Hamilton's Model

Hamilton's rule is rb - c > 0. Here c is the cost to the giver's fitness (c fewer offspring because of helping), and b is the benefit to the recipient's fitness (offspring gained by the recipient from the help). Here again, "r" is a measure of the relatedness between giver and the receiver

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Hamilton’s rule says that for unrelated individuals (r = 0) no benefit can overcome the cost of loss of the altruist's fitness (0 - c can't be greater than 0) and aid giving is selected against. If the giver and receiver are identical twins (r = 1) then as long as the receiver gains more offspring than the giver loses (b > c) giving will be favored.

Now consider two full sibs (r = 1/2). Here b/2-c must be greater than 0 in order for selection to favor helping. The gain to a brother or sister must be more than twice the cost in fitness to the giver. The inclusive fitness advantage soon disappears as relatedness decreases. So the point is, helping close relatives may be favored by selection when the costs and benefits balance.

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Sterile workers in the Hymenoptera (ants, bees and wasps) puzzled Darwin. How could selection favor these workers who were sacrificing their own reproduction to help their mother produce new queens and drones? Darwin viewed the workers as a sort of extended individual (workers = external cells of the queen's body). Hamilton's inclusive fitness theory offered a great solution to the problem. He pointed out a neat feature of the biology of Hymenoptera that enhanced the inclusive fitness effect (made Hamilton’s rule more likely to work). Males are haploid; they come from unfertilized eggs - and thus they have no fathers. That leads to sisters being 3/4 related (as long as they have the same father). Given that high degree of relatedness it is easy to see why extreme helping by daughters might be more likely in these kinds of insects. Here workers are sacrificing their reproduction to help their sisters reproduce.

Should workers help their brothers? Sisters and brothers have no father in common so r =.25. Therefore we would not expect them to gain much from taking care of brothers - they don't! Instead they try to produce sons of their own (r = 0.5). This they can sometimes do since males are haploid and workers do not need to have mated to produce sons. That brings workers into conflict with the queen over who produces the males -- something we will discuss. Hamilton’s theory really got a lot of attention as a result of how well it seemed to fit social insects. The real story is more complex. For example, what happens if queens mate with several males? We now know that they often do. As a way of thinking about aid giving behavior, Hamilton's theory has been very important. It may not , however, explain the social behavior of termites. Why? Look for alternative explanations in Alcock.

Explains why members of a species will sacrifice themselves for offspring that are not their own.