Encyclopedia of Evolutionary Psychological Science

Living Edition
| Editors: Todd K. Shackelford, Viviana A. Weekes-Shackelford

Hamilton’s Rule

  • Hans HämäläinenEmail author
  • Antti O. Tanskanen
  • Mirkka Danielsbacka
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-16999-6_1357-1



According to Hamilton’s rule, the cost of an investment must be less than the benefit weighted by the genetic relatedness of the investor and recipient. Based on the condition “all else being equal,” individuals are predicted to invest more in closely genetically related kin compared to more distantly related kin or non-kin.


William D. Hamilton (1964) formulated a rule that defined the conditions under which altruism can evolve and spread in sexually breeding populations. Altruism refers to a behavior that decreases the fitness of the actor while increasing the fitness of another individual (West et al. 2011).

The Rule

Hamilton argued that in addition to the parent–offspring relation, other relatives who share a common descent carry identical copies of the same alleles (Mock 2011). Therefore, individuals can spread their own genes (inclusive fitness) not only by reproducing themselves (direct fitness) but also by supporting their relatives’ reproduction (indirect fitness), even at the expense of their own direct reproductive success. Hamilton’s rule, a mathematical formula of the above-described inclusive fitness theory, specifies the conditions under which altruistic behavior spreads in a population. The simplistic version of the rule can be formulated as follows:
$$ \mathrm{Br}>\mathrm{C} $$

In the equation, B refers to the benefits of an investment, and C refers to the costs of the altruistic act. Benefits and costs are measured in terms of the investor’s inclusive fitness. The coefficient r refers to the genetic relatedness between individuals, indicating the probability that the investor and recipient have an identical allele at a random locus by common descent (Salmon and Shackelford 2011). In theory, the degree of relatedness may vary between 0 and 1. For instance, among humans the degree of relatedness is 1 with monozygotic twins; 0.5 with a biological child and sibling; 0.25 with a half-sibling, grandchild, niece, nephew, aunt, and uncle; 0.125 with a great-grandchild and first cousin; 0.0625 with a first cousin once removed; 0.0313 with a second cousin; etc. The coefficient r mediates the benefit–cost ratio, and the greater the r, the easier the benefits exceed the costs. Hence, all other things being equal, the level of altruistic acts between individuals should correspond to the degree of their genetic relatedness.


According to Hamilton’s rule, for the “altruistic gene” to be selected for and spread in a population, the fitness benefits weighted by the degree of relatedness must exceed the fitness costs of altruistic behavior. By contrast, if the altruistic gene decreases the inclusive fitness of individuals, it will be selected against by natural selection. Hamilton’s rule is a simple but elegant equation that defines the circumstances in which altruism can evolve. Hamilton’s rule also explains and predicts the variation in the level of altruistic behavior among kin.



  1. Hamilton, W. D. (1964). The genetical evolution of social behaviour I & II. Journal of Theoretical Biology, 7, 1–52.CrossRefGoogle Scholar
  2. Mock, D. W. (2011). The evolution of relationship in nonhuman families. In C. A. Salmon & T. K. Shackelford (Eds.), The Oxford handbook of evolutionary family psychology (pp. 211–229). Oxford: Oxford University Press.Google Scholar
  3. Salmon, C. A., & Shackelford, T. K. (2011). Toward an evolutionary psychology of the family. In C. A. Salmon & T. K. Shackelford (Eds.), The Oxford handbook of evolutionary family psychology (pp. 3–11). Oxford: Oxford University Press.Google Scholar
  4. West, S. A., El Mouden, C., & Gardner, A. (2011). Sixteen common misconceptions about the evolution of cooperation in humans. Evolution and Human Behavior, 32, 231–262.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hans Hämäläinen
    • 1
    Email author
  • Antti O. Tanskanen
    • 2
  • Mirkka Danielsbacka
    • 3
  1. 1.Pompeu Fabra UniversityBarcelonaSpain
  2. 2.University of TurkuTurkuFinland
  3. 3.Population Research Institute of FinlandHelsinkiFinland

Section editors and affiliations

  • Douglas Sellers
    • 1
  1. 1.Penn State Worthington ScrantonScrantonUSA