Biology Reference
In-Depth Information
This line of reasoning is, however, still too simple. To see why we have to introduce the
concept of the value of males and females, the proportion they will contribute to the
gene pool of future generations. Recall that when the sex ratio is 3:1 in favour of females,
the expected reproductive success of a male, or in other words his value as a machine for
making grandchildren, is three times that of a female. If you include this factor, the pay-
off for raising siblings and offspring must be calculated as (number raised
relatedness). Taking the example where the sex ratio of the population as a whole is 3:1
(this applies, therefore, to the average ratio of offspring and of siblings), we get the
following answers.
For helping to raise a sibling:
×
value
×
(3 / 4 × 1× 3 / 4) + (1 / 4 × 3 ×1 / 4) = 12 / 16
For raising an offspring:
(3/4×1×1/2)+(1/4×3×1/2)=12/16
(In each line the first bracket is for females, the second for males. So on the top line the
first bracket means 'three-quarters of siblings are females, with a value of one and a
relatedness of three-quarters'.) Therefore, with a population sex ratio set at three
reproductive females for every male, the critical value for helping to pay is
> (12 / 16) / (12 / 16) =
… but this is
exactly balanced
by a reduced
value of females
BC / 1 , the same as for a diploid species! In other words, when the
sex ratio in the population as a whole is female biased to reflect the helper optimum
haplodiploidy gives no advantage to helping: the extra relatedness to females is counter-
balanced by the higher value of males (Trivers & Hare, 1976; Craig, 1979).
So can haplodiploidy ever tip the balance in favour of helping, or is it totally irrelevant?
Trivers and Hare (1976) realized the above complications and suggested that a female
bias might still favour helping if it occured in a way that does not lower the value of
females quite as much. This could happen if the sex ratio within the nest is female biased
while the overall population sex ratio is not. For example, if the bias in the nest was 3:1
and the population sex ratio was 1:1, the value of males and females would be equal
and we would be back to the simple calculation of B / C based on relatedness which gave
B / C > 4/5. This could occur when worker control of the sex ratio spreads through
population or through other mechanisms that lead to 'split sex ratios', with a relative
excess of females produced in some nests and a relative excess of males produced in
others (Trivers & Hare, 1976; Seger, 1983; Grafen, 1986).
However, there are two potential problems with even these mechanisms. Firstly, the
increased value of helping in the female-biased colonies will be negated by a reduced
value of helping in the male-biased colonies (Gardner et al ., 2012). The point here is that
if a mutation leads to increased quality or amount of helping, this will be favoured when
in relatively female-biased broods, but we must also consider that it will be selected
against in relatively male-biased broods (Gardner et al ., 2012). Secondly, our above
calculations have assumed that any potential worker would also produce an equally
female-biased same-sex ratio if they bred independently. As the population sex ratio is
female biased, males are worth more than females, so independently breeding females
would be selected to produce only sons. The increased reproductive value of males means
that sons would be of more value than a female-biased mixture of siblings (J. Alpedrinha
et al ., unpublished). In the extreme, if the sex ratio is biased 3:1 in favour of females,
then the pay-off from raising sons is
Split sex ratios
favour helping at
nests which
produce relatively
female biased sex
ratios...
... but disfavours
helping at nests
which produce
relatively male
biased sex ratios
(
)
1×3×1/ 2 =3/2 , and so the critical value for
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