Concept

Kin selection

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Statement

Hamilton's rule explains altruism among relatives.

Why it matters

Classical fitness accounting, an individual's own survival and reproduction, struggles to explain altruism: a trait reducing the actor's own reproductive output should, on its face, be eliminated by natural selection. Kin selection resolves this apparent paradox by broadening the accounting from an individual's own reproduction to its inclusive fitness — the propagation of copies of its genes wherever those copies reside, including in relatives. This gives the field its clearest, most quantitative explanation of altruism, especially the extreme self-sacrifice seen in social insect colonies.

coevolution and neutral-theory both extend evolutionary reasoning beyond simple individual selection; kin selection does so specifically by redefining the unit whose reproductive success selection is tracking.

Hypotheses

A gene's evolutionary success is measured by the number of copies of itself propagated to the next generation, regardless of which individual body carries those copies.This is the conceptual shift, from individual reproduction to gene copies generally, that inclusive-fitness thinking requires. Relatedness \(r\) between two individuals, the same quantity underlying inbreeding-heterozygosity's inbreeding coefficient, can be calculated from pedigree relationships, and altruism is systematically more likely to evolve, and be observed, toward more closely related recipients.Without a way to quantify relatedness, the theory could not generate the specific, testable numerical threshold given in the Proof. Hamilton's rule as stated below is a simplified, additive approximation assuming cost and benefit combine linearly; more detailed treatments relax this and can give quantitatively different thresholds without overturning the basic direction of the logic.

Proof

\[ C = \text{reduction in the actor's own reproductive output}; \qquad B = \text{increase in the recipient's reproductive output} \]

These are the two quantities the altruistic act trades off against each other. A

\[ \text{The altruism-promoting gene is present, with probability } r, \text{ as an identical-by-descent copy in the recipient as well.} \]

This is the direct role relatedness plays: it discounts the benefit \(B\) by the probability the recipient actually carries the same gene. A

rB > C

The net change in the frequency of copies of the altruism-promoting gene across the population is favourable exactly when the relatedness-weighted benefit exceeds the direct cost to the actor — Hamilton's rule. A

r > C/B

Rearranging Step3: altruism is favoured whenever relatedness exceeds the cost-to-benefit ratio — closer relatedness, or a larger benefit relative to cost, both make the trait more readily favoured. A

\[ r=1 \ \Rightarrow\ B>C \text{ (ordinary individual selection recovered as a special case).} \]

Helping a genetically identical copy of oneself reduces Hamilton's rule to the ordinary requirement that benefit exceed cost, showing the rule generalises, rather than replaces, standard individual-selection reasoning. A

Result

rB > C

Reading. An altruistic gene spreads exactly when its relatedness-weighted benefit to gene copies elsewhere exceeds its direct cost to the actor's own reproduction.

Scope. Requires reasonably estimable, roughly additive cost and benefit terms and a computable relatedness; becomes only a rough qualitative guide once effects are strongly nonlinear or interact with other selective forces (Hypotheses, t3).

Corollaries & converses

Haplodiploid social insects (many ants, bees, and wasps) have sisters more closely related to one another (\(r=0.75\) under strict haplodiploidy with a singly-mated queen) than a mother is to her own daughters (\(r=0.5\)), a widely cited illustration of why sterile worker castes helping raise sisters can satisfy Hamilton's rule especially readily in these lineages, though haplodiploidy alone is neither necessary nor sufficient for eusociality.
Kin selection predicts, and field observations broadly confirm, that the intensity and frequency of altruistic or cooperative behaviour tends to scale with relatedness between the individuals involved, exactly as \(r\) appears directly in Step3's inequality.
Converse: observing an animal reliably directing costly help preferentially toward closer relatives over more distantly related or unrelated individuals, all else equal, is itself standard behavioural evidence consistent with kin selection operating.

Fails without

Drop the inclusive-fitness accounting of gene copies (Hypothesis 1), scoring fitness purely by the actor's own direct reproduction: any trait reducing the actor's own reproductive output would then always be selected against regardless of its effect on relatives, and no purely altruistic trait directed at kin could be explained as gene-level advantageous — precisely the paradox kin selection was formulated to resolve.
Drop relatedness as a factor (Hypothesis 2), treating \(r\) as effectively zero: Hamilton's rule collapses to requiring \(B>C\) for any recipient regardless of relationship, predicting altruism directed indiscriminately at relatives and non-relatives alike, contrary to the strong, well-documented bias of altruistic behaviour toward closer relatives actually observed.

Common errors

Treating kin selection as requiring conscious calculation of relatedness by the animal; the selective process operates on gene frequency over evolutionary time, not on real-time cognitive assessment.
Assuming Hamilton's rule predicts altruism only toward full siblings or offspring; it applies continuously across any degree of relatedness \(r\), with the required benefit-to-cost ratio simply rising as relatedness falls.
Confusing kin selection with group selection (favouring traits benefiting a whole group regardless of relatedness within it); kin selection specifically requires genetic relatedness between actor and recipient.
Assuming haplodiploidy alone explains eusociality; many eusocial insects lack haplodiploidy, and many haplodiploid species are not eusocial, so elevated relatedness is at most a contributing factor, not a sufficient explanation.

Discussion

W.D. Hamilton formalised inclusive fitness theory and the rule bearing his name in 1964, providing the first rigorous, quantitative resolution of a puzzle Darwin himself had acknowledged in On the Origin of Species (1859): how could sterile worker castes in social insects evolve at all, if selection acts only through an individual's own reproduction?

Inclusive fitness theory does not require haplodiploidy or even eusociality to apply; Hamilton's rule is a fully general statement about any costly helping behaviour between any two related individuals of any species, and has since been applied far beyond social insects, to cooperative breeding and alarm-calling behaviour across many vertebrate taxa as well.

Common misconception: that kin selection means organisms "know" their relatedness and calculate Hamilton's rule directly. In practice, relatedness-sensitive behaviour typically arises from much simpler evolved rules of thumb, such as preferentially helping individuals encountered within the natal nest or group, a reliable enough proxy for relatedness in most natural conditions.

Worked examples

\[ \text{A ground squirrel gives an alarm call at cost } C \text{ (raised own predation risk), benefiting nearby kin by } B \text{ (allowing them to flee).} \]

If the caller's average relatedness to nearby individuals is \(r\) and \(rB>C\), the alarm-calling gene is favoured even though it measurably raises the caller's own individual predation risk. A

\[ \text{The same calculation with nearby individuals entirely unrelated (}r\approx0\text{) requires } B>C \text{ alone for the behaviour to be favoured.} \]

This illustrates why alarm-calling is typically observed preferentially in kin-structured populations rather than toward strangers. A

\[ \text{alarm-calling favoured toward kin} (rB>C) \quad\text{but not toward strangers} (r\approx0,\ B<C\text{ typically}) \]

Reading. The identical cost/benefit trade-off is favoured or disfavoured purely as a function of relatedness to the recipient.

Scope. The same logic applies to any costly helping behaviour, not only alarm-calling.

Further example. A male meerkat spends time babysitting the pups of his full sister. This behaviour costs him \(C = 0.2\) units of his own reproductive success (due to energy expenditure and missed mating opportunities). In return, the pups survive and reproduce, providing a benefit of \(B = 0.5\) units of reproductive success to the sister. Calculate the minimum relatedness coefficient \(r\) required for this altruistic behaviour to be favoured by natural selection according to Hamilton's rule.

\[ \text{Hamilton's rule states that altruism is favoured when } rB > C. \]

This is the fundamental condition for kin selection, balancing the genetic benefit to recipients against the cost to the actor. A

\[ \text{Substitute the given values: } r(0.5) > 0.2. \]

We insert the specific cost and benefit values provided in the problem statement into the inequality. A

\[ r > \frac{0.2}{0.5} \]

Dividing both sides by the benefit \(B\) isolates the relatedness coefficient \(r\). A

\[ r > 0.4 \]

The arithmetic calculation \(0.2 \div 0.5\) yields the threshold relatedness value. A

\[ r > 0.4 \]

Reading. The male meerkat must be related to the recipient pups by more than 0.4 for the gene promoting babysitting to spread in the population. Since full siblings share \(r=0.5\), this condition is met, explaining why the behaviour is observed.

Scope. This calculation assumes additive genetic effects and that the cost and benefit are measured in equivalent units of reproductive fitness.

Problems

A worker bee (\(r=0.75\) to full sisters under standard haplodiploid assumptions) forgoes her own reproduction to help raise sisters. State the condition, using Hamilton's rule, under which this is favoured by selection.
Solution
Favoured whenever \(0.75\,B > C\), i.e. whenever the benefit to her sisters' reproduction, discounted by the 0.75 relatedness, exceeds the cost of her own forgone reproduction (Step3).
Explain why the same costly helping behaviour might be favoured toward a full sibling (\(r=0.5\)) but not toward a first cousin (\(r=0.125\)), holding cost and benefit fixed.
Solution
Hamilton's rule requires \(r>C/B\) (Step4); if \(C/B\) lies between 0.125 and 0.5, the behaviour satisfies the rule toward the more closely related sibling but fails it toward the more distantly related cousin, even though \(B\) and \(C\) themselves are unchanged.
Distinguish kin selection from group selection using a scenario in which an individual helps an unrelated member of its social group.
Solution
Kin selection predicts this behaviour is favoured only if \(rB>C\) with the relevant \(r\) for an unrelated individual being effectively zero, making it unfavoured unless \(B\) alone exceeds \(C\); group selection, by contrast, would attribute such helping to a benefit for the group as a whole regardless of relatedness, a mechanism kin selection does not invoke (Common errors).
A bird species exhibits cooperative breeding. A helper bird incurs a cost \(C = 1.0\) unit of fitness by staying to assist the nest. The benefit \(B\) to the nestlings is 4.0 units of fitness. Determine if this behaviour is favoured by selection when the helper is helping: (a) a full sibling (\(r = 0.5\)) (b) a half-sibling (\(r = 0.25\))
Solution
Hamilton's rule requires \(rB > C\). For (a): \(rB = 0.5 \times 4.0 = 2.0\). Since \(2.0 > 1.0\), the behaviour is favoured. For (b): \(rB = 0.25 \times 4.0 = 1.0\). Since \(1.0\) is not greater than \(1.0\) (it is equal), the condition \(rB > C\) is not strictly met; selection is neutral with respect to this trait under these specific parameters. Thus, it is favoured for full siblings but not for half-siblings.
In a haplodiploid insect colony, a worker female is related to her full sisters with coefficient \(r = 0.75\). She is considering whether to help raise her sisters or to reproduce herself. If the cost to her own reproduction is \(C = 3\) units, what is the minimum benefit \(B\) that must be conferred to her sisters for the helping behaviour to be favoured?
Solution
Using Hamilton's rule \(rB > C\): \(0.75 \times B > 3\) \(B > \frac{3}{0.75}\) \(B > 4\) Therefore, the benefit to the sisters must exceed 4 units of fitness for the altruistic behaviour to be favoured by natural selection.