APS 323 Social Insects: Lecture 9

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APS 323 Social Insects Lecture 9
Francis L. W. Ratnieks Laboratory of Apiculture
Social Insects
Department of Animal Plant Sciences University
of Sheffield
Lecture 9 Sex Allocation Predictions Tests
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Kin Value
Aims 1. To show how to use theory to determine
worker-optimum and queen-optimum sex-allocation
ratios. 2. To show how these predictions have
been tested empirically 3. Understand some
mechanisms by which queen and workers may be able
to influence their colonys sex allocation, and
the final outcome of the conflict. Objectives 1.
Learn how to determine worker-optimum and
queen-optimum sex allocation ratios. 2. Learn
some of the key studies that have tested sex
allocation predictions in social Hymenoptera.
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Determining Worker-Optimum Queen-Optimum Sex-
Allocation Ratios
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Kin Value
Regression relatedness x SSreproductive value x
SSmating success. Consider two simple examples
the kin value of the males and the queens reared
in a colony with a single queen mated to a single
male to the workers. Relatedness of workers to
males, bmw 0.5 Relatedness of workers to
queens, bqw 0.75 As all the males are
queens sons, VF/VM 2 (we can say VF 2 and
VM 1) If the sex-allocation ratio is equal,
MF/MM 1 (we can say MF 1 and MM 1, where
M is mating success) The kin value of a male is
bmwVMMM 0.5 x 1 x 1 0.5 The kin value of a
female is bqwVFMF 0.75 x 2 x 1 1.5
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Kin Value
The previous slide shows that a queen has three
times the kin value of a male to the workers when
the sex-allocaton ratio is even. What
implications does this have on queen-worker
conflict over sex allocation? Can you already
see what the sex-ratio optimum of the workers is?
Is it male bias, female bias, or equal?
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Worker-Optimum Sex-Allocation Ratio
At an equal sex-allocation ratio in the
population, the kin values of males and queens to
investing workers are not equal. Kin value of a
male is bmwVMMM 0.5 x 1 x 1 0.5 Kin value
of a female is bqwVFMF 0.75 x 2 x 1
1.5 What must happen to the mating success of
males females to make their kin values equal
(for given values of b and V)? Answer the
mating success of males must increase. By how
much? By 3 times. How could this come about? By
a 3F1M sex-allocation ratio in the population.
This will mean that allocation to males has 3
times the mating success of allocation to
females.
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Mother Queens Interests
We can do exactly the same thing to determine the
sex-allocation optimum of the mother queen. The
relatedness of a donor mother to the males and
young queens being reared is not the same as for
donor workers. Relatedness of queen to sons,
bm,mother 1 Relatedness of queen to
daughters, bq,mother 0.5 All the males are
queens sons, VF/VM 2 (we can say VF 2 and
VM 1) And the sex-allocation ratio is equal,
MF/MM 1 (we can say MF 1 and MM 1) The
kin value of a male is bmwVMMM 1 x 1 x 1
1 The kin value of a female is bqwVFMF 0.5 x 2
x 1 1
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Queen-Worker Conflict
What the previous slides tell us is that the
sex-allocation optimum of the mother queen is an
even sex ratio (1F1M) while the optimum of the
workers is a female-biased sex ratio
(3F1M). There is a conflict over sex allocation
within the colony, between queen and
workers. There is no conflict among individual
workers. Each worker has the same optimum. How
do we test this idea of queen-worker conflict
over sex allocation? Who will win? Queen or
workers?
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Trivers Hare 1976
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Sex Allocation (Weights) in Ants
The allocation ratio is determined from the
numerical sex ratio (y-axis) and the weight ratio
of queens to males (x-axis). Queens are generally
heavier than males.
1F1M allocation ratio
3F1M allocation ratio
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Significance of Trivers Hare 1976
The preceding figure is the main part of Figure 4
in Trivers Hare (1976). This paper has proved
to be highly influential. It was the best test of
inclusive fitness theory made up to that time,
1976, which was 12 years after Hamilton had
published his theory (Hamilton 1964). It combined
sex-allocation theory with inclusive fitness
theory to predict that sex allocation should be
female biased in eusocial Hymenoptera. Trivers
and Hare tested this with data from 21 ant
species. Investment in queens was significantly
greater than in males, as predicted by IF
theory. The study also showed that there must be
conflict between queen and workers. To be able to
cause female-biased sex allocation the workers
must be fully or partly in control of colony sex
allocation. Trivers and Hare provided additional
data to back this up. Sex allocation was not
female biased in a few ant species that were
slave makers. In these species allospecific
slaves rear the brood. Because they are unrelated
to the brood, natural selection should allow the
slave maker queen to win the sex allocation
conflict with her offspring workers. Trivers, R.
L. Hare, H. 1976. Haplodiploidy and the evolution
of the social insects. 1976. Science 191
249-263.
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Slave Makers
This is part B of Figure 4 of Trivers Hare
1976. The two crosses are from two slave-making
species and the circles three non slave-making
species of Leptothorax ants.
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Alexander Sherman 1977
Provided an alternative explanation to inclusive
fitness for the female-biased sex allocation
documented by Trivers and Hare. Local Mate
Competition (LMC). If males compete locally for
matings, not panmictically, the optimum sex
allocation ratio of the investing party is female
bias. Ironically, W. D. Hamilton also was
responsible for the theory of LMC.
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Logic of LMC
Female-biased sex ratio
Even sex ratio
You can understand the logic behind LMC from the
above figure. In both cases, there is
brother-sister mating. On the right, the
investing party (mother or workers) rear two
males and two females. As a result, there are two
females who disperse with their genes. On the
left, the investing party rear one male and three
females. There are now three females who disperse
with their genes as the male can mate with many
females. Note that for LMC to work each brood
must contain at least one male. It is no good if
1/4 broods are male only and 3/4 female only.
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Nonacs 1986
Data are from 21 monogynous ( single queen per
nest) ant species (black bars) and 6 polygynous
(more than one queen per nest) ant
species. Sex-allocation ratios of individual
colonies have a bimodal distribution. That is,
most colonies specialize in male production or
queen production. The overall sex-allocation
ratio is less female biased in polygynous
species Neither support LMC predictions. Both
support inclusive fitness predictions. LMC would
predict that all colonies have similar investment
in males, and no difference between monogynous
and polygynous species.
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Facultative Sex Allocation
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Tests Within One Species

• Trivers and Hare provided an ingenious test but
  it required 21 species of ants.
• How can we make further tests to show that
  workers bias the sex ratio of their colony due to
  inclusive fitness benefits?
• Answer compare sex ratios among colonies in a
  single species, where the theory predicts that
  different colonies should have different sex
  ratios.
• Advantages of this method
• No need to worry about differences among species
• Can make many tests (on different species)
• Less work

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Facultative Sex Allocation
Colony kin structure females, bfwVF males,
bmwVM M single-mated queen 0.75 x 2 1.5 0.5 x
1 x 2.5 1.25 double-mated queen 0.5 x 2
1 0.5 x 1 x 2.5 1.25 relative mating
success of males to females is 2.5 if workers
completely control sex allocation, and 50
colonies are headed by a double-mated queen and
50 by a single-mated queen. mother-queen 0.75
x 2 1.5 0.5 x 1 x 1.8 0.9 sister-queen
0.375 x 2 0.75 0.75 x 1 x 1.8 1.35
relative mating success of males to females is
1.8 if workers completely control sex allocation,
and 50 colonies are headed by a mother queen and
50 by a sister queen.
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Facultative Sex Allocation
The previous slide shows that the queens can be
worth more than males to investing workers in
some colonies in the population, and less in
others. Colonies headed by a single queen mated
to 1 or 2 males Single-mated queen young queens
worth more than males Double-mated queen males
worth more than young queens (young queens are
worth less in colonies headed by a double-mated
queen because double mating reduces relatedness
of workers to young queens, but does not affect
relatedness of workers to brothers. This is
because the males have no father) Colonies
headed by a mother queen or a sister queen Mother
queen young queens worth more than males Sister
queen males worth more than young queens
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Mueller 1991
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Mueller 1991
Studied colonies of the Halictidae bee
Augochlorella striata (Halictidae Halictinae
Augochlorini) in New York State. Nests are
annual, founded in spring in a hole in the ground
by a mated female. The first females reared are
workers. These rear more females that overwinter
(queens ) and males later in the season. Colonies
may lose their mother queen, in which case one of
the daughters becomes the queen and mates. In
this case, the workers are her sisters
(parasocial colonies). Colonies headed by a
mother queen have more female-biased allocation,
as predicted by inclusive fitness theory.
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Sundstrom 1994
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Sundstrom 1994
This study was carried out in Finland on a
species of wood ant, Formica truncorum, that
nests under a fallen log. Nests have a single
queen who can be mated to one or multiple,
typically two or three, males. As predicted,
colonies headed by a single-mated queen (grey
bars) have more female-biased allocation. The
effect is quite striking and is consistent in 4
different years of study on the same colonies.
There are a few mistakes. Some colonies do the
wrong thing. The fact that ant colonies can
specialize according to the number of mates of
the mother queen implies that the workers can
figure this out. How do they do it? Probably by
assessing some measure of phenotypic diversity in
their colony that is correlated to genetic
diversity. On average, multiple-mated queens will
have more diverse workers.
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Sundstrom et al. 1996
Sex-allocation ratios in individual colonies of
Formica exsecta in two years. Colonies could have
a single-mated queen (white) or a multiple-mated
queen (black). As in F.truncorum, colonies headed
by a single-mated queen have proportionately more
investment in young queens.
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Sundstrom et al. 1996
Changes in sex ratio from egg to pupal stage in
colonies with a single-mated queen (white) or a
multiple-mated queen (black). In single-mated
colonies there is a significant change to more
females. In multiple-mated colonies there is a
non-significant change to more males.
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Sundstrom et al. 1996
This study was carried out in Finland on another
species of wood ant, Formica exsecta. As in
Formica truncorum, nests have a single queen who
can be mated to one or multiple males and
colonies headed by a single-mated queen (black
bars) have more female biased allocation. This
study also measured the sex ratio of eggs and
pupae. It appears that in colonies headed by a
multiple-mated queen the workers do not alter the
sex ratio from that of the eggs laid by the
queen, or alter only a small amount. But in the
colonies headed by a single-mated queen they bias
towards more females. In many ants this is quite
easy to do as there are extra female larvae
available, most of which will be reared into
workers.
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Queen Power Tactics
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Passera et al 2001
Sex ratio of male pupae and adults reared in fire
ant colonies, Solenopsis invicta, with their
original queen (black) or a new queen (white).
Left queens were swapped between male-specialist
and female-specialist colonies. Right queens
were swapped male specialist to male specialist,
female specialist to female specialist. The data
show that it is the queen, not the workers, who
is driving colony sex ratio.
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Passera et al 2001
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Passera et al 2001
Sex ratio of eggs laid by queens in
male-specialist and female-specialist colonies of
fire ants. Male-specialist colonies have a queen
who lays mainly male eggs. The female eggs have
to be used to rear both young queens and workers.
If there are few female eggs the workers will be
constrained. There are not enough to rear all the
queens and workers they would most benefit from
rearing. So they are forced to rear more males.
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Passera et al 2001
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Passera et al 2001
The study was carried on on colonies of the fire
ant Solenopsis invicta, an introduced species in
the USA. Colonies have a single queen who is
always mated to a single male. However, even
though there is no difference in the kin
structure of colonies, some colonies are male
specialist and some are female specialist. Male-sp
ecialist colonies have queens that lay a lot of
male eggs, forcing the workers to rear more
males. By underproducing female eggs, the colony
probably does not do as well because there will
be fewer workers reared. But if there is a
female-biased sex-allocation ratio in the
population, queens can benefit by forcing workers
to rear males even if the total amount of
reproduction by her colony is reduced, because
males are worth more. In general, queens can
control the sex of the eggs laid and workers can
control which larvae are reared.
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Advantage of Forcing More Male Rearing
We can use inclusive fitness theory to understand
why a queen may benefit by forcing the rearing of
more males. Consider a species with colonies all
headed by a single queen mated to a single male,
and in which the workers have full control over
sex allocation. The sex-allocation ratio in the
population will be 3F1M. This means that one
unit of allocation to males will have three times
the mating success of allocation to females. To
the mother queen, regression relatedness x sex
specific reproductive value are equal for sons
and daughters (1 x 1 0.5 x 2). Thus, the overall
kin value of investment in males (queens sons)
is worth three times the kin value of investment
in young queens. Thus, the queen can increase her
inclusive fitness by causing the colony to invest
in males, even if the investment in males costs
three units of investment in young queens.
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Advantage of Forcing More Queen Rearing
We can also use inclusive fitness theory to
understand why the workers may benefit by forcing
the rearing of more males. Consider a species
with colonies all headed by a single queen mated
to a single male, and in which the queens have
full control over sex allocation. The
sex-allocation ratio in the population will be
1F1M. This means that one unit of allocation to
males will have the same mating success on one
unit of allocation to females. To workers,
regression relatedness x sex specific
reproductive value, is three times less for
brothers than sisters (0.5 x 1 0.75 x 2). Thus,
the overall kin value of investment in young full
sister queens is worth three times the kin value
of investment in brothers. Thus, the workers can
increase their inclusive fitness by causing the
colony to invest more in queens, even if the
investment in queens costs three units of
investment in males.
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The More You Are Losing the More You May Gain
Overall, the conflict over sex allocation is
likely to end up with an overall sex-allocation
ratio somewhere between the queen optimum and the
worker optimum, if both parties have some power
to affect colony sex allocation. This is because
the benefit of manipulating sex allocation
depends on who is winning the conflict. At the
worker-optimum ratio of 3F1M, the queen has a
great incentive to cause the colony to rear more
males and the workers have no incentive to
resist. At the queen-optimum ratio of 1F1M, the
workers have a great incentive to cause the
colony to rear more young queens and the queen
has no incentive to resist.
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Worker incentive
Queen incentive
The More You Are Losing the More You May Gain