Hamilton's Rule
A Hamilton's Rule is a Behavioral Rule in biology evolutionary that explains the conditions under which altruistic behavior can evolve.
- Context:
- It can be mathematically described by the following inequality: [math]\displaystyle{ rB\gt C }[/math] which means that behavioural interaction could evolve, so long as the benefit ($B$) to the recipient, weighted by their degree of relatedness ($r$), is larger than the cost ($C$) to the actor.
- Example(s):
- a behavioral rule that can explain Inclusive Fitness,
- a behavioral rule that can exaplian Kin Selection.
- Counter-Example(s):
- See: Locus (Genetics), Kin Selection, Relatedness, Coefficient of Relationship, Identical by Descent, Spite.
References
2023
- (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Kin_selection#Hamilton Retrieved:2023-7-16.
- Formally, genes should increase in frequency when :
[math]\displaystyle{ rB \gt C }[/math]
where
$r$ = the genetic relatedness of the recipient to the actor, often defined as the probability that a gene picked randomly from each at the same locus is identical by descent.
$B$ = the additional reproductive benefit gained by the recipient of the altruistic act,
$C$ = the reproductive cost to the individual performing the act.
This inequality is known as Hamilton's rule after W. D. Hamilton who in 1964 published the first formal quantitative treatment of kin selection.[1][2]
The relatedness parameter (r) in Hamilton's rule was introduced in 1922 by Sewall Wright as a coefficient of relationship that gives the probability that at a random locus, the alleles there will be identical by descent.
A 2014 review of many lines of evidence for Hamilton's rule found that its predictions were confirmed in a wide variety of social behaviours across a broad phylogenetic range of birds, mammals and insects, in each case comparing social and non-social taxa.[3] Among the experimental findings, a 2010 study used a wild population of red squirrels in Yukon, Canada. Surrogate mothers adopted related orphaned squirrel pups but not unrelated orphans. The cost of adoption was calculated by measuring a decrease in the survival probability of the entire litter after increasing the litter by one pup, while benefit was measured as the increased chance of survival of the orphan. The degree of relatedness of the orphan and surrogate mother for adoption to occur depended on the number of pups the surrogate mother already had in her nest, as this affected the cost of adoption. Females always adopted orphans when rB was greater than C, but never adopted when rB was less than C, supporting Hamilton's rule.[4] [5]
- Formally, genes should increase in frequency when :
- ↑ Hamilton, W. D. (1964). "The Genetical Evolution of Social Behaviour". Journal of Theoretical Biology. 7 (1): 1–16. Bibcode:1964JThBi...7....1H. doi:10.1016/0022-5193(64)90038-4. PMID 5875341.
- ↑ Hamilton, W. D. (1964). “The Genetical Evolution of Social Behaviour. II". Journal of Theoretical Biology. 7 (1): 17–52. Bibcode:1964JThBi...7...17H. doi:10.1016/0022-5193(64)90039-6. PMID 5875340.
- ↑ Bourke, Andrew F. G. (2014). "Hamilton's rule and the causes of social evolution". Philosophical Transactions of the Royal Society B: Biological Sciences. The Royal Society. 369 (1642): 20130362. doi:10.1098/rstb.2013.0362. ISSN 0962-8436. PMC 3982664. PMID 24686934.
- ↑ Gorrell, Jamieson C.; McAdam, Andrew G.; Coltman, David W.; Humphries, Murray M.; Boutin, Stan (June 2010). "Adopting kin enhances inclusive fitness in asocial red squirrels". Nature Communications. 1 (22): 22. Bibcode:2010NatCo...1...22G. doi:10.1038/ncomms1022. hdl:10613/3207. PMID 20975694.
- ↑ Note: Further detail of Hamilton's rule is available at Simulating the Evolution of Sacrificing for Family: Discovering the specific definitions of r, B, and C, and at Hamilton’s Rule and Its Discontents: Why the general definitions of the variables always applies, but one specific definition can fail.