I am writing a series of posts on the work of George Price. For the most recent one, with links to the others, see here I was planning next to cover Price’s treatment of group selection, but this raises side issues more conveniently dealt with separately. A previous post here considered what is meant by group selection. In the present post I look at definitions of altruism as used in biology. It has taken me a while to complete, partly because I found there is a lot of recent literature on the subject which I needed to digest. A valuable but difficult recent survey is here.
Of course in biology the term ‘altruism’ does not imply conscious intention on the part of the altruist. The altruist could be a plant, an insect, or a bacterium. Definitions of altruism such as ‘regard for others as a principle of action’ (Pocket Oxford Dictionary) are therefore not appropriate in biology. What is needed is a definition in terms of reproductive fitness.
The recent interest in biological altruism stems from W. D. Hamilton’s brief 1963 paper on ‘The evolution of altruistic behaviour’ and his two-part paper of 1964 on ‘The genetical evolution of social behaviour’. Both papers refer frequently to altruism, but Hamilton’s concept of altruism has to be inferred from what he says about it rather than from an explicit definition. Altruistic behaviour involves a ‘loss’, ‘cost’, ‘risk’ or ‘disadvantage’ to the personal fitness of the altruist, as measured by its production of offspring, while conferring a ‘gain’, ‘benefit’, or ‘advantage’ to one or more other individuals in the population. An altruist gains no direct benefit from its actions. It is implicit in Hamilton’s treatment that the altruist has lower personal fitness as a result of its altruistic behaviour than if it had not behaved altruistically. Later, in 1975, Hamilton more explicitly modelled the circumstances in which altruism could evolve, and again assumed that the benefits of altruistic behaviour go only to other members of the population. In this model altruism can only evolve if altruists receive sufficient benefits from each other to offset the costs.
Hamilton took the starting point for his discussion of altruism from J. B. S. Haldane, the only previous author to give it a mathematical treatment. In a section of Haldane’s book The Causes of Evolution (1932) devoted to ‘socially valuable but individually disadvantageous characters’, Haldane refers to ‘altruistic’ or ‘self-sacrificing’ conduct. In his mathematical model altruism is defined in relation to fitness within a group, not (as in Hamilton’s approach) in terms of its effects on the altruist’s own fitness. Haldane assumes that a population is divided into groups, some of which contain altruists and others do not. The possession of the altruistic trait decreases the fitness (measured by ‘probable progeny’) of the altruist to (1 – k) times that of the non-altruists in its own group. The benefit of altruism is measured by its effects on the fitness of all members of the group, including the altruists: the presence of a fraction x of altruists increases the ‘probable progeny’ of all members of the group to (1 + Kx) times that of a group with no altruists. In this model an ‘altruist’ obtains some of the benefits of its own altruism. Within a group, non-altruists are always fitter than altruists, but an altruist may still be fitter than non-altruists in the population generally. It is therefore possible in principle that an individual who ‘converts’ to altruism may have more offspring than otherwise.
The distinction between Hamilton-type and Haldane-type altruism is sometimes described as a difference between ‘strong’ and ‘weak’ altruism. ‘Weak’ altruism can be defined by one or both of the following characteristics:
1. a weak altruist is less fit than non-altruists within its own group, but not necessarily in the general population;
2. a weak altruist receives some net fitness benefit from its own altruistic acts, but not as much as other members of its group.
A scenario that fits description (1) will also usually fit description (2), and vice versa, but they tend to lead to different mathematical formulations that are not easily interconvertible. The natural way of formulating description (1) is to set the fitness of an altruist as some fixed proportion of that of non-altruists within its group, as in Haldane’s model. The natural way of formulating description (2) is to suppose that an altruist donates some fixed benefit B to all the N members of its group, including itself, while incurring a cost C, so that its net benefit from its own action is B/N – C. On this approach the fitness of an altruist cannot be expressed as a fixed proportion of the fitness of non-altruists, since this will depend on the number of altruists in the group. If there is more than one altruist, the altruists will derive some benefit from each other, and their fitness relative to non-altruists will vary with the composition of the group. As the proportion of altruists in a group rises, the larger the proportion of the total benefit they receive, so that the fitness of altruists approximates to that of non-altruists. [See Note 1 for a numerical example.]
The distinction between strong and weak altruism may seem a rather minor one, but it is important in some contexts. Notably, if altruism is ‘strong’, it cannot evolve by natural selection if the distribution of altruistic benefits in the population is random. If an altruist distributes a benefit B randomly to the other members of the population, while incurring a cost C, the benefit is shared in proportion to the existing frequency of altruists and non-altruists [but see Note 2], while the cost falls only on the altruists. Altruism will always be at a disadvantage. A division of the population into groups, followed by an equal or random distribution of benefits within them, makes no difference if the division itself is random in every generation, as this is just a roundabout way of distributing the benefit randomly.
If altruism is ‘weak’, on the other hand, division of the population into groups may well give altruism an advantage. An altruist is always in its own group to receive the benefit of its actions. Suppose that the population N is divided randomly into groups of size n, and that each altruist distributes a benefit B/n to each member of its group, including itself. The altruist incurs a cost C, so its net benefit from its own actions is B/n – C. The other members of the group each receive the larger benefit B/n. But in the population as a whole not all members will receive a benefit from that altruist, and if altruism is rare some non-altruists may not receive a benefit from any altruist. Even if altruism is common, each altruist still has a privileged access to the benefits of its own action [see Note 3].
It may be misleading to put so much emphasis on the fact that a weak altruist receives a benefit from its own actions. If we reformulate the model so that an altruist distributes the benefit to a group of individuals randomly selected from the entire population, including the altruist itself, then altruism is still ‘weak’ by the usual definitions. But under this model the distribution of benefits is truly random, and therefore neither increases or decreases the frequency of altruists in the population, while the costs fall only on the altruists. Altruism is therefore doomed. In contrast, under the usual models of weak altruism, the formation of groups is random, but the distribution of benefits is not, since an altruist has a guaranteed share of its own benefit. It is this non-randomness which can give ‘altruism’ an edge.
We would get the same result if each altruist gave part of its benefit to some other selected altruist, while the rest of the benefit was distributed randomly to the whole population except the donor itself. This model would fall under the usual definition of strong altruism, but would behave like weak altruism. The crucial point is not whether or not the altruist enjoys part of its own benefit, but whether there is preferential treatment of altruists. In the model just described, it is obvious that the overall distribution of benefits is not fully random: it is a mixture of random and selective distribution. In the usual models of weak altruism, the selective element is obscured by the fact that distribution within the group is random, and it is easy to overlook the altruist’s non-random access to its own benefit.
Whether one chooses to call ‘weak’ altruism a form of altruism at all is a matter of taste. Definitions are not right or wrong, but convenient or inconvenient. The choice need not however be entirely arbitrary. We do not make definitions just for fun: there is some underlying point to them. In the case of biological altruism, the main point of classifying some actions as altruistic is that they seem to require some special evolutionary explanation, beyond straightforward natural selection of individual reproductive fitness. If an action does not, on closer analysis, require any such special explanation, no purpose seems to be served by classifying it as altruistic, and there is a danger of confusion by lumping it together with actions which do require such explanations.
Note 1
Suppose baseline fitness (the fitness of a non-altruist in a group with no altruists) is 1, the group size N = 4, the benefit B = 10, and the cost C = 1. In a group with one altruist, the fitness of the altruist will be 1 + 10/4 – 1 = 2.5, while the fitness of the non-altruists will be 1 + 10/4 = 3.5, giving a ratio of 2.5/3.5 = .714. In a group with two altruists, the fitness of the altruists will be 1 + (2 x 10/4) – 1 = 5, while the fitness of the non-altruists will be 1 + (2 x 10/4) = 6, giving a ratio of 5/6 = .833. In a group with three altruists, the fitness of the altruists will be 1 + (3 x 10/4) – 1 = 7.5, while the fitness of the non-altruists will be 1 + (3 x 10/4) = 8.5, giving a ratio of 7.5/8.5 = .882.
Note 2
For mathematical convenience it is common to assume that the population is infinite, with a population frequency P of altruism. If groups of size n are formed at random, then the frequency of altruism among the fellow group members of any given altruist is still P, and if the benefits are distributed equally or randomly to the fellow members, the benefits will go to altruists and non-altruists in the proportions P:(1-P). In any real, finite, population this cannot strictly be true. If there are K altruists in a total population of N, then the frequency of altruism among the fellows of a given altruist will be (K -1)/(N – 1), which is slightly less than K/N (assuming N > K, and both N and K are reasonably large). Thus proportionately slightly more of the benefit will go to non-altruists than to altruists. For most purposes this slight discrepancy does not matter, but in special cases – for example, very small populations – it should not be overlooked.
Note 3
A numerical example may illustrate the point. I will avoid the simplification mentioned in Note 2.
Suppose there is a population of 100, divided into 50 altruists and 50 non-altruists. The population is randomly divided into groups of 10. Each altruist distributes a total benefit of 20 fitness units equally among the members of its group, including itself. Each therefore receives 2 units. The altruist incurs a cost of 1 unit and therefore receives a net benefit of 1 unit from its own actions.
Since the division of the population into groups is random, the 9 fellow group members of a given altruist will, on average, have the same proportion of altruists and non-altruists as in the population excluding the given altruist itself, namely 49/99 and 50/99. The expected value of the altruist’s benefits distributed within the group to non-altruists is therefore 50/99 x 9 x 2 = 9.0909… fitness units. The expected value of the altruist’s benefits distributed within the group to altruists other than itself is 49/99 x 9 x 2 = 8.90909…
As already noted, the net benefit to the altruist from its own actions is 1. The total net benefit to all altruists in the group, including the ‘focal’ altruist, is 1 + 8.90909… = 9.9090… , which is greater than the 9.0909… units going to non-altruists. Overall, the altruist therefore confers more fitness units on altruists (including itself) than on non-altruists. But the initial frequency of altruists in the population was 50:50, so altruists are getting more than their proportionate share of the benefits, and the frequency of altruism in the population will increase.