The Extended Phenotype: The Long Reach of the Gene (Popular Science) (39 page)

It is my belief that thinking in terms of individuals striving to maximize something has led to outright error, in a way that thinking in terms of genes striving to maximize something would not. By outright error, I mean conclusions that their perpetrators would admit are wrong after further reflection. I have documented these errors in the section labelled ‘Confusion’ of Dawkins (1978a), and in Dawkins (1979a, especially Misunderstandings 5, 6, 7 and 11). These papers give detailed examples, from the published literature, of errors which, I believe, result from ‘individual-level’ thinking. There is no need to harp on them again here, and I will just give one example of the kind of thing I mean, without mentioning names, under the title of the ‘Ace of Spades Fallacy’.

The coefficient of relationship between two relatives, say grandfather and grandson, can be taken to be equivalent to two distinct quantities. It is often expressed as the mean
fraction
of a grandfather’s genome that is expected to be identical by descent with that of the grandson. It is also the
probability
that a named gene of the grandfather will be identical by descent with a gene in the grandson. Since the two are numerically the same, it might seem not to matter which we think in terms of. Even though the probability measure is logically more appropriate, it might seem that either measure could be used for thinking about how much ‘altruism’ a grandfather ‘ought’ to dispense to his grandson. It does matter, however, when we start thinking about the variance as well as the mean.

Several people have pointed out that the fraction of genome overlap between parent and child is exactly equal to the coefficient of relationship, whereas for all other relatives the coefficient of relationship gives only the mean figure; the actual fraction shared might be more and it might be less.
It has been said, therefore, that the coefficient of relationship is ‘exact’ for the parent/child relationship, but ‘probabilistic’ for all others. But this uniqueness of the parent/child relationship applies only if we think in terms of
fractions
of genomes shared. If, instead, we think in terms of
probabilities
of sharing particular genes, the parent/child relationship is just as ‘probabilistic’ as any other.

This still might be thought not to matter, and indeed it does not matter until we are tempted to draw false conclusions. One false conclusion that has been drawn in the literature is that a parent, faced with a choice between feeding its own child and feeding a full sibling exactly the same age as its own child (and with exactly the same mean coefficient of relationship), should favour its own child purely on the grounds that its genetic relatedness is a ‘sure thing’ rather than a ‘gamble’. But it is only the
fraction
of genome shared that is a sure thing. The
probability
that a particular gene, in this case a gene for altruism, is identical by descent with one in the offspring is just as chancy as in the case of the full sibling.

It is next tempting to think that an animal might try to use cues to estimate whether a particular relative happens to share many genes with itself or not. The reasoning is conveniently expressed in the currently fashionable style of subjective metaphor: ‘All my brothers share, on average, half my genome, but some of my brothers share more than half and others less than half. If I could work out which ones share more than half, I could show favouritism towards them, and thereby benefit my genes. Brother A resembles me in hair colour, eye colour and several other features, whereas brother B hardly resembles me at all. Therefore A probably shares more genes with me. Therefore I shall feed A in preference to B.’

That soliloquy was supposed to be spoken by an individual animal. The fallacy is quickly seen when we compose a similar soliloquy, this time to be spoken by one of Hamilton’s ‘intelligent’
genes
, a gene ‘for’ feeding brothers: ‘Brother A has clearly inherited my gene colleagues from the hair-colour department and from the eye-colour department, but what do I care about them? The great question is, has A or B inherited a copy of
me?
Hair colour and eye colour tell me nothing about that unless I happen to be linked to those other genes.’ Linkage is, then, important here, but it is just as important for the ‘deterministic’ parent/offspring relationship as for any ‘probabilistic’ relationship.

The fallacy is called the Ace of Spades Fallacy because of the following analogy. Suppose it is important to me to know whether your hand of thirteen cards contains the ace of spades. If I am given no information, I know that the odds are thirteen in fifty-two, or one in four, that you have the ace. This is my first guess as to the probability. If somebody whispers to me that you have a very strong hand in spades, I would be justified in revising upwards my initial estimate of the probability that you have the ace. If I am
told that you have the king, queen, jack, 10, 8, 6, 5, 4, 3 and 2, I would be correct in concluding that you have a very strong hand in spades. But, so long as the deal was honest, I would be a mug if I therefore placed a bet on your having the ace! (Actually the analogy is a bit unfair here, because the odds of your having the ace are now three in forty-two, substantially lower than the prior odds of one in four.) In the biological case we may assume that, linkage aside, knowledge of a brother’s eye colour tells us nothing, one way or the other, about whether he shares a particular gene for brotherly altruism.

There is no reason to suppose that the theorists who have perpetrated the biological versions of the Ace of Spades Fallacy are bad gamblers. It wasn’t their probability theory they got wrong, but their biological assumptions. In particular, they assumed that an individual organism, as a coherent entity, works on behalf of copies of all the genes inside it. It was as if an animal ‘cared’ about the survival of copies of its eye-colour genes, hair-colour genes, etc. It is better to assume that only genes ‘for caring’ care, and they only care about copies of themselves.

I must stress that I am not suggesting that errors of this kind follow inevitably from the inclusive fitness approach. What I do suggest is that they are traps for the unwary thinker about individual-level maximization, while they present no danger to the thinker about gene-level maximization, however unwary. Even Hamilton has made an error, afterwards pointed out by himself, which I attribute to individual-level thinking.

The problem arises in Hamilton’s calculation of coefficients of relationship,
r
, in hymenopteran families. As is now well known, he made brilliant use of the odd
r
values resulting from the haplodiploid sex-determining system of Hymenoptera, notably the curious fact that
r
between sisters is ¾. But consider the relationship between a female and her father. One half of the female’s genome is identical by descent with that of her father: the ‘overlap’ of her genome with his is ½, and Hamilton correctly gave ½ as the coefficient of relationship between a female and her father. The trouble comes when we look at the same relationship the other way round. What is the coefficient of relationship between a male and his daughter? One naturally expects it to be reflexive, ½ again, but there is a difficulty. Since a male is haploid, he has half as many genes as his daughter in total. How, then, can we calculate the ‘overlap’, the fraction of genes shared? Do we say that the male’s genome overlaps with half his daughter’s genome, and therefore that
r
is ½? Or do we say that every single one of the male’s genes will be found in his daughter, and therefore
r
is 1?

Hamilton originally gave ½ as the figure, then in 1971 changed his mind and gave 1. In 1964 he had tried to solve the difficulty of how to calculate an overlap between a haploid and a diploid genotype by arbitrarily treating the male as a kind of honorary diploid. ‘The relationships concerning males are
worked out by assuming each male to carry a “cipher” gene to make up his diploid pair, one “cipher” never being considered identical by descent with another’ (Hamilton 1964b). At the time, he recognized that this procedure was ‘arbitrary in the sense that some other value for the fundamental mother–son and father–daughter link would have given an equally coherent system’. He later pronounced this method of calculation positively erroneous and, in an appendix added to a reprinting of his classic paper, gave the correct rules for calculating
r
in haplodiploid systems (Hamilton 1971b). His revised method of calculation gives
r
between a male and his daughter as 1 (not ½), and
r
between a male and his brother as ½ (not ¼). Crozier (1970) independently corrected the error.

The problem would never have arisen, and no arbitrary ‘honorary diploid’ method would have been called for, had we all along thought in terms of selfish genes maximizing their survival rather than in terms of selfish individuals maximizing their inclusive fitness. Consider an ‘intelligent gene’ sitting in the body of a male hymenopteran, ‘contemplating’ an act of altruism towards a daughter. It knows for certain that the daughter’s body contains a copy of itself. It does not ‘care’ that her genome contains twice as many genes as its present, male, body. It ignores the other half of her genome, secure in the knowledge that when the daughter reproduces, making grandchildren for the present male, it, the intelligent gene itself, has a 50 per cent chance of getting into each grandchild. To the intelligent gene in a haploid male, a grandchild is as valuable as an ordinary offspring would be in a normal diploid system. By the same token, a daughter is twice as valuable as a daughter would be in a normal diploid system. From the intelligent gene’s point of view, the coefficient of relationship between father and daughter is indeed 1, not ½.

Now look at the relationship the other way round. The intelligent gene agrees with Hamilton’s original figure of ½ for the coefficient of relationship between a female hymenopteran and her father. A gene sits in a female and contemplates an act of altruism towards the father of that female. It knows that it has an equal chance of having come from the father or from the mother of the female in which it sits. From its point of view, then, the coefficient of relationship between its present body and either of the two parent bodies is ½.

The same kind of reasoning leads to an analogous non-reflexiveness in the brother–sister relationship. A gene in a female sees a sister as having ¾ of a chance of containing itself, and a brother as having ¼ of a chance of containing itself. A gene in a male, however, looks at the sister of that male and sees that she has ½ a chance of containing a copy of itself, not ¼ as Hamilton’s original cipher gene (‘honorary diploid’) method gave.

I believe it will be admitted that had Hamilton used his own ‘intelligent-gene’ thought experiment when calculating these coefficients of relationship,
instead of thinking in terms of
individuals
as agents maximizing something, he would have got the right answer the first time. If these errors had been simple miscalculations it would obviously be pedantic to discuss them, once their original author had pointed them out. But they were not miscalculations, they were based on a highly instructive conceptual error. The same is true of the numbered ‘Misunderstandings of Kin Selection’ that I quoted before.

I have tried to show in this chapter that the concept of fitness as a technical term is a confusing one. It is confusing because it can lead to admitted error, as in the case of Hamilton’s original calculation of haplodiploid coefficients of relationship, and as in the case of several of my ‘12 Misunderstandings of Kin Selection’. It is confusing because it can lead philosophers to think the whole theory of natural selection is a tautology. And it is confusing even to biologists because it has been used in at least five different senses, many of which have been mistaken for at least one of the others.

Emerson, as we have seen, confused fitness[3] with fitness[1]. I now give an example of a confusion of fitness[3] with fitness[2]. Wilson (1975) provides a useful glossary of terms needed by sociobiologists. Under ‘fitness’ he refers us to ‘genetic fitness’. We turn to ‘genetic fitness’ and find it defined as ‘The contribution to the next generation of one genotype in a population relative to the contributions of other genotypes.’ Evidently ‘fitness’ is being used in the sense of the population geneticist’s fitness[2]. But then, if we look up ‘inclusive fitness’ in the glossary we find: ‘The sum of an individual’s own fitness plus all its influence on fitness in its relatives other than direct descendants …’ Here, ‘the individual’s own fitness’ must be ‘classical’ fitness[3] (since it is applied to individuals), not the genotypic fitness (fitness[2]) which is the only ‘fitness’ defined in the glossary. The glossary is, then, incomplete, apparently because of a confusion between fitness of a genotype at a locus (fitness[2]) and reproductive success of an individual (fitness[3]).

As if my fivefold list were not confusing enough already, it may need extending. For reasons concerned with an interest in biological ‘progress’, Thoday (1953) seeks the ‘fitness’ of a long-term lineage, defined as the probability that the lineage will continue for a very long time such as 10
⁸
generations, and contributed to by such ‘biotic’ factors (Williams 1966) as ‘genetic flexibility’. Thoday’s fitness does not correspond to any of my list of five. Then again, the fitness[2] of population geneticists is admirably clear and useful, but many population geneticists are, for reasons best known to themselves, very interested in another quantity which is called the mean fitness of a population. Within the general concept of ‘individual fitness’, Brown (1975; Brown & Brown 1981) wishes to make a distinction between ‘direct fitness’ and ‘indirect fitness’. Direct fitness is the same as what I am
calling fitness[3]. Indirect fitness can be characterized as something like fitness[4] minus fitness[3], i.e. the component of inclusive fitness that results from the reproduction of collateral relatives as opposed to direct descendants (I presume grandchildren count in the direct component, though the decision is arbitrary). Brown himself is clear about the meaning of the terms, but I believe they have considerable power to confuse. For instance, they appear to lend weight to the view (not held by Brown, but held by a distressing number of other authors, e.g. Grant 1978, and several writers on ‘helpers at the nest’ in birds) that there is something unparsimonious about ‘kin selection’ (the ‘indirect component’) as compared with ‘individual selection’ (the ‘direct component’), a view which I have criticized sufficiently before (Dawkins 1976a, 1978a, 1979a).