Biology Reference
In-Depth Information
Mother
Father
Sister
Brother
Son
Daughter
Niece or
nephew
(via sister)
Table 13.1
Degrees of
relatedness
between close
relatives in a
haplodiploid species
(assuming females
mate only once).
Female
0.5
0.5
0.75
0.25
0.5
0.5
0.375
Male
1
0
0.5
0.5
0
1
0.25
two sisters for every three offspring that she would have raised on her own. The magic
thing here is that the
B
/
C
ratio required is <1, so a sterile worker could potentially evolve
even if helping is less efficient than raising its own offspring! In contrast, with diploids,
the relatedness to full siblings and offspring are both given by
r
… and could
predispose this
group to evolve
eusociality
0.5, so
B
/
C
> 1 is
required. In other words it pays a diploid to help if it can replace one lost offspring with
just over one sibling.
But sadly, things aren't so simple. Robert Trivers and Hope Hare (1976) pointed
out that Hamilton's haplodiploidy hypothesis wouldn't necessarily hold, because
haplodiploidy also leads to a female being less related to a brother. Specifically, a
female is related to her brother by only 0.25, since the 50% of her genes that come
from her father have no chance of being shared with a brother, and the other half of
her genes have a 50% chance of being shared: 0.5
=
0.25 (Box 13.1). The key
point is that we need to compare the relative value of sons and daughters with that
of brothers and sisters, not just sisters versus daughters. Assuming that queens
produce equal numbers of male and female reproductives (drones and queens), as
expected from Fisher's theory of equal investment (Chapter 10) this would then
mean that the average relatedness of a worker to their brothers and sisters would be
only 0.5 (the mean of 0.75 and 0.25), exactly the same as they would have to their
own progeny if they had decided to leave home and have their own offspring. This
reduced relatedness to brothers exactly cancels the benefit of increased relatedness
to sisters, suggesting that haplodiploidy doesn't help (i.e.
B
/
C
> 1 would be required,
as with diploids).
Trivers and Hare suggested, though, that the haplodiploidy hypothesis could be saved
if the workers rear more queens (sisters) than drones (brothers). Workers are favoured
to rear more queens than drones, because they are more related to sisters than brothers
(Table 13.1). Specifically, as we shall describe in a later section, the evolutionarily stable
strategy (ESS) sex ratio of reproductives, from a workers perspective, is to produce three
queens for every one drone. With such a female bias, the average relatedness to the
offspring of the queen is (3/4
×
0.5
=
The increased
relatedness to
sisters is cancelled
by a decreased
relatedness
to brothers
If sex ratios are
female biased,
then workers will
be more related
to the offspring
of their mother,
than their own
offspring…
5/8. This represents the relatedness
to sisters multiplied by the proportion of brood that are sisters, plus the relatedness to
brothers multiplied by the proportion of brood that are brothers. Plugging this into
Hamilton's rule, the critical value of
B
/
C
is 1/2/5/8
×
3/4)
+
(1/4
×
1/4)
=
4/5. In other words, instead of
having to rear just over one sibling for every potential offspring lost, the worker has to
raise just over four siblings for every five offspring sacrificed. Consequently, if the sex
ratio is female biased it would appear that haplodiploidy makes it easier for helping to
evolve (i.e. the critical
B
/
C
< 1).
=
