The Theory of Sex Allocation 
by Eric Charnov.
Princeton, 355 pp., £29.80, December 1982, 0 691 08311 8
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Why, in the great majority of animals, are there equal numbers of males and females? For John Arbuthnot, writing in 1710, it was evidence of the beneficence of God: ‘for by this means it is provided, that the species may never fail, nor perish, since every male may have its female, and of a proportionable age.’ But while that might do for man, it will hardly do for those many species in which there is no monogamous pair bond and no parental care, and in which one male can fertilise many females, and yet which have an equal sex ratio.

Darwin, in the 1871 edition of The Descent of Man, came close to the solution, but ended by speaking of ‘the survival of those varieties which were subjected to the least waste ... by the production of superfluous individuals of either sex’. In other words, he saw the sex ratio as being an advantage for the variety or species, and not for the individual parent producing offspring of a given sex. By the second edition he had recognised his error, and wrote: ‘I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species, it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution to the future.’

In essence, the correct solution was proposed by R.A. Fisher in 1930, in his book The Genetical Theory of Natural Selection. Now Eric Charnov has devoted a whole book to the topic, and to the related questions of why some species consist of hermaphrodites instead of separate sexes, and of how hermaphrodites allocate their time and energy between the two sexual functions. His book is intended for professional biologists: it is too full of algebra and of technical terms to be readily accessible to others. The basic ideas, however, although mathematical, are so simple that they should be general knowledge.

The first point to grasp is the one Darwin was grappling with: the 1:1 sex ratio cannot be explained as conferring a benefit on the species as a whole. Even if sex itself is needed to confer genetic variability and evolutionary potential on the population (a proposition which is in any case much debated, but that is another, more perplexing story), one male in ten would be ample to ensure fertilisation. The higher the proportion of females, the faster the population can grow. Why waste material on males? Some animals, like the greenfly on roses and the water fleas in ponds, abandon males altogether during seasons of increase. The females produce daughters by virgin birth, and produce males only when times get hard.

What is needed is an explanation of the 1:1 ratio in terms of individual advantage to the parent producing the children. Fisher argued as follows. Imagine that mothers could choose the sex of their children: which sex should they choose? We must be clear about the criterion on which choice is to be made. Since, in evolutionary terms, the ‘choice’ made by a female will, ultimately, be determined by her genes, the choice she makes will be that which maximises the number of genes she passes to future generations. Suppose that there were more women than men (because mothers tend to produce daughters). Then a mother who produced only sons would have, on average, more grandchildren; this follows necessarily from the fact that every child has one father and one mother. Therefore, in a population with an excess of females, genes causing mothers to produce sons will spread; in the same way, if there is an excess of males, genes causing mothers to produce daughters will spread. The only stable state will be one with equal numbers of the two sexes. QED.

I have written as if the sex of the child was determined by the mother: an exactly similar conclusion emerges if sex is determined by the father. Fisher took matters a little further. Suppose that children of one sex cost more to produce: for example, in red deer male fawns take more milk than females, and a hind which has a son is more likely to miss breeding the next year. Fisher argued that, in such cases, parents should equalise the effort expended on the two sexes, producing fewer of the more expensive sex.

At this point I must mention a rather serious snag, which arises from the way the sex of a child is determined. In mammals, males produce two kinds of sperm in equal numbers, carrying ‘X’ and ‘Y’ chromosomes respectively. Females produce eggs carrying an X chromosome. If the egg is fertilised by a Y-bearing sperm it develops as a male, and if by an X sperm as a female. Thus the immediate cause of the 1:1 ratio is that X and Y sperm are produced in equal numbers, and are equally good at reaching the egg. So far, all efforts in domestic animals to separate the two kinds of sperm have failed. Now Fisher’s argument hinges on the idea that genes can influence the sex ratio. But if males produce exactly equal numbers of X and Y sperm, and if these sperm are in other respects indistinguishable, there is no way in which genes in a parent can influence the sex of their children.

I take this snag more seriously than most biologists. There is little evidence that parental genes can affect the sex ratio in species with an X-Y mechanism. I would therefore not expect to find species making a fine adjustment of the sex ratio to variations in the cost of the two sexes, although some apparent examples of such adjustment have been reported. However, I cannot accept this as a general explanation of the 1:1 sex ratio. If it were not for the fact that, in most species, most of the time, the selectively favoured ratio is 1:1, I am sure that natural selection would have found some other way of determining sex; as we shall see, other ways do exist.

Fortunately, there is one group of animals in which we can forget about the fear that the sex ratio is 1:1 only because there is no way of changing it. This group is the hymenoptera, which includes the bees, ants and wasps, and various parasites such as ichneumon flies. In these insects, the female stores sperm in a receptacle after mating, and decides the sex of each egg as she lays it by either fertilising it, in which case it becomes a female, or by not fertilising it, so that it becomes a male. We know that females can in fact select the sex of each child, because some parasites lay female eggs in large host caterpillars and male eggs in small ones: it pays them to do so because large size increases the reproductive success of females more than it does of males – at least in these insects.

The first major advance in sex ratio theory after Fisher was made by W.D. Hamilton, who realised that Fisher had made a tacit assumption about the breeding system. The nature of the assumption is best seen by considering an exception. Suppose that the offspring of a particular female always mate among themselves, brother with sister. Since one male can mate with many females, a mother will maximise the number of genes she transmits to grandchildren if she produces mainly daughters, and only enough sons to ensure that they are fertilised. Such inbreeding is unusual, but it does occur in parasitic wasps which lay many eggs in one host caterpillar; the young pupate on the caterpillar, and mate with each other when they emerge, without dispersing. As expected, Hamilton found that the sex ratio in such species is strongly biased towards females; there can be as many as ten females to one male.

Things get more complicated when more than one female lays eggs in the same caterpillar. This develops into a competitive game between the two females, in which the best sex ratio for each to choose depends on what the other does. Recently Jack Werren, a student of Charnov’s, has shown that a female wasp can detect whether a caterpillar has already been parasitised, and adjusts the sex ratio of its eggs accordingly. Further, it adjusts the sex ratio to a different degree, according to the number of eggs it lays, in just the way predicted by theory.

My own interest in these matters was stimulated because I was trying to apply game theory to the evolution of other traits, from fighting behaviour to plant growth. Some years ago, Eric Charnov visited me in Sussex, and we discussed how game theory could be applied in biology. We agreed that the problem of why some species are hermaphroditic, and in others the sexes are separate, was one which ought to be treated by game theory. I did not, however, pursue the matter for over a year. When I did return to the problem, I found that one can offer a very elegant and simple theory predicting which species should be hermaphroditic, and sent a brief account of it to Charnov. A few days later I was surprised to find in my post a letter from him, since there had not been time for him to receive my letter in Utah and to reply. It turned out to contain exactly the theory I had sent him. I am happy to say that we published it jointly, instead of engaging in a row about priorities.

Our explanation of hermaphroditism is mathematical, but it can be partly explained by the concept of a ‘law of diminishing returns’. A plant which produced twice as many seeds would probably not produce twice as many offspring, because the seedlings, falling close to the parent plant, would inevitably compete with one another. Similarly, a plant which produced twice as much pollen would not father twice as many offspring. Therefore, a plant which divided its efforts between producing seeds and pollen would pass its genes on to more offspring than would a specialist male or female. In fact, most plants are hermaphrodites, and many of those which have separate sexes have probably evolved that habit as a method of avoiding self-fertilisation. Animals are less often hermaphrodites – no mammals or birds are so. This may be because there is often a law of increasing returns for male investment. A red deer stag which was 10 per cent larger would probably increase his harem size by more than 10 per cent.

Among vertebrates, several kinds of fish are hermaphroditic, but they are usually ‘sequential hermaphrodites’: that is, they start out as one sex, and switch to the other. For example, there is a wrasse which lives in groups of five to ten females and one male. If the male is removed, the dominant female changes into a male. Although hermaphroditic fish are usually sequential, one group, the hamlets, are simultaneous hermaphrodites. Eric Fischer studied the behaviour of one species, the black hamlet. The fish do not fertilise their own eggs, although they can produce eggs and sperm on the same day. Some hours before dusk, they court in pairs. Alter some time, one member of the pair lays a few eggs, which the other fertilises. It is then the turn of the partner to lay eggs to be fertilised. In one evening, each fish will lay a number of batches of eggs, usually taking turns to lay.

What is the reason for this curious process of ‘egg-trading’? Fischer has analysed it as a game, in which each partner has something to gain and to lose. Why should not one partner lay all its eggs, wait for them to be fertilised, and then fertilise all the eggs laid by its partner? Surely this would save time and trouble? Fischer’s answer is that a fish which laid all its eggs would be too open to exploitation. Its partner could fertilise the eggs, and then leave and pair with another fish. In a game in which the aim is to pass as many genes as possible to future generations, a fish which laid all its eggs at once would risk failure, because it would risk having no eggs to fertilise. This illustrates a point which comes up repeatedly in the analysis of animal courtship: sperm ate cheap but eggs are expensive.

Charnov’s book considers three related questions. In a bisexual species, what ratio of sons and daughters is it best to produce? In a simultaneous hermaphrodite, how should an individual allocate effort between male and female functions (e.g. between seeds and pollen)? In a sequential hermaphrodite, at what age should an individual switch sex? One important message of his book is that these are all the same question. As his title suggests, they are all questions about the allocation of resources to the male and female roles.

There are still many unsolved problems. Lurking in the background is the biggest question of all: why do organisms reproduce sexually at all? Charnov assumes sex, and asks subsidiary questions. Let me finish with one puzzle which has cropped up recently. In most animals, sex is determined genetically – for example, by the presence of a Y chromosome, or by whether the egg is fertilised. In tortoises, turtles and some other reptiles, this is not so. The sex of a turtle is determined, when it is an egg, by the temperature at which it is incubated. Eggs incubated above about 30°C become females, and below that temperature males. This state of affairs is almost certainly not primitive: both fish and amphibia have genetic sex determination. At first sight, it does not seem a sensible arrangement. In some local populations there is an excess of males, and in others of females. We do not understand why this odd arrangement has evolved. Such questions will continue to be a critical testing ground for theories of evolution.

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