Transcript Hamilton`s Rule

Hamilton’s Rule – Kin Selection
KIN SELECTION & ALTRUISM
Kin Selection: selection of a trait through helping
relatives, either
1.
descendant kin (offspring):
direct selection
- or -
2.
non-descendant relatives:
indirect selection
inclusive fitness = direct + indirect
nepotism = helping relatives other than offspring
(descendant kin)
Fitness Accounting
A female Belding ground squirrel is dying. During her life she
has successfully raised a total of 10 of her own offspring. She
has helped her parents rear 8 offspring, 2 of which would not
have survived without her help. Her altruistic acts (e.g., alarm
calls) have resulted in her having the equivalent of 3 more
offspring. In terms of numbers of offspring, what is her
 Direct fitness? 10
 Indirect fitness? 2 + 3 = 5
 Inclusive fitness? 10 + 5 = 15
Three factors are important in the spread and
maintenance of an altruism gene by kin selection:
1. benefit to recipient, B
2. cost to altruist, C
3. degree of relatedness between altruist and recipient, r
Coefficient of Relatedness “r” =
1. probability that a rare gene is shared by two
individuals,
OR
2. the proportion of genes shared by two individuals
Taken From: Hamilton's Theory, by: B Brembs, 2001 Academic Press
Hamilton’s Rule states the conditions under
which altruism will spread. In its simplest
form it is:
rB > C
“The Story of The Surfing Brothers”
Two brothers (close in age, not fathers yet, reproductively fertile)
decide to go surfing. As they are surfing, one brother (the
beneficiary) is dragged under the current and is in danger of
drowning. The other brother (the altruist) decides to attempt to
save his brother, thus risking his own life. This decision, on its
face, seems very natural and devoid of conscious thought.
However, we need to find out if there are ultimate (evolutionary,
even “selfish”) causes for the altruist’s decision.
Let’s quantify this decision using Hamilton’s Rule!
rB > C
r = .5 (sibling = .5 co-efficient of relatedness
B = 2 (amt. of projected offspring for beneficiary)
C = 2 x .05 (amt. of proj.offspring for altruist x RISK)
(the risk of the altruist dying while trying to save the brother is .05)
Thus: rB = .5 x 2 = 1
C = 2 x .05 = .1
or
rB > C = 1 > .1
Thus, Hamilton’s Rule would dictate that this
action would be profitable in a genetic or
evolutionary sense!
Other Cases
• Uncle saving Nephew: .25 x 2 = .5 > .1
– Profitable!
• 1st Cousin saving 1st Cousin:
.125 x 2 = .25 > .1
– Profitable!
Kin Selection Weakens with Hereditary Distance!
Other Considerations – Haplodiploidy
Relationships
•
Haplodiploidy. The Hymenoptera (bees, ants and wasps) provide the perfect window
into sociobiology as explained by Hamilton's rule. They are haplodiploid; males are
produced from unfertilized eggs, having only half the normal genetic number as the
females. The result of this is that sisters, who usually have the same father and all of his
genes, are related by 3/4. To their mother and to their offspring they are related by only
1/2. Therefore, Hamilton's rule essentially predicts that sisters should be prone to
sacrificing for each other. In a family situation (a hymenopteran colony for example)
this amounts to sisters cooperating in raising more of their own generation and in risking
their lives to defend the colony, which is made up mostly of sisters.
•
Problems with the genetic explanation. In most eusocial colonies, the primary
reproductive ("queens") mates more than once, reducing the degree of relatedness
between her daughters. Therefore, the effects of haplodiploidy in kin selection are
reduced. Also, the termites, the only completely eusocial order, are not haplodiploid at
all.
A Final Word
This situation is purely fictitious and not
meant to suggest that a human being would
actually calculate the benefit of saving
another human being. This example deals
with deeply engrained ultimate causes of
behavior, meant to preserve a species,
which have been passed on genetically over
time (evolution) . Hamilton’s Rule
quantifies a rationale for passing on a gene
for altruistic behavior.