Hamilton’s Rule

Business / By / November 21, 2023

Hamilton’s Rule, a fundamental principle in biology, explains how altruistic behaviors evolve. It relies on concepts like inclusive fitness and genetic relatedness, expressed as “r * B > C.” This rule has far-reaching implications, from understanding social insect colonies to the evolution of altruism in various species, shedding light on the complexities of cooperative behaviors in nature.

Introduction to Hamilton’s Rule

Altruism in the context of evolutionary biology refers to behaviors in which an individual sacrifices its own fitness, often by incurring costs, to benefit others. This seemingly selfless behavior has long puzzled scientists, as it appears to contradict the principles of natural selection, which favor traits that enhance an individual’s own reproductive success.

Hamilton’s Rule, expressed as an equation, offers a way to reconcile altruistic behaviors with the theory of evolution. It states that altruistic behavior can evolve when the benefits to the recipient, corrected for their relatedness to the altruist, exceed the cost to the altruist. Mathematically, Hamilton’s Rule is often represented as:

rb−c>0

Where:

  • r represents the genetic relatedness between the altruist and the recipient.
  • b represents the benefit to the recipient.
  • c represents the cost to the altruist.

In simple terms, Hamilton’s Rule suggests that altruistic behavior is favored by natural selection when the genetic relatedness between the altruist and the recipient is sufficiently high, such that the benefits to the recipient outweigh the costs to the altruist.

Key Components of Hamilton’s Rule

To understand Hamilton’s Rule in more detail, let’s break down its key components:

  1. Genetic Relatedness (r): Genetic relatedness quantifies the degree of genetic similarity between the altruist and the recipient. It is often expressed as a fraction or proportion, with values ranging from 0 (completely unrelated) to 1 (genetically identical). In many cases, altruistic behaviors are more likely to evolve when individuals share a higher proportion of their genes with the recipient.
  2. Benefit to the Recipient (b): b represents the fitness benefit gained by the recipient as a result of the altruistic behavior. This benefit can manifest in various forms, such as increased reproductive success, enhanced survival, or improved access to resources. The magnitude of the benefit influences the potential for altruism to evolve.
  3. Cost to the Altruist (c): c represents the fitness cost incurred by the altruist when engaging in the altruistic behavior. This cost can take the form of reduced reproductive success, increased risk of predation, or expenditure of energy and resources. The greater the cost, the more challenging it is for altruism to evolve.

Real-World Examples of Hamilton’s Rule

Hamilton’s Rule can be applied to a wide range of examples in nature, helping to explain the evolution of altruistic behaviors among animals and even some human societies. Here are a few notable examples:

1. Kin Selection in Social Insects

Social insects like ants, bees, and termites are known for their highly organized colonies, where many individuals exhibit altruistic behaviors. These behaviors include worker ants foraging for food, nursing the young, and defending the nest, often at the cost of their own reproductive potential. Hamilton’s Rule is particularly relevant in these cases because colony members are highly related, sharing a large proportion of their genes. Thus, the benefit of supporting the reproductive success of close relatives can outweigh the cost to individual workers.

2. Alarm Calls in Ground Squirrels

Ground squirrels are vulnerable to predation by hawks and other aerial predators. In some species of ground squirrels, individuals will emit alarm calls when they spot a predator, alerting others to take cover. Emitting an alarm call carries a cost to the caller, as it increases their own risk of being targeted by the predator. However, the close genetic relatedness among members of a squirrel group increases the likelihood that the warning call benefits close relatives who share a significant portion of their genes. In this context, Hamilton’s Rule helps explain why some individuals engage in risky alarm calling to protect their kin.

3. Human Cooperation and Altruism

Hamilton’s Rule is not limited to non-human animals. It has been used to explain various forms of human cooperation and altruism, such as cooperation among extended family members and reciprocal altruism among unrelated individuals. In the case of human cooperation with close relatives, individuals often invest in their family members’ well-being, as these actions indirectly benefit their shared genetic heritage. Similarly, in situations involving reciprocal altruism, individuals may engage in altruistic behaviors with the expectation of receiving assistance in return, thus increasing the overall fitness of both parties.

Significance of Hamilton’s Rule

Hamilton’s Rule has several significant implications and contributions to the field of evolutionary biology:

  1. Explaining Altruism: It provides a theoretical framework for understanding the evolution of altruistic behaviors, which had long been considered problematic within the framework of natural selection.
  2. Kin Selection: Hamilton’s Rule is central to the concept of kin selection, where altruistic behaviors are more likely to evolve when directed toward close genetic relatives. This concept has been crucial in explaining social behaviors in various species.
  3. Social Evolution: The rule helps us understand the evolution of complex social structures in animals, including eusociality in insects and cooperative breeding in birds.
  4. Human Behavior: It offers insights into human behaviors like cooperation, reciprocity, and nepotism, shedding light on the evolutionary origins of social and ethical norms.
  5. Conservation: Hamilton’s Rule can inform conservation efforts by helping us understand the importance of preserving habitats and populations that support kin selection and altruistic behaviors.

Criticisms and Extensions

While Hamilton’s Rule has been highly influential, it is not without criticism and ongoing debate. Some of the criticisms and extensions of Hamilton’s Rule include:

  1. Simplification: The rule makes simplifications and assumptions that may not always hold true in complex ecological and genetic contexts.
  2. Inclusive Fitness Theory: Hamilton’s Rule is closely tied to the concept of inclusive fitness, which has been refined and expanded over time. Inclusive fitness theory considers a broader range of interactions and genetic relatedness structures.
  3. Group Selection: The debate over the relative importance of group selection versus individual selection in shaping social behaviors continues. Some argue that group-level selection can also play a role in the evolution of altruism.
  4. Behavioral Ecology: Advances in behavioral ecology have led to a deeper understanding of the ecological and social factors that influence the evolution of altruistic behaviors.

Conclusion

Hamilton’s Rule has been instrumental in advancing our understanding of altruistic behaviors in the context of evolution. By considering the relatedness between individuals, the benefits to recipients, and the costs to altruists, this rule provides a valuable framework for explaining why organisms, from social insects to humans, engage in behaviors that appear to prioritize the welfare of others. While it is not without controversy and debate, Hamilton’s Rule remains a foundational concept in the study of social evolution and the evolution of altruism, contributing to our understanding of the complex interplay between genes, behavior, and ecology in the natural world.

Case Studies

1. Social Insects:

  • Ant Colonies: Worker ants in a colony are often sterile and do not reproduce. Instead, they support and protect the reproductive queen because they are highly related to her, ensuring the passing on of their shared genes.
  • Honeybees: Worker bees devote their lives to collecting nectar and protecting the hive. This altruistic behavior is explained by the close genetic relatedness within the hive.

2. Cooperative Breeding Birds:

  • In some bird species, such as the Florida scrub-jay, non-breeding individuals help raise the offspring of close relatives. This assistance ensures the survival of shared genetic material.

3. Alarm Calls in Prairie Dogs:

  • Prairie dogs give alarm calls to warn their group of approaching predators. This behavior benefits the group but also puts the calling individual at risk. The genetic relatedness among prairie dogs makes this an example of kin selection.

4. Ground Squirrels:

  • Ground squirrels exhibit sentinel behavior, where some individuals keep watch for predators while others forage. This division of labor benefits the group as a whole, and the individuals involved are often closely related.

5. Lions and Cheetahs:

  • Female lions in a pride are often closely related, and they cooperate in raising their cubs. Lionesses may nurse each other’s cubs and protect them from threats. Similarly, cheetah siblings may form coalitions to increase hunting success.

6. Vampire Bats:

  • Vampire bats share blood meals with roost-mates who have not fed successfully. This reciprocal altruism is observed primarily among individuals that are genetically related.

7. Humans:

  • Human families often exhibit altruistic behaviors, such as parents providing for their children, even at personal cost. This can be explained by the genetic relatedness within families.

8. Red Squirrels:

  • In some populations of red squirrels, females may breed cooperatively, with related females helping to raise a single litter of offspring.

Key Highlights

  • Genetic Relatedness: Hamilton’s Rule is based on genetic relatedness, where individuals are more likely to help or be altruistic toward others who share their genes.
  • Hamilton’s Rule Formula: The formula “B*r > C” is central to Hamilton’s Rule, where “B” represents benefit, “C” represents cost, and “r” represents genetic relatedness.
  • Altruistic Behavior: The theory explains altruistic behaviors where individuals incur a cost to benefit others, favoring behaviors that increase inclusive fitness.
  • Evolution of Social Structures: It explains the evolution of social structures, including cooperative breeding and reciprocal altruism in various species.
  • Cooperative Breeding: Kin selection often applies to species with cooperative breeding systems, where non-breeding individuals assist in raising kin’s offspring.
  • Altruism and Inclusive Fitness: Inclusive fitness combines personal reproductive success with that of genetically related kin, making altruistic behaviors evolutionarily advantageous.
  • Examples in Nature: Numerous examples across species, from social insects to humans, illustrate kin selection and Hamilton’s Rule in action.
  • Limitations and Controversies: Kin selection faces debates and challenges, especially in quantifying relatedness and applying predictions in real-world scenarios.
  • Applications in Behavioral Ecology: These concepts are widely applied in behavioral ecology to understand the evolution of social behaviors in animals.
  • Insights into Human Behavior: Kin selection ideas extend to human behavior, explaining cooperation within families and communities and the evolution of emotions like empathy.

Connected Thinking Frameworks

Convergent vs. Divergent Thinking

convergent-vs-divergent-thinking
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.

Critical Thinking

critical-thinking
Critical thinking involves analyzing observations, facts, evidence, and arguments to form a judgment about what someone reads, hears, says, or writes.

Biases

biases
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.

Second-Order Thinking

second-order-thinking
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.

Lateral Thinking

lateral-thinking
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.

Bounded Rationality

bounded-rationality
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.

Dunning-Kruger Effect

dunning-kruger-effect
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.

Occam’s Razor

occams-razor
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.

Lindy Effect

lindy-effect
The Lindy Effect is a theory about the ageing of non-perishable things, like technology or ideas. Popularized by author Nicholas Nassim Taleb, the Lindy Effect states that non-perishable things like technology age – linearly – in reverse. Therefore, the older an idea or a technology, the same will be its life expectancy.

Antifragility

antifragility
Antifragility was first coined as a term by author, and options trader Nassim Nicholas Taleb. Antifragility is a characteristic of systems that thrive as a result of stressors, volatility, and randomness. Therefore, Antifragile is the opposite of fragile. Where a fragile thing breaks up to volatility; a robust thing resists volatility. An antifragile thing gets stronger from volatility (provided the level of stressors and randomness doesn’t pass a certain threshold).

Systems Thinking

systems-thinking
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.

Vertical Thinking

vertical-thinking
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.

Maslow’s Hammer

einstellung-effect
Maslow’s Hammer, otherwise known as the law of the instrument or the Einstellung effect, is a cognitive bias causing an over-reliance on a familiar tool. This can be expressed as the tendency to overuse a known tool (perhaps a hammer) to solve issues that might require a different tool. This problem is persistent in the business world where perhaps known tools or frameworks might be used in the wrong context (like business plans used as planning tools instead of only investors’ pitches).

Peter Principle

peter-principle
The Peter Principle was first described by Canadian sociologist Lawrence J. Peter in his 1969 book The Peter Principle. The Peter Principle states that people are continually promoted within an organization until they reach their level of incompetence.

Straw Man Fallacy

straw-man-fallacy
The straw man fallacy describes an argument that misrepresents an opponent’s stance to make rebuttal more convenient. The straw man fallacy is a type of informal logical fallacy, defined as a flaw in the structure of an argument that renders it invalid.

Streisand Effect

streisand-effect
The Streisand Effect is a paradoxical phenomenon where the act of suppressing information to reduce visibility causes it to become more visible. In 2003, Streisand attempted to suppress aerial photographs of her Californian home by suing photographer Kenneth Adelman for an invasion of privacy. Adelman, who Streisand assumed was paparazzi, was instead taking photographs to document and study coastal erosion. In her quest for more privacy, Streisand’s efforts had the opposite effect.

Heuristic

heuristic
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.

Recognition Heuristic

recognition-heuristic
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.

Representativeness Heuristic

representativeness-heuristic
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.

Take-The-Best Heuristic

take-the-best-heuristic
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.

Bundling Bias

bundling-bias
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.

Barnum Effect

barnum-effect
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.

First-Principles Thinking

first-principles-thinking
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.

Ladder Of Inference

ladder-of-inference
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.

Goodhart’s Law

goodharts-law
Goodhart’s Law is named after British monetary policy theorist and economist Charles Goodhart. Speaking at a conference in Sydney in 1975, Goodhart said that “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” Goodhart’s Law states that when a measure becomes a target, it ceases to be a good measure.

Six Thinking Hats Model

six-thinking-hats-model
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.

Mandela Effect

mandela-effect
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.

Crowding-Out Effect

crowding-out-effect
The crowding-out effect occurs when public sector spending reduces spending in the private sector.

Bandwagon Effect

bandwagon-effect
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.

Moore’s Law

moores-law
Moore’s law states that the number of transistors on a microchip doubles approximately every two years. This observation was made by Intel co-founder Gordon Moore in 1965 and it become a guiding principle for the semiconductor industry and has had far-reaching implications for technology as a whole.

Disruptive Innovation

disruptive-innovation
Disruptive innovation as a term was first described by Clayton M. Christensen, an American academic and business consultant whom The Economist called “the most influential management thinker of his time.” Disruptive innovation describes the process by which a product or service takes hold at the bottom of a market and eventually displaces established competitors, products, firms, or alliances.

Value Migration

value-migration
Value migration was first described by author Adrian Slywotzky in his 1996 book Value Migration – How to Think Several Moves Ahead of the Competition. Value migration is the transferal of value-creating forces from outdated business models to something better able to satisfy consumer demands.

Bye-Now Effect

bye-now-effect
The bye-now effect describes the tendency for consumers to think of the word “buy” when they read the word “bye”. In a study that tracked diners at a name-your-own-price restaurant, each diner was asked to read one of two phrases before ordering their meal. The first phrase, “so long”, resulted in diners paying an average of $32 per meal. But when diners recited the phrase “bye bye” before ordering, the average price per meal rose to $45.

Groupthink

groupthink
Groupthink occurs when well-intentioned individuals make non-optimal or irrational decisions based on a belief that dissent is impossible or on a motivation to conform. Groupthink occurs when members of a group reach a consensus without critical reasoning or evaluation of the alternatives and their consequences.

Stereotyping

stereotyping
A stereotype is a fixed and over-generalized belief about a particular group or class of people. These beliefs are based on the false assumption that certain characteristics are common to every individual residing in that group. Many stereotypes have a long and sometimes controversial history and are a direct consequence of various political, social, or economic events. Stereotyping is the process of making assumptions about a person or group of people based on various attributes, including gender, race, religion, or physical traits.

Murphy’s Law

murphys-law
Murphy’s Law states that if anything can go wrong, it will go wrong. Murphy’s Law was named after aerospace engineer Edward A. Murphy. During his time working at Edwards Air Force Base in 1949, Murphy cursed a technician who had improperly wired an electrical component and said, “If there is any way to do it wrong, he’ll find it.”

Law of Unintended Consequences

law-of-unintended-consequences
The law of unintended consequences was first mentioned by British philosopher John Locke when writing to parliament about the unintended effects of interest rate rises. However, it was popularized in 1936 by American sociologist Robert K. Merton who looked at unexpected, unanticipated, and unintended consequences and their impact on society.

Fundamental Attribution Error

fundamental-attribution-error
Fundamental attribution error is a bias people display when judging the behavior of others. The tendency is to over-emphasize personal characteristics and under-emphasize environmental and situational factors.

Outcome Bias

outcome-bias
Outcome bias describes a tendency to evaluate a decision based on its outcome and not on the process by which the decision was reached. In other words, the quality of a decision is only determined once the outcome is known. Outcome bias occurs when a decision is based on the outcome of previous events without regard for how those events developed.

Hindsight Bias

hindsight-bias
Hindsight bias is the tendency for people to perceive past events as more predictable than they actually were. The result of a presidential election, for example, seems more obvious when the winner is announced. The same can also be said for the avid sports fan who predicted the correct outcome of a match regardless of whether their team won or lost. Hindsight bias, therefore, is the tendency for an individual to convince themselves that they accurately predicted an event before it happened.

Read Next: Biases, Bounded Rationality, Mandela Effect, Dunning-Kruger Effect, Lindy Effect, Crowding Out Effect, Bandwagon Effect.

Main Guides:

More Resources

About The Author

Gennaro is the creator of FourWeekMBA, which reached about four million business people, comprising C-level executives, investors, analysts, product managers, and aspiring digital entrepreneurs in 2022 alone | He is also Director of Sales for a high-tech scaleup in the AI Industry | In 2012, Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
Scroll to Top
FourWeekMBA