In lower animals, genetic variation on the surface of cells determines whether a sperm is allowed to fertilise a particular egg. If the two cells are too similar, then fertilisation fails. Perhaps this is why the complicated system of genetic identification on the cell surface evolved in the first place. The repeated failure of pregnancy in genetically similar husbands and wives may be a remnant of a method of ending fertilisations which arise from the attentions of too close a relative. Spontaneous abortion, perhaps in the first few weeks of pregnancy, kills them off.

Mice have the mechanism in more dramatic form. Females can tell from scent how close a relative a male might be. Given the chance, they avoid mating with their brothers. What is more, if a mouse pregnant by a relative is offered an unrelated male (or even the scent of his urine) she aborts and mates with the new partner. The genes responsible for mouse scent are linked to those that control cell-surface variation.

Among the Hutterites, too, married couples are less similar to one another for certain genes in the immune system than are pairs who are just friends. The genes involved are related to those which drive sexual choices in mice. Perhaps, quite unconsciously, most Hutterites — and most people — fall for someone with a set of identity cues different from their own. What is more, they arc keenest to avoid a partner whose genes are too much like their mother's: the Hutterite mother is to he avoided as a role model in the choice of a wife. Just how the mechanism works, no one knows, but scent may be involved somewhere.

Accidental genetic change is close to how God might play dice. Statistics is needed to study it. Population genetics is infested with mathematics, much of which is incomprehensible even to population geneticists. It is, nevertheless, unavoidable. The importance of random change depends on the size of the population. It is not enough just to know the number of people around today. What is important is its average size since it began; after all, a large town may once have had just a few ancestral inhabitants. What is more, a special kind of average is needed. This pays particular attention to episodes of reduced numbers. Like so many ideas in evolution, the idea of the "harmonic mean' comes from economics. Think of a village in ancient times, with one rich squire and many hungry peasants. Perhaps the fifty poor peasants each had an average income of a hundred pounds a year, while the squire gloried in a million. The average income was nineteen thousand pounds, which is a rather pointless statistic for anyone interested in rural reality. The harmonic mean income, in contrast, was a hundred and two pounds, which is a better reflection of what society was actually like.

The same logic applies to populations which change in number. Thus, the average size of a population whose size in succeeding generations is 1000, 1000, 10, iooo, and iooo is 802 but its harmonic mean size is only 48. Any population bottleneck — ten individuals, in this case — has a dramatic effect that can persist for many generations.

To measure the real size of a population involves other subtleties. Variation in the number of children produced by each person means that its effective size may be less chan first appears. Many tribal populations (and perhaps most ancient societies) show big differences in reproductive success, most of all among males. A few (ias.mov.is monopolise the females, while lots of reluctant celibates do not get their fair share. Freud, in Totem and Tabim (di/light-fully subtitled Some Points of Agreement between the Mental Lives of Savages and Neurotics) built his theory of psychoanalysis on this: a supposed time of a primal horde led by a dominant father with sexual rights to all the women. His sons killed and ate him, inheriting the Oedipus complex which has been such a nuisance ever since.

Many societies do have a rather Freudian structure. In one Yanomamo village, four of the old men had 41, 42, 46 and 62 grandchildren respectively, while twenty-eight had only one grandchild and many more had none. Women, on the other hand, each had about the same number of descendants. A simple count of the men would much overestimate the real population size. From evolution's point of view, many of them might just as well not be there.

All populations have a history. The iron rules of chance mean that any episode of reduced size — a population bottleneck — will have a prolonged effect. From earliest antiquity humans have been colonisers, first as they filled the world from their African home and later as economic pressure drove people to conquer new lands. The emigrants were a small group, a tiny sample of the people left behind. The new colony may grow into millions, but all its inhabitants carry only the genes of the founders. As there were so few pioneers, the new population may be, by accident, quite different from those who stayed at home.

This 'founder effect', as it is known, is important throughout evolution. Darwin's first port of call on the Heaglt' voyage w.is the island of Madeira. He commented on how ditlcmu its snails were from their European ancestors. This difference became even more conspicuous when he began to look at the birds and tortoises of the Galapagos. Perhaps, Darwin thought, the accidents of history, with chance colonisations of each island, helped to explain why archipelagos were natural laboratories for evolution.

The quirks of colonisation have been just as important in our own past. Ironically enough, the best example of evolutionary accident comes from not an escape but a return: the Afrikaners' journey back to their ancestral continent after an absence of more than a hundred thousand years. They began their migration from Europe in the 1650s. The pioneers brought with them a lasting legacy. It included more than Calvinism and bigotry. The surnames and the genes of their descendants are still a bequest from the first migrants. The three million Afrikaners in South Africa all derive from a small group of settlers, some of whom were so enthusiastic in their fecundity as to leave tens of thousands of descendants today. A million Afrikaners share just twenty names (Botha being one). This fits what history tells us about the number of immigrant families. Even today, half the surnames arrived before 1691 and the other half before 1717.

The migrants also brought, quite unawares, some rare genes drawn by chance from the people of Holland. One of the partners in the marriage of Gerrit Jansz and his wife Ariaantje Jacobs (who was one of a group of girls sent from a Rotterdam orphanage in the 1660s) must have carried a copy of the gene for a form of porphyria. This disease (which is related to that which may have afflicted George III) is due to a failure in the synthesis of the red pigment of the blood. Sometimes, light-sensitive chemicals are laid down in the skin. ****  they react with sunlight and produce painful sores. In certain forms of porphyria hair grows on exposed areas. Sometimes the waste material accumulates in the brain and leads to mental disorder. Part is excreted in the urine, to give a characteristic port-wine, almost blood-red, colour. Werewolves — creatures that come out at night, howl and drink blood — may have begun with the porphyria gene.

The South African form is mild but became important when barbiturate drugs were used in the 1950s. Carriers of the gene suffered pain and delirium when they took them. Porphyria is rare in Europe, but thirty thousand Afrikaners bear it. Johannesburg has more carriers lhan does the whole of Holland. All descend from one member of the small population of founders that grew in numbers to produce today's Afrikaners. Because it is so common in one family, porphyria in South Africa is sometimes called 'van Roojen disease'. A gene and a surname tell the same story.