The occurrence of apparently altruistic behaviors – as exemplified by the sterile castes of insects – seemed to threaten Darwin’s entire theory of Natural Selection. Instead, Kin Selection, an extension of Natural Selection theory that explains such behaviors, has become the cornerstone of Behavioral Ecology and Sociobiology. Kin Selection has particular relevance to ground-dwelling squirrels and, as a consequence, they have been called the social hymenopterans of the mammalian world.
Lloyd Spencer Davis

Altruism

It is obvious to any naturalist that animals often appear to behave co-operatively (e.g. lions hunting prey). How, then, can we account for the evolution of co-operative behavior in terms of advantage to the individual? Moreover, how could “altruistic” behavior evolve that seemingly benefited another individual at the expense of the performer (e.g. birds and mammals that give alarm calls to warn their conspecifics or the sterile castes of insects like worker bees)?

Altruism is defined as acting in a way that increases another individual’s lifetime number of offspring at a cost to one’s own survival and reproduction.

Kin Selection

William Hamilton first published his theory of kin selection in 1963 and 1964. The best way to understand the importance of kinship is to take a gene's eye view of evolution and natural selection. For while natural selection acts on individuals (i.e. it is individuals that die or reproduce), it is the genes that are being preserved. The gene is the unit of selection, not individuals. If you look at Natural Selection from this perspective, it opens up the possibility that there could be selection for genes that ensure their own replication even at the expense of the individual.

Thus, through Hamilton's theory of kin selection, the concept of the selfish gene was born. What Hamilton did was to formalize the concept in a way that could be quantified and measured. And like many revolutionary concepts in science, its elegance lay in its simplicity.

Hamilton's formula predicted that selection will favour altruism (i.e. genes for altruistic behaviour will increase in frequency) when:

k > 1/r


where
Benefit to the recipient = k
Cost to the actor

and
r = Wright's coefficient of genetic relatedness

Calculation of r – the Coefficient of Relatedness

r , the Coefficient of Relatedness, is the probability that a gene in one individual is an identical copy, by descent, of a gene in another individual. To calculate r, draw a diagram of the individuals concerned and their common ancestors, indicating the generation links by arrows. At each generation there is meiosis, so that there is a 0.5 probability that a copy of a particular gene will get passed on. For L generation links the probability is (0.5). To calculate r, sum this value for all possible pathways between the two individuals.
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Inclusive Fitness

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A marmot: another ground-dwelling Sciurid where kin selection can be significant
Because r decreases geometrically the more distantly two individuals are related (and, therefore, the benefit of the behavior to the recipient must exceed the cost to the actor by an amount that increases geometrically), Hamilton’s rule implicitly predicts that:
where altruism occurs, it is likely to be between closely related individuals.

The point is that Hamilton showed that there are cases where altruism should occur through Kin Selection, and that an animal’s fitness consists not only of its direct fitness (the component of fitness gained through its own production of offspring), but also its indirect fitness (the component gained by aiding the survival and reproduction of kin). Together, both components make up what Hamilton termed, the animal’s inclusive fitness.

The Significance of Kin Selection

Kin selection, as demonstrated by Hamilton, is not an alternative to natural selection, but a logical and imperative extension of it. The important question is not whether kin selection occurs, but whether it is significant. To test its significance it is necessary to show:

  1. Opportunity - kin must overlap in time and space so as to have the opportunity to influence each other’s reproductive output or survival,
  2. Mechanism - there must be a mechanism to allow animals to behave differentially towards kin (i.e. a means of differentiating kin from non-kin),
  3. Asymmetries - animals must exhibit asymmetries in behavior based upon kinship, and
  4. Advantageous - differential behavior towards kin must be shown to positively influence the survival or reproductive success (fitness) of the recipients.