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Hamilton’s Rule – Kin Selection

Hamilton’s Rule – Kin Selection. KIN SELECTION & ALTRUISM Kin Selection: selection of a trait through helping relatives, either descendant kin (offspring): direct selection - or - non-descendant relatives: indirect selection

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Hamilton’s Rule – Kin Selection

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  1. Hamilton’s Rule – Kin Selection

  2. KIN SELECTION & ALTRUISM Kin Selection: selection of a trait through helping relatives, either • descendant kin (offspring): direct selection - or - • non-descendant relatives: indirect selection inclusive fitness = direct + indirect nepotism= helping relatives other than offspring (descendant kin)

  3. 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

  4. 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

  5. Taken From: Hamilton's Theory, by: B Brembs, 2001 Academic Press

  6. 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.

  7. 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 = 1C = 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!

  8. 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!

  9. 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.

  10. 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.

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