K. Chandrashekara,
Anindya Sinha, N. V. Joshi, Wayne Getz, Peter Nonacs, Kern
Reeve, William Wcislo, David Queller, and three anonymous referees for comments on a previous version of this paper. This work was
supported in part by grants from the Indian National Science
Academy and Ministry of Environment and Forests, Government of
India.
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44. Buss, L. W. (1987) The Evolution of Individuality (Princeton
Univ. Press, Princeton, NJ).
45. Bonner, J. T. (1988) The Evolution of Complexity (Princeton
Univ. Press, Princeton, NJ).
1. Michener, C. D. (499) Annu. Rev. Entomol. 14, 299-342.
2. Wilson, E. 0. (197D -The Insect Societies (Harvard Univ.
Press, Cambridge, MA).
3. Jarvis, J. U. M. (1981) Science 212, 571-573.
4. Sherman, P. W., Jarvis, J. U. M. & Alexander, R. D. (1991)
The Biology of the Naked Mole-Rat (Princeton Univ. Press,
Princeton, NJ).
5. Hamilton, W. D. (1964) J. Theor. Biol. 7, 1-16.
6. Hamilton, W. D. (1964) J. Theor. Biol. 7, 17-52.
7. Queller, D. C. (1989) Proc. Nati. Acad. Sci. USA 86, 32243226.
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25. Queller, D. C. & Strassmann, J. E. (1989) in The Genetics of
Social Evolution, eds. Breed, M. D. & Page, R. E., Jr. (Westview, Boulder,-CO), pp. 103-122.
26. Reeve, H. K. (1991) in The Social Biology of Wasps, eds. Ross,
K. G. & Matthews, R. W. (Cornell Univ. Press, Ithaca, NY),
pp. 99-148.
27. Nonacs, P. (1991) Oikos 61, 122-125.
28. Gadagkar, R. (1991) in The Social Biology of Wasps, eds. Ross,
K. G. & Matthews, R. W. (Cornell Univ. Press, Ithaca, NY),
pp. 149-190.
29. Michener, C. D. (1974) The Social Behaviour of the Bees: A
Comparative Study (Harvard Univ. Press, Cambridge, MA).
30. Gadagkar, R., Bhagavan, S., Malpe, R. & Vinutha, C. (1991)
Entomon 16, 167-174.
31. Gadagkar, R., Chandrashekara, K., Chandran, S. & Bhagavan,
S. (1990) in Social Insects and the Environment, Proceedings of
the 11th International Congress of IUSSI, eds. Veeresh, G. K.,
Mallik, B. & Viraktamath, C. A. (Oxford & IBH, New Delhi),
pp. 227-228.
32. Chandrashekara, K., Bhagavan, S., Chandran, S., Nair, P. &
Gadagkar, R. (1990) in Social Insects and the Environment,
Proceedings of the 11th International Congress of IUSSI, eds.
Veeresh, G. K., Mallik, B. & Viraktamath, C. A. (Oxford &
IBH, New Delhi), p. 81.
33. Chandrashekara, K. & Gadagkar, R. (1992) J. Insect. Behav.,
in press.
34. Gadagkar, R. & Joshi, N. V. (1983) Anim. Behav. 31, 26-31.
35. Chandrashekara, K. & Gadagkar, R. (1991) Ethology 87, 269-
2832.
Vol. 88, pp. 10993-10997, December 1991
Evolution
Demographic predisposition to the evolution of eusociality:
A hierarchy of models
(altruism/Ropalidia/demography/assured fitness returns/delayed reproductive maturation)
RAGHAVENDRA GADAGKAR
Centre for Ecological Sciences and Centre for Theoretical Studies, Indian Institute of Science, Bangalore, 560012 India
Communicated by Charles D. Michener, July 22, 1991
I present a hierarchy of models that illustrate,
ABSTRACT
within the framework of inclusive fitness theory, how demographic factors can predispose a species to the evolution of
eusociality. Delayed reproductive maturation lowers the inclusive fitness of a solitary foundress relative to that of a worker.
Variation in age at reproductive maturity makes the worker
strategy more profitable to some individuals than to others and
thus predicts the coexistence of single-foundress and multiplefoundress nesting associations. Delayed reproductive maturation and variation in age at reproductive maturity also select for
mixed reproductive strategies so that some individuals whose
reproductive maturation is expected to be delayed can first act
as workers and later switch over to the role of a queen or
foundress. Assured fitness returns shows how identical mortality rates can have different consequences for workers and
solitary nest foundresses because a solitary foundress will have
to necessarily survive for the entire duration of development of
her brood, whereas a worker can hope to get proportional
fitness returns for short periods of work. In concert with
assured fitness returns, delayed reproductive maturation and
variation in age at reproductive maturity become more powerful in selecting for worker behavior, and mixed reproductive
strategies become available to a wider range of individuals.
These phenomena provide a consistently more powerful selective advantage for the worker strategy than do genetic asymmetries created by haplodiploidy.
When members of a species live in groups comprising individuals of more than one generation, cooperate in brood care,
and relegate reproduction to one or a small number of
individuals in the group, they are thought to represent the
most highly evolved stage in social evolution in the animal
kingdom and are appropriately termed eusocial (1, 2). All ants
and termites, many species of bees and wasps, and the naked
mole rat Heterocephalus glaber are eusocial (1-4). The most
striking feature of eusociality is the presence of a sterile
worker caste.
In the highly eusocial termites, ants, and honey bees, the
workers are often morphologically differentiated, have lost
most or all ability to mate and reproduce, and may have
reached an evolutionary cul-de-sac from which a return to
fertile or solitary life may be difficult, if not impossible. In
many species of primitively eusocial wasps and bees on the
other hand, social nest foundation is facultative; a nest may
be founded either by a single female or by a group of females,
only one of whom assumes the role of the queen and the rest
remain sterile and work to rear the queen's brood. A newly
eclosed female in a primitively eusocial species appears to
have several options: she may leave her natal nest to found
a new single- or multiple-foundress nest, she may leave to
usurp another foundress's nest, she may stay back on her
natal nest and work for her mother, or she may stay back and
eventually inherit the role of the queen in the nest of her birth.
Thus, given that they have the choice of reproducing, explaining worker behavior is even more challenging in primitively eusocial insects.
Predisposition to the Evolution of Eusociality
Hamilton (5, 6) argued that the sterile worker castes in
eusocial species are explained if we can show that the
inclusive fitness of a sterile worker is greater than that of a
solitary nest foundress and thus provided a powerful theoretical framework for the study of social evolution. The
inclusive fitness of a solitary nest foundress or a worker can
be conveniently represented as the product of three components (7, 8): (i) an intrinsic productivity component that
represents the number of individuals that she can rear provided she survives for their entire developmental period, (ii)
the coefficient of genetic relatedness, representing the probability that genes present in the solitary foundress or worker
are also present in the brood she cares for, and (iii) a
demographic correction factor that should be used to devalue
the intrinsic productivity factor because of the fact that the
solitary foundress or worker may not survive for the entire
developmental period of the brood under her care. Thus a
nonreproducing worker will get more inclusive fitness than a
solitary foundress, and natural selection will favor the evolution of a worker caste if
3p
a> b rs,
[1]
where f3 is the intrinsic productivity of a worker, p is the
coefficient of genetic relatedness of a worker to the brood
under her care, a is the demographic correction factor for a
worker, and b, r, and s are the corresponding parameters for
a solitary foundress. ClearlyI three kinds of factors can
contribute to Inequality 1.
Ecological or physiological predisposition: f3> b. Workers
are able to rear more brood per capita than a solitary
foundress. This may happen because of better protection
from parasites, predators, and conspecific usurpers in a
group nesting situation compared to a single foundress nest
(9-16) or because those who opt for worker roles may be
subfertile individuals whose b would be relatively small if
they became solitary foundresses but whose (3 as workers
would be relatively high (17-21).
Genetic predisposition: p > r. Workers have access to
brood that are more closely related genetically to themselves
than a solitary foundress is to her offspring. The male haploid
genetic system in the Hymenoptera coupled with an ability to
bias investment in favor of female brood can make this
possible (5, 6, 22-24).
Demographic predisposition: a > s. This has seldom been
considered explicitly for social insects (but see refs. 7, 8, and
25-27) and will form the subject of the rest of this paper. The
inequality a > s may imply that workers have a lower rate of
The publication costs of this article were defrayed in part by page charge
payment. This article must therefore be hereby marked "advertisement"
in accordance witb 18 U.S.C. §1734 solely to indicate this fact.
10993
10994
Evolution:
Gadagkar
mortality compared to solitary foundresses. This is probably
true, but quantitative data on survivorship of solitary
foundresses are hard to obtain (7, 8). Besides, I wish to show
that even if workers and solitary foundresses have identical
mortality rates, the consequences of such mortality for the
magnitude of the demographic correction factors and thus for
inclusive fitness can be quite different for workers and
solitary foundresses. To do so I shall use survivorship data
obtained from workers in field colonies of Ropalidia marginata (see below) (8) throughout this paper. By using survivorship data from workers to estimate the demographic
correction factor for solitary foundresses, I will perhaps
overestimate the inclusive fitness of solitary foundresses but,
to the extent that I do so, my estimate of the advantage of the
worker strategy will be conservative.
In what follows I shall contrast the inclusive fitness of a
solitary foundress on the one hand and a worker in a
multifemale nest on the other and assume for simplicity that
each nest produces a single batch of synchronous brood. I
shall use field and laboratory data on the primitively eusocial
tropical wasp R. marginata (Lep.) (Hymenoptera: Vespidae)
throughout, to illustrate the models (28). R. marginata, like
most primitively eusocial wasps, is a progressive provisioner
where the brood is entirely dependent on the adults for food
and protection. This makes my models particularly applicable to them and, by the same token, somewhat less applicable, although not entirely inapplicable (see ref. 24), to mass
provisioners such as the many species of primitively eusocial
Halictines (29).
Delayed Reproductive Maturation
Experiments involving isolation of freshly eclosed virgin R.
marginata females into individual laboratory cages have
revealed two forms of preimaginal caste bias. First, about
50%o of the females tested died without building a nest and
laying eggs; second, even those that did build a nest and lay
eggs took a long and variable amount of time to start doing so
(19, 20). Both these forms of preimaginal caste bias appear to
be mediated by the quantity of larval nutrition, such that
individuals fed relatively well as larvae have a high probability of developing into egg layers and early reproducers.
Conversely, those fed relatively poorly as larvae have a high
probability of developing into non-egg-layers or late reproducers (21). The time required to attain reproductive maturity
ranged from 14 to 191 days (mean ± SD = 48 + 31 days) (30)
(Fig. 1). Such delayed reproductive maturation will differentially affect the inclusive fitnesses of solitary foundresses and
workers (7, 8, 17). This is because, to successfully rear brood
to the age of independence, solitary foundresses will have to
survive for the sum of the period required for reproductive
maturation and the brood developmental period. Workers
are, however, unaffected by any delay in their reproductive
maturation as their work (and fitness) depends on the queen
supplying them with brood. It will thus be sufficient for them
to survive for the duration of the brood developmental
period.
By using the mean delay in reproductive maturation of 48
days (Fig. 1), an estimate of the brood developmental period
of 62 days for R. marginata (8), and survivorship data from
field colonies of R. marginata (8), I compute the asymmetrical fitness consequences of such delayed reproduction
maturation for the inclusive fitnesses of solitary foundresses
and workers. The demographic correction factor s for solitary
foundresses is the probability of survival for 48 + 62 = 110
days, which is 0.015 (8). The demographic correction factor
afor workers on the other hand is the probability of survival
for the duration of the brood developmental period of 62
days, which is 0.12 (8). These rather different values for the
demographic correction factors obtained for a solitary nest-
Proc. Natl. Acad. Sci. USA 88 (1991)
(D
z
tn 20-
-:
J
V~~
0
(D
a.V)
16
UL
12-
Or -I
8-
z
4-
m
4m
NH"~~J~F1
LO
0
-
(D)
-Z
to
0
t-
a)
It
k6
D
LO
0)
-1
CD
I
0
A
AGE (DAYS) AT THE TIME OF LAYING THEIR FIRST EGG
FIG. 1. Frequency distribution of wasps in different age classes
at the time of laying their first eggs. Two hundred ninety-nine freshly
eclosed female R. marginata were isolated in individual laboratory
cages (19, 20, 30). Of these, 147 died without laying eggs. Of the
remaining 152 that built a nest and laid eggs, 73 were "caught" in
winter, which is unfavorable for the initiation of egg laying by
isolated females in the laboratory (30). The remaining 79 individuals
that initiated egg laying before getting caught in winter were used to
construct this frequency distribution, which has a mean SD of 48
31 days and a range of 14-191 days.
±
±
ing female on the one hand, and a worker on the other hand,
illustrate the disadvantage of delayed reproduction maturation for a solitary foundress compared to a worker. Assuming
that b = A, the threshold p value required for satisfying
Inequality 1 is given by the equation
threshold p = s/2o, = 0.06.
12]
Alternatively, assuming that p = r = 0.5, the threshold b/,
value required for satisfying Inequality 1 is given by the
equation
threshold b/,
=
a/s
=
8.0.
[3]
This means that, other things being equal, workers would
break even with solitary foundresses in spite of rearing brood
related to them by a mere 0.06, or if p = r, then they would
do so in spite of solitary foundresses being capable of
performing 8 times more work per unit time. Compared to the
maximum threshold of 1.5 obtained under haplodiploidy
(when the brood consists entirely of full sisters), delayed
reproductive maturation is thus 5.3 times more effective than
haplodiploidy in promoting the evolution of a worker caste.
Variation in Age at Reproductive Maturity
Thus delayed reproductive maturation appears to be capable
of providing a substantial advantage for workers over their
solitary nesting counterparts (Table 1). Indeed, the advantage
for workers is so great that one begins to wonder why the
solitary founding strategy persists at all. However, a mixture
of single-foundress and multiple-foundress nests is common
in a variety of primitively eusocial species (26, 29). Any
reasonable theory should therefore not only explain the
existence of multiple-foundress associations with their sterile
worker castes but should also explain why single-foundress
and multiple-foundress associations coexist. The variation in
age at reproductive maturity with a range of 14-191 days (Fig.
1) may provide just such an expectation. With increasing
delay in reproductive maturation, the threshold p required for
satisfying Inequality 1 decreases while the threshold b/B
Evolution:
Proc. Natl. Acad. Sci. USA 88 (1991)
Gadagkar
Table 1. The advantage of assured fitness returns, delayed
reproduction, and both acting in concert in the primitively
eusocial wasp R. marginata
Assured
fitness
Both acting
Delayed
in concert
returns
reproduction
Parameter
Demographic
correction
factor for
solitary nest
0.015
0.12
foundresses s
0.015
Demographic
correction
factor for
0.43
0.43
0.12
workers a
0.017
0.14
Threshold p
0.06
28.7
3.6
8.0
Threshold b/l
Relative strength
compared to
2.4
19.1
5.3
haplodiploidy
increases (Fig. 2, dashed line). Since the advantage of the
worker strategy is small for early reproducers and large for
late producers, a polymorphism with single-foundress and
multiple-foundress associations will be favored by natural
selection.
Mixed Reproductive Strategies
The models and data considered above also suggest the
possibility of selection for an individual to adopt a mixture of
worker and queen strategies. If there is likely to be a delay in
attaining reproductive maturity, then such an individual
would maximize her inclusive fitness by first being a worker
and then, approximately at the time of attaining reproductive
maturity, changing over to the role of a foundress or queen.
The data in Fig. 1 on the time required for R. marginata
females to start laying eggs show that 28% of the wasps could
0.5-
LLJ
have completed rearing one entire brood (by working for 62
days) before they became reproductively mature (Fig. 3). R.
marginata follows a perennial indeterminate colony cycle
where queen supersedure leading to serial polygyny is common (28, 31, 32). Thus, many females first act as workers and
later become queens in their natal colonies. Since there is
always a substantial advantage of becoming the queen of a
large well-established colony, there should always be selection for any individual to take over the role of the queen.
However, if there is a delay in attaining reproductive maturity, individuals should be selected to first work for their
colonies before becoming queens. This explains why social
organization in R. marginata colonies does not appear to be
wrecked by potential queens who instead appear to behave
like all other nonqueens until they become queens. Indeed,
we are not able to predict the identity of the potential queen
or the timing of occurrence of a queen supersedure (33). In
addition, we also occasionally witness wasps working for
some time in their natal colonies and later leaving to found
single- or multiple-foundress colonies away from their natal
nests (R.G. and K. Chandrashekara, unpublished observations).
It should be mentioned however that if the adoption of a
worker role results in a significant drain on the physiology of
an individual, this may further -delay its reproductive maturation. In the course of our studies of R. marginata, we have
often been struck by what seem to be adaptations for reducing, if not overcoming, the negative consequence of assuming
worker duties for the possibility of future reproduction. Not
all individuals take on equally energetic or risky tasks, and
opportunities for future reproduction are not evenly distributed. Indeed, female wasps in R. marginata can be classified,
by a statistical analysis of their time-activity budgets, into
three behavior castes that we have labeled sitters, fighters,
and foragers (34). Sitters and fighters perform the less energetic and less risky intranidal tasks of feeding larvae and
building the nest and have relatively better developed ovaries, whereas foragers perform the bulk of the energetic and
risky extranidal tasks of leaving the nest in search of food and
have poorly developed ovaries (35).
Assured Fitness Returns
0.4
-J
10995
The asymmetry in the demographic correction factors for
solitary foundresses and workers seen so far was due to the
requirement that solitary foundresses have to survive longer
0.3
0 2-
i
100AFR
401
~ % Wasps that have
not yet begun to lay
eggs by 62 days 28
a
Ui
_
60
z
c]j
60-
403 0 -/
I)
AFR VARM 0
20
o--0
4
iO
IO 40-
VARM
3
---
20
Mean egg to adult
brood developmental
time =62 days
|
<
0
20-
--
40
60
80
100
AGE (DAYS) AT REPRODUCTIVE MATURITY
FIG. 2. The advantage of variation in age at reproductive maturity and assured fitness returns. Threshold p (A) and threshold b/(8
(B) required to satisfy Inequality as a function of age at reproductive
maturity for the individual action of variation in age at reproductive
maturity (VARM; dashed line) and for assured fitness returns (AFR)
and variation in age at reproductive maturity acting in concert (solid
line) are shown.
0
20
60
AGE IN DAYS
40
80
100
FIG. 3. Scope for mixed reproductive strategies. The data in Fig.
1 are rearranged to show that 28% of the wasps had not yet begun to
lay eggs by 62 days, which is the egg to adult brood developmental
period for the species. These wasps could thus have reared one entire
brood as workers before switching over to the role of queen or
foundress.
109%
Evolution:
Gadagkar
Proc. Natl. Acad. Sci. USA 88 (1991)
than workers to rear the same number of brood. I will now
consider a factor that will cause differences in the magnitudes
of the demographic correction factors for solitary
foundresses and workers, even when they survive for the
same period of time (7, 8, 25, 27).
While solitary foundresses have to necessarily survive
until the end of the developmental period of their brood,
failing which they will lose all their investment in it, workers
have a special advantage. If a worker cares for some brood
for a part of its developmental period and dies before bringing
it to independence, there is a good chance that another
worker from that colony will continue to care for the same
brood. Thus workers in multifemale nests are assured of
some fitness returns for their labor even if they work only for
a fraction of the brood developmental period (8). The demographic correction factor for solitary foundresses, s, is once
again the probability of surviving up to the end of the brood
developmental period (62 days); which is 0.12 (8). To allow
for the fact that workers can get fitness returns in proportion
to the fraction of the brood developmental period for which
they survive, the demographic correction factor for a worker,
a, was computed as
r=
I
i=l
pi(i/n)
+
E Pi= 0.43,
In the absence of assured fitness returns, the advantage of
mixed reproductive strategies can only be exploited by
individuals who have a delay of 62 or more days in attaining
reproductive maturity. When assured fitness returns and
mixed reproductive strategies act in concert, however, the
advantage of mixed reproductive strategies becomes available to individuals with a variety of values of age at reprodqctive maturity. Their labor as workers is not wasted even
if they leave their natal nests to become solitary foundresses
or queens of other multiple-foundress nests, because assured
fitness returns will give them fitness returns in proportion to
the fraction of the brood developmental period thatthey have
worked for. By making the advantage of mixed ieproductive
strategies available to a wide range of individuals, assured
fitness returns and mixed reproductive strategies'acting in
concert facilitate selection for the worker strategy because
suitable conditions for'an individual to shift -over 'from a
worker role to that of a queen can hardly be expected to
appear predictably after 62 days or its multiples!
Discussion
x0
n-I
Assured Fitness Returns and Mixed Reproductive Strategies
Acting in Concert
[41
i=n
where Pi is the proportion of workers who have a life span of
i days. Using Eqs. 2 and 3, the threshold p and b/l required
for satisfying Inequality 1 are0.14 and 3.6, respectively. Thus
the relative strength of assured fitness returns compared to
haplodiploidy is 2.4.
I will now show how assured fitness returns can act in
concert with the three other factors we have considered so
far-namely, delayed reproductive maturation, variation in
age at reproductive maturity, and mixed reproductive strategies-to provide an even more powerful force in selecting
for worker behavior.
Assured Fitness Returns and Delayed Reproductive
Maturation Acting in Concert
Assured fitness returns and delayed reproductive maturation
in concert because delayed reproductive maturation
can lower the fitness of a solitary foundress and assured
fitness returns can simultaneously boost the fitness of workers. To quantify the consequences of such action of assured
fitness returns and delayed reproductive maturation in concert, I simply need to' use the value of the ,Iemographic
correction factor s for solitary foundresses of 0.015 from the
section on delayed reproductive maturation and the value of
the demographic correction factor orfor workers of0.43 given
by Eq. 4, from thie section on assured fitness returns. Now,
Eqs.'2 and 3 yield values of 0.015 and 28.7 for the threshold
p and by/, respeptively, required for satisfying Inequality 1.
Thus assured fitness returns and delayed reproductive maturation acting in concert have a relative strength of 19.1
compared to haplodiploidy (Table 1).
can act
Assured Fitness Returns and Variation in Age at
Reproductive Maturity Acting in Concert
Just as assured fitness returns and delayed reproductive
maturation can act in concert and provide a more powerful
advantage for workers, assured fitness returns and variation
in age at reproductive maturity can also act in concert and
provide, for any given delay in attaining reproductive maturity, a more powerful advantage for the worker strategy (Fig.
2, solid line).
The models presented here show how several factors acting
either singly or in concert with one of them (namely, assured
fitness returns) can differentially affect the demographic
correction factor in the inclusive fitness equation and make
the worker strategy more advantageous thana solitary nestfounding strategy. A particularly satisfying feature of these
models is that such an advantage of the worker strategy over
the solitary nest-founding strategy can be more pronounced
for some individuals than for others, thereby suggesting ways
by which a coexistence of both strategies in a population can
be selected.
Three kinds of data pertaining to the primitively eusocial
tropical wasp R. marginata have been used to illustrate these
models. The first concerns field data on the survivorship of
marked females in natural nests. The sepond concerns brood
developmental time calculated from natural nests. The
third-namely, the time taken to build nests and start laying
eggs by freshly eclosed virgin females, isolated into individual laboratory cages-needs some justification. Solitary nest
founding is quite common in this and many similar species
(26, 28, 36); isolating the females is therefore not particularly
unnatural. There is good reason to believe that mating is not
essential for a female to develop her ovaries and lay eggs and
even to establish herself as the sole egg layer of a colony (in
spite of the presence of other mated females in that colony),
to prevent all her-nestmates from developing their ovaries,
and to maintain apparently normal social organization (37).
The behavior of virgin females isolated in laboratory cages is
therefore unlikely to' be so artificial as to tell'us nothing about
natural situations. Although the distribution of the time taken
for reproductive maturation under natural conditions may not
be identical to that in Fig. 1, some extent of delayed reproductive maturation and some variation in age at reproductive
maturity are certain to exist in nature. In natural colonies of
R. marginata that exhibit perennial indeterminate colony
cycles (32) with frequent natural queen successions (31), the
age at the time of takeover for 17 queens from four colonies
ranged from 7 to 78 days (mean ± SD 38 23) (31). My goal
in using the data in Figs. 1 and 3 has therefore been to
illustrate the models, indicate expected trends,' and draw
attention to the need to, obtain good data'on demographic
parameters under natural conditions..
The models presented here provide a consistently more
powerful selective advantage for worker behavior when
compared to the advantage of haplodiploidy (Table 1). But
Evolution:
Gadagkar
Proc. Natl. Acad. Sci. USA 88 (1991)
10997
they do not explain why eusociality has arisen 11 times
independently in the Hymenoptera but only twice in the rest
ofthe animal kingdom (2). Stated in this form, the distribution
of eusociality certainly suggests an obvious role for haplodiploidy (which is nearly universal in the Hymenoptera) in
the evolution of eusociality. The paradox of the taxonomic
distribution of eusociality is unlikely. to be solved unless we
begin to ask why, for example, is eusociality restricted to the
Aculeata within the Hymenoptera (38). One way to do so
would be to look for other kinds of predispositions for social
life in those groups that do show eusociality. The models
presented here point to some factors that should be examined
in this context. But a word of caution may be in order here.
Delayed reproductive maturation and variation in age at
reproductive maturity seen in today's eusocial species may
not necessarily reflect the situation that may have prevailed
in their solitary ancestors. This is because delayed reproductive maturation and variation in age at reproductive maturity
can also coevolve with eusociality. For instance, late reproducers will be at a relatively smaller selective disadvantage in
a eusocial species compared to a solitary species because of
the possibility of gaining indirect (inclusive) fitness in the
former: Nevertheless, any delayed reproductive maturation
and variation in age at reproductive maturity that may have
accidentally existed in the solitary ancestors of today's
eusocial species would have predisposed them to the evolution of eusociality. One pleasing consequence of this argument however is the realization that delayed reproductive
maturation and variation in age at reproductive maturity can
play a role both in the origin as well as in the maintenance of
eusociality!
I suspect that the models and ideas developed here will
have wider applications beyond the evolution of eusociality
in the Hymenoptera. Two obvious examples come to mind.
(i) In many species of birds, some individuals postpone
breeding and remain as "helpers" in their natal nests, assisting their parents in foraging and defense. The helpers
may, in later years, establish their lwn nests and breed
(39-42). (ii) An interaction between cooperation and conflict
is being increasingly recognized as a central paradigm in
understanding a whole range of phenomena, including aggregation in cellular molds (43), the evolution of development in
multicellular organisms, and indeed the evolution of multicellularity itself (44, 45).
8. Gadagkar, R. (1990) Philos. Trans. R. Soc. London Ser. B 329,
17-25.
9. Lin, N. & Micheiier, C. D. (1972) Q. Rev. Biol. 47, 131-159.
10. Gamboa, G. J. (1978) Science 199, 1463-1465.
11. Litte, M. (1977) Behav. Ecol. Sociobiol. 2, 229-246.
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I thank Madhav Gadgil, V. Nanjundiah, K. Chandrashekara,
Anindya Sinha, N. V. Joshi, Wayne Getz, Peter Nonacs, Kern
Reeve, William Wcislo, David Queller, and three anonymous referees for comments on a previous version of this paper. This work was
supported in part by grants from the Indian National Science
Academy and Ministry of Environment and Forests, Government of
India.
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