tags: - colorclass/evolutionary game theory ---see also: - Typology of Cooperation - Altruism - Evolutionary Game Theory - Evolutionary Psychology - Cooperation - Morality As Cooperation
Hamilton’s Rule is a foundational principle in evolutionary biology that formalizes the conditions under which altruistic behavior can evolve through kin selection. Proposed by William D. Hamilton in 1964, the rule explains how natural selection can favor altruistic acts that benefit relatives, thereby promoting the reproductive success of shared genes.
Formalization of Hamilton’s Rule
Hamilton’s Rule is expressed mathematically as:
where: - ( r ) is the genetic relatedness between the altruist and the recipient. This is the probability that a gene in the recipient is identical by descent to a gene in the altruist. - ( B ) is the benefit to the recipient of the altruistic act, measured in terms of the increase in the recipient’s reproductive success. - ( C ) is the cost to the altruist, measured in terms of the decrease in the altruist’s reproductive success.
The rule states that an altruistic behavior will be favored by natural selection if the genetic relatedness between the altruist and the recipient, multiplied by the benefit to the recipient, is greater than the cost to the altruist.
Understanding Genetic Relatedness (( r ))
Genetic relatedness (( r )) quantifies the probability that two individuals share the same gene inherited from a common ancestor. Some common values for ( r ) are: - Parent-offspring: ( r = 0.5 ) - Full siblings: ( r = 0.5 ) - Half siblings: ( r = 0.25 ) - Grandparent-grandchild: ( r = 0.25 ) - First cousins: ( r = 0.125 )
Implications of Hamilton’s Rule
1. Kin Selection: Hamilton’s Rule provides a mechanism for the evolution of altruism among relatives. By helping relatives, individuals can ensure the propagation of their own genes indirectly.
2. Inclusive Fitness: Hamilton introduced the concept of inclusive fitness, which includes both direct fitness (an individual’s own reproductive success) and indirect fitness (the reproductive success of relatives due to the individual’s actions).
3. Eusociality: Hamilton’s Rule helps explain the evolution of eusocial behavior in certain species, such as bees, ants, and termites, where individuals may forego reproduction to help relatives reproduce.
4. Human Altruism: In humans, behaviors such as parental care, sibling support, and extended family networks can be understood through Hamilton’s Rule. People are more likely to exhibit altruistic behavior towards close relatives.
Examples and Applications
1. Parental Care: Parents invest significant resources in their offspring because the genetic relatedness (( r = 0.5 )) is high, and the benefits (( B )) of ensuring offspring survival and reproduction outweigh the costs (( C )).
2. Alarm Calls in Animals: Some animals give alarm calls to warn relatives of predators, despite the risk to themselves. For example, a ground squirrel may call to alert its kin, increasing their survival chances (( B )), with the caller’s action being favored if ( rB > C ).
3. Helping Behavior in Birds: Certain bird species exhibit cooperative breeding, where individuals help raise their siblings or half-siblings. The helpers gain indirect fitness benefits by increasing the reproductive success of closely related individuals.
Mathematical Example
Consider a scenario where an individual can help its sibling by providing food, increasing the sibling’s chances of survival and reproduction by 10 offspring (( B = 10 )). The cost to the individual is that it will have 2 fewer offspring (( C = 2 )) as a result of the altruistic act. The genetic relatedness between full siblings is ( r = 0.5 ).
Using Hamilton’s Rule:
Since ( 5 > 2 ), the altruistic behavior is favored by natural selection.
Conclusion
Hamilton’s Rule is a critical concept in evolutionary biology that explains the evolution of altruism through kin selection. By formalizing the conditions under which altruistic behaviors can be advantageous, it provides insights into a wide range of social behaviors in both humans and other animals. This rule underscores the importance of genetic relatedness in the evolution of cooperation and has profound implications for understanding social behavior and moral norms.