Evolution, 4th Edition

CooPERATIoN AND CoNFlICT 301

The overall effect of an allele on its inclusive fitness is the sum of the allele’s indi-

rect and direct effects, which is: r B – C.

In short, Hamilton’s rule says that an allele will spread if the increase in indirect

fitness outweighs the loss of direct fitness caused by the altruistic behavior. In fact,

the rule applies to all behaviors, not just altruistic ones. It even works when B or C

is negative, as when the actor benefits directly (in which case C < 0).

To make these ideas concrete, consider an autosomal locus in a female of a dip-

loid species (BOX 12B). If she carries a rare allele for an altruistic behavior, there is

a probability of 1/2 that it came from her mother and an equal chance that it came

from her father, so a female’s relatedness to each of her parents is r = 1/2. What

about her relatedness to her siblings? No matter which parent the female inherited

the allele from, there is a chance of 1/2 that a brother or a sister also inherited the

The relatedness between the copies of a gene in two indi-

viduals, symbolized by r, depends on how those individu-

als are related and how the gene is inherited. Relatedness

is simplest to calculate when an allele for altruism is rare. In

that case, r is the probability that if an actor carries the al-

lele, then the recipient also carries it. For the autosomes of

a diploid species (Figure 12.B1), the alleles in a mother are

related to those in her offspring, with r = 0.5. The alleles in

a given daughter are also related to those in her brothers

and sisters, with r = 0.5. Patterns of relatedness are dif-

ferent in hymenopterans, which are haplodiploid (Figure

12.B2). Alleles in a mother (queen) are related to those in

her sons and daughters by r = 0.5. Males are haploid, have

no father, and inherit all of their genes from their mother.

If a worker (female) carries a rare allele, the only way her

brother can also carry it is if she inherited the allele from

their mother (probability = 1/2) and if the mother passed

the allele to her son (probability = 1/2). The alleles in the

brother are therefore related to those in the worker by

r = 1/2 × 1/2 = 0.25. However, there are two ways that a

new queen (the worker’s sister) might also carry the work-

er’s allele. The worker might have inherited the allele from

their mother (with probability = 1/2), and if so the mother

might have passed it to the sister (with probability = 1/2).

Alternatively, the worker might have inherited the allele

from their father (with probability 1/2). If so, then her sister

is certain to carry it also, because males are haploid and

always transmit all of their genes to all of their offspring.

The alleles in the new queen are therefore related to those

in the worker by r = (1/2 × 1/2) + 1/2 = 0.75.

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

Troutt Visual Services

Evolution4e_Box12B_FigA.ai Date 11-29-2016

Mother Father

Daughter Son

0.5

Daughter

0.5 0.5

0.5

FIGURE 12.B1 Relatedness in diploid species. FIGURE 12.B2 Relatedness in haplodiploid species.

Futuyma Kirkpatrick Evolution, 4e

Sinauer Associates

Troutt Visual Services

Evolution4e_Box12B_FigB.ai Date 11-29-2016

0.25 0.75

Queen Male

Male Worker New queen

0.5 0.5

BOX 12B

Calculating Relatedness

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