Hamilton's Rule

A Hamilton's Rule is a behavioral rule in evolutionary biology that explains the conditions under which altruistic behavior can evolve through kin selection.

• AKA: Hamilton's Inequality, Kin Selection Rule, Altruism Evolution Rule.
• Context:
  • It can be mathematically expressed through the inequality rB > C, where:
    • r is the genetic relatedness between actor and recipient
    • B is the reproductive benefit to the recipient
    • C is the reproductive cost to the actor
  • It can predict Evolutionary Outcomes through mathematical models and empirical observations.
  • It can explain Social Evolution through genetic relatedness and reproductive success.
  • It can quantify Altruistic Behavior through cost-benefit analysis and relatedness coefficients.
  • It can guide Evolutionary Research through testable predictions and empirical verifications.
  • ...
  • It can often apply across different species and social systems.
  • It can often predict adoption behavior in natural populations.
  • It can often explain cooperative behavior in animal societies.
  • It can often influence social structure through genetic relationships.
  • ...
  • It can range from being a Simple Linear Model to being a Complex Network Model, depending on its mathematical implementation.
  • It can range from being a Species-Specific Rule to being a Universal Principle, depending on its taxonomic application.
  • It can range from being a Theoretical Framework to being an Empirical Tool, depending on its research context.
  • ...
• Examples:
  • Empirical Validations, such as:
    • Red Squirrel Studys showing selective adoption based on relatedness.
    • Social Insect Research demonstrating worker altruism.
    • Bird Behavior Studys revealing cooperative breeding.
  • Mathematical Applications, such as:
    • Relatedness Calculations using coefficient of relationship.
    • Cost-Benefit Analysis of social behavior.
    • Fitness Calculations across populations.
  • Evolutionary Phenomenons, such as:
    • Worker Sterility in social insects.
    • Cooperative Breeding in birds.
    • Parental Care in mammals.
  • ...
• Counter-Examples:
  • Tit-for-Tat Strategy, which relies on reciprocity rather than genetic relatedness.
  • Selfish Behavior, which maximizes individual fitness without regard for kin.
  • Group Selection, which operates at the group level rather than through genetic relationships.
  • Reciprocal Altruism, which depends on future interactions rather than shared genes.
• See: Kin Selection, Inclusive Fitness, Coefficient of Relationship, Genetic Relatedness, Evolutionary Game Theory, Altruistic Behavior.

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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.

    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. 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.

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