Editing Kin selection (section)

==Hamilton's rule==
{{Redirect|Hamilton's rule|the physical principle|Hamilton's principle}}
{{see also|Biological rules}}

Formally, genes should increase in frequency when

:<math>rB > 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 (genetics)|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.<ref name="Hamilton 1964 1–16"/><ref name="Hamilton 1964 17–52"/>

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 (genetics)|locus]], the [[allele]]s there will be [[identical by descent]].<ref>{{cite journal |last=Wright |first=Sewall |author-link=Sewall Wright |year=1922 |title=Coefficients of inbreeding and relationship |url=https://zenodo.org/record/1431365|journal=[[American Naturalist]] |volume=56 |issue=645|pages=330–338 |doi=10.1086/279872 |bibcode=1922ANat...56..330W |s2cid=83865141 }}</ref> Modern formulations of the rule use [[Alan Grafen]]'s definition of relatedness based on the theory of linear regression.<ref>{{Cite web |last=Grafen |first=Alan |date=1985 |title=A geometric view of relatedness |url=https://users.ox.ac.uk/~grafen/cv/oseb.pdf}}</ref>

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.<ref name="Bourke 2014">{{cite journal |last=Bourke |first=Andrew F. G. |title=Hamilton's rule and the causes of social evolution |journal=Philosophical Transactions of the Royal Society B: Biological Sciences |publisher=The Royal Society |volume=369 |issue=1642 |date=2014 |issn=0962-8436 |doi=10.1098/rstb.2013.0362 |page=20130362|pmid=24686934 |pmc=3982664 |doi-access=free }}</ref>  Among the experimental findings, a 2010 study used a wild population of [[Tamiasciurus hudsonicus|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.<ref name="Gorrell et al 2010">{{cite journal |last1=Gorrell |first1=Jamieson C. |last2=McAdam |first2=Andrew G. |last3=Coltman |first3=David W. |last4=Humphries |first4=Murray M. |last5=Boutin |first5=Stan |title=Adopting kin enhances inclusive fitness in asocial red squirrels |journal=Nature Communications |date=June 2010 |volume=1 |issue=22 |pages=22 |doi=10.1038/ncomms1022 |doi-access=free |pmid=20975694 |bibcode=2010NatCo...1...22G |hdl=10613/3207 |hdl-access=free }}</ref><ref group=note>Further detail of Hamilton's rule is available at [https://www.youtube.com/watch?v=iLX_r_WPrIw Simulating the Evolution of Sacrificing for Family]: Discovering the specific definitions of r, B, and C, and at  [https://www.journals.uchicago.edu/doi/10.1093/bjps/axt016 Hamilton’s Rule and Its Discontents]: Why the general definitions of the variables always applies, but one specific definition can fail.</ref>