r B > C. In this formula B is the benefit to the recipient of the altruistic act, C is the cost to the actor and r is the coefficient of relatedness between the actor and the beneficiary. In other words r measures the probability that any two individuals share the same gene because they inherited it from the same common ancestor. Calculating r within our species is relatively simple. For example we inherit half our genes from our mother and half our genes from our father. Therefore the r value between an individual and their mother is 0.5, and the r value between the individual and their father is also 0.5. Full siblings (i.e. those sharing the same mother and father) also have an r value of 0.5 between them. However half siblings only have an r value of 0.25. This suggests that we are just as close to our siblings than any of our offspring or parents. This would further suggest that in terms of evolution and Hamilton’s Rule, it makes no difference whether we help to bring up our offspring or help bring up our siblings. Either way the fitness gain will be the same. However, this can have profound implications for individual reproductive decisions. Although Hamilton’s Rule states that fitness gain for siblings and offspring are the same, individuals do generally tend to help their offspring more than their siblings.
In this formula benefit and cost are measured in the same way (i.e. the number of extra offspring gained or lost). The coefficient of relatedness is the probability that the two individuals concerned share the same gene by descent from a common ancestor or ancestors. It is crucial that the benefits to the recipient must be calculated in terms of extra offspring that result from the altruist’s actions.
According to this rule altruistic behaviour should only occur when the benefit accruing to the beneficiary, devalued by the probability that the two individuals share the same gene in question, is greater than the cost to the altruist. Therefore of those individuals who are unrelated (r=0), the left hand side of the formula is reduced to zero, and altruistic behaviour should not occur. Furthermore, Hamilton’s Rule also demonstrates that the higher the degree of relatedness, the smaller the benefit needs to be in order to for altruistic behaviour to be worthwhile. As a result, altruistic acts are expected to occur with greater frequency between close relatives than between more distant relative due to the reason that the conditions satisfying Hamilton’s Rule will occur with greater frequency between individuals with a high r value.
Examples that support Hamilton’s Rule include prairie dogs. Hoogland (1983) found that, far from calling indiscriminately, individual prairie dogs are more likely to alarm call when close relatives are nearby, and least likely to call when there are only unrelated individuals present to hear them. Prairie dogs are therefore prepared to take a risk if it will increase their inclusive fitness, but tend to keep very quiet if this isn’t the case. Similarly, female lions within a pride also tend to be closely related, and by suckling their sisters’ offspring as well as their own, they are helping to increase their inclusive fitness by promoting the survival of the genes that they share with their nephews and nieces. The same is also apparent among the Ye’Kwana women. These individuals devote most of their time to caring for a mother’s offspring and include her sisters, aunts, cousins and grandmothers (Hames, 1988).
Hamilton’s Rule does not imply that we should be altruistic towards relatives in any case. Every decision made is based on various alternatives. So, the decision to favour a relative, for example, involves the actor incurring a cost to, and he/she has to evaluate the benefit incurred by favouring that relative against the benefit that would have been gained by acting in his/her own interest in instead. The latter is known as the opportunity cost (or as in economics the regret) of opting for the action being considered (so in this case, favouring a relative).This contrast between alternative courses of action is built into the Hamilton’s Rule inequality, but in many cases it is overlooked in most attempts to evaluate the evolutionary significance of behaviour.
Although Hamilton’s Rule is highly influential, there are various implications concerned with it. For example limited dispersal was thought to favour altruism by keeping relatives together. Nevertheless, altruism towards a relative is less advantageous if their benefits come at a cost to your other relatives and limited dispersal may increase competition between relatives. Therefore an extension to Hamilton’s Rule was necessary. West (2002) introduced the following formula:
rxy b-c-rxed>0. In this formula rxy is the altruist’s relatedness to the beneficiary of its altruism (i.e. r in Hamilton’s Rule) and rxe is the altruist’s relatedness to individuals that suffer increased competition from the beneficiary. D is a general decrement in fitness associated with the altruistic act.
Further implications include the fact that much of data carried out on kin selection has been based on observations and consequently are controversial. Animals are more amenable to experimentation, and results of these experiments of these experiments illustrate the problem of oversimplification in some models of human behaviour. For example the Florida scrub jay provides an instance of direct and indirect benefits of helping. Breeding pairs may be helped by up to 6 others, with help mainly taking the form of anti-predator defence. Removing helpers reduces the chances of offspring surviving. However, helping may also aid helpers directly. In such cases the question is ‘why stay at home and help?’ Birds stay because the chances of survival are increased, the chance of successful dispersal to a new breeding site are low (the habitat is near saturation), and because (if male) they may inherit part of their father’s territory. Birds help because it increases the parent’s survival, increases the production of relatives and may increase territory size. Therefore as can be seen with this particular example what is observed is not necessarily what it reflects.
Most but not all helpers help close relatives. Even non relatives may sometimes benefit from helping. Birds may even repel potential helpers, accepting them only in poor conditions. Potential direct benefits of helping include current or future reproduction sharing, increased survival, improved parental skill, and territory inheritance. Helping may also be adaptive, but it has been questioned whether it is an adaptation. For example helping birds may result from a basic rule of ‘feed offspring in my territory’, and helpers help because they have no territory of their own. However help has been shown to be directed to related young, e.g. white-fronted bee eaters choose to help the most closely related brood in 94% of cases where they had the choice.
Hamilton’s Rule has been used as a good tool to measure an individuals or family’s inclusive fitness. However to what degree all primates follow such rule is questionable. Much of the research carried out has used observational data which in most cases is likely to be subjective and cannot be fully relied upon as it depends on the observer’s interpretation of the situation.
References:
Hames, R. (1988). ‘The allocation of parental care among the Ye’Kwana’, in: L.
Betzig, M Borgerhoff Mulder and P. Turke (eds) Human Reproductive Behaviour: a Darwinian Perspective, pp. 237-52. Cambridge: Cambridge University Press.
Hamilton, W. D. (1964). ‘The genetic evolution of social behaviour’. I, II. Journal of
Theoretical Biology 7: 1-52.
Hoogland, J. L. (1983). ‘Nepotism and alarm calling in the black tailed prairie dog,
Cynomys ludovicianus’. Animal Behaviour 31: 472-79.
West, M. (2002). Cooperation and competition between relatives. Competition
between relatives may negate the kin-selected benefits of altruism toward relatives, Science, 296, 72-75.