Hamilton’s Rule

Hamilton’s rule, also known as Hamilton’s principle, explains how altruistic behaviours evolve by considering the balance between the benefits to relatives and the costs to the individual. Hamilton’s Rule example is seen in altruistic behaviour in animals, where individuals sacrifice themselves to benefit relatives. This concept helps us understand why organisms, like ants and humans, engage in actions that help others even at their own expense.

It’s a key idea in evolutionary biology, shedding light on the emergence of cooperation and selflessness in populations over time. In this article, we will cover the Hamilton rule, formula, kin selection and more.

What is Hamilton’s Rule?

Hamilton’s Rules state that organisms adapt to encourage genetic success, not individualized reproductive success. In simple terms, the survival of one’s genes is determined not only by the number of offspring a parent has but also by the reproductive success of near relatives. Hamilton’s Rules helps to understand the presence of family systems in nature.

Genes should increase in frequency when:

r B > C

• 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 imbalance is known as Hamilton’s rule, after W. D. Hamilton, who published the first systematic quantitative study of kin selection in 1964.

How to Calculate Hamilton’s Rule

To understand the calculation of Hamilton’s Rule few terms are important like:

• Relatedness (r): Relatedness measures how much genetic material two individuals have in common. In simpler words, it’s like looking at how much DNA they share. For instance, siblings usually have about half of their DNA in common, so their relatedness would be expressed as r=0.5.
• Benefit (B): Benefit is the advantage gained by the one who receives selfless actions. Put simply, it’s what the recipient gets out of the behavior. This could mean better chances of survival, more success in reproduction, or any other positive outcome.
• Cost (C): Cost refers to the drawback or sacrifice experienced by the individual who acts selflessly. It could mean giving up resources, spending time, or missing out on opportunities.

Once we get the values of r, B, and C one can easily put the values in the formula r B > C to calculate Hamilton’s Rule.

Hamilton’s Rule Example Problems

Example 1:

In a colony of ants, a worker ant foregoes reproducing to help raise the offspring of the queen. The worker ant is more closely related to its sisters (with whom it shares 75% of its genes) than to its own offspring (with whom it shares 50% of its genes). If the benefit to the colony of raising one additional offspring is 10 units of reproductive success, and the cost to the worker ant of not reproducing itself is 5 units, does Hamilton’s rule predict that the worker ant will engage in this behavior?

r=0.75 (relatedness to sisters)

B=10 (benefit to the colony)

C=5 (cost to the worker ant)

Pthese values into Hamilton’s rule:

0.75×10>5=7.5

The result is 7.5, which is greater than 5, so the worker ant is expected to engage in this behavior.

Example 2:

In a family, a sibling sacrifices their time and resources to care for their younger siblings. If the benefit of this care to the younger siblings’ survival and well-being is 20 units of reproductive success, and the cost to the caring sibling in terms of lost opportunities for their own reproduction is 15 units, does Hamilton’s rule predict that the caring sibling will engage in this behavior?

Suppose siblings share 50% of their genes.

r=0.5 (relatedness to siblings)

B=20 (benefit to the siblings)

C=15 (cost to the caring sibling)

Putting these values into Hamilton’s rule:

0.5×20>15=10

The result is 10, which is greater than 15, so the caring sibling is expected to engage in this behavior.

Kin Selection

Kin selection, proposed by biologist W.D. Hamilton in the 1960s, explains how altruistic behaviors evolve based on genetic relatedness. The idea is that individuals are more likely to help close relatives because they share some of their genes. By aiding relatives in survival and reproduction, individuals indirectly promote the spread of their own genes to future generations, even if they don’t directly reproduce themselves.

Examples of Kin Selection

• Social insects like bees and ants, where worker bees sacrifice their own reproduction to care for their queen and siblings. This makes sense evolutionarily because workers are genetically closer to their siblings than to unrelated individuals, increasing the chances of their shared genes being passed down through the queen’s reproduction.
• In many bird and mammal species, adults provide parental care to their offspring, even at the expense of their own survival and reproduction. This parental investment enhances the survival and reproductive success of genetically similar offspring, thereby boosting the overall fitness of the family group.

Conclusion – Hamilton’s Rule

Hamilton’s rule provides a useful way to study how altruistic behaviors evolve in living things. By considering how much genetic material individuals share, along with the benefits and costs of being altruistic, we can understand why creatures collaborate and help each other out in nature. This concept is not just for humans—it applies across the animal kingdom, from bugs to mammals. Understanding these ideas helps scientists unlock the secrets of social relationships and plays a role in keeping Earth’s biodiversity thriving.

FAQs on Hamilton’s Rule

What does Hamilton’s Rule Explain?

Hamilton’s Rule explains the conditions under which altruistic behavior evolves in a population based on genetic relatedness, benefit to the recipient, and cost to the altruistic individual.

What is Hamilton’s Equation in Ecology?

Hamilton’s equation in ecology is rB – C > 0 here r is the genetic relatedness, B is the benefit, and C is the cost

What is an Example of the Hamilton Rule?

An example of Hamilton’s Rule is the alarm calls in ground squirrels, where individuals warn others of predators, even at personal risk.

How Does Hamilton’s Rule Apply to Human Behavior?

Hamilton’s Rule can be used to understand various forms of altruistic behavior observed in human societies, such as caregiving, cooperation, and sharing. It underscores the importance of kinship and reciprocal relationships in shaping human social interactions apnd cooperation.

What does Hamilton’s Rule Help us to Predict?

Hamilton’s rule is a central theorem of inclusive fitness (kin selection) theory and predicts that social behaviour evolves under specific combinations of relatedness, benefit and cost.

What is Hamilton’s Rule of Genetic Relatedness?

Hamilton’s rule asserts that a trait is favored by natural selection if the benefit to others, , multiplied by relatedness, exceeds the cost to self.

What is the Importance of Hamilton’s Principle?

The implication of Hamilton’s principle is that the time integral of the total energy that the moving body experiences is a minimum, and the experienced time should be proper time.