Now, absurd as such an idea is in reality, it is theoretically conceivable that pigs are really closer to yeast than they are to horses. It is theoretically possible that pigs and horses have evolved their close resemblance to one another (their cytochrome c texts are only three letters apart, and their bodies are basically built to an almost identical mammalian pattern) by massive coincidence. The reason we don't believe this is that the ways in which pigs resemble horses vastly outnumber the ways in which pigs resemble yeast. Admittedly, there is a single DNA letter in which pigs appear closer to yeast than to horses, but this is swamped by millions of resemblances going the other way. The argument is one of parsimony. If we assume that pigs are close to horses, we need to accommodate only one coincidental resemblance. If we try to assume that pigs are close to yeast, we have to postulate a prodigiously unrealistic concatenation of independently acquired coincidental resemblances.

In the cases of horses, pigs and yeast, the parsimony argument is too overwhelming to be in doubt. But in the mitochondrial DNA of different human races there is nothing {50} overwhelming about the resemblances. Parsimony arguments still apply, but they are slight, quantitative arguments, not massive, knock-down arguments. Here's what the computer, in theory, has to do. It has to make a list of all possible family trees relating the 135 women. It then examines this set of possible trees and picks out the most parsimonious one – that is, the one that minimizes the number of coincidental resemblances. We must accept that even the best tree will probably force us to accept a few little coincidences, just as we were forced to accept the fact that, with regard to one DNA letter, yeasts are closer to pigs than to horses. But – in theory, at least – the computer should be able to take that in its stride and announce to us which of the many possible trees is the most parsimonious, the least coincidence-ridden.

That is in theory. In practice, there is a snag. The number of possible trees is greater than you, or I, or any mathematician, can possibly imagine. For horse, pig and yeast there are only three possible trees. The obviously correct one is [[pig horse] yeast], with pig and horse nested together inside the innermost brackets and yeast as the unrelated “outgroup.” The other two theoretical trees are [[pig yeast] horse] and [[horse yeast] pig]. If we add a fourth creature – say, squid – the number of trees goes up to fifteen. I won't list all fifteen, but the true (most parsimonious) one is [[[pig horse] squid] yeast]. Again, pig and horse, as close relatives, are cosily nested together in the innermost brackets. Squid is the next to join the club, having a more recent ancestor with the pig/horse lineage than yeast does. Any of the fourteen other trees – for instance, [[pig squid] [horse yeast]] – is definitely less parsimonious. It is highly improbable that pig and horse could have independently evolved their numerous resemblances if pig {51} were really a closer cousin to squid and horse were really a closer cousin to yeast.

If three creatures yield three possible trees, and four creatures yield fifteen possible trees, how many possible trees could be constructed for a hundred and thirty-five women? The answer is such a risibly large number that there is no point in writing it out. If the largest and fastest computer in the world were set to work listing all the possible trees, the end of the world would be upon us before the computer had made a perceptible dent in the task.

Nevertheless, the problem is not hopeless. We are used to taming impossibly large numbers by judicious sampling techniques. We can't count the number of insects in the Amazon Basin, but we can estimate the number by sampling small plots dotted at random through the forest and assuming that these plots are representative. Our computer can't examine all possible trees uniting the 135 women, but it can pull out random samples from the set of all possible trees. If, whenever you draw a sample from the gigabillions of possible trees, you notice that the most parsimonious members of the sample have certain features in common, you can conclude that probably the most parsimonious of all the trees has the same features.

This is what people have done. But it isn't necessarily obvious what is the best way to do it. Just as entomologists might disagree over the most representative way to sample the Brazilian rain forest, so DNA genealogists have used different sampling methods. And unfortunately the results don't always agree. Nevertheless, for what they are worth, I'll present the conclusions the Berkeley group reached in their original analysis of human mitochondrial DNA. Their conclusions {52} were extremely interesting and provocative. According to them, the most parsimonious tree turns out to be firmly rooted in Africa. What this means is that some Africans are more distantly related to other Africans than to anybody in the whole of the rest of the world. The whole of the rest of the world – Europeans, Native Americans, Australian aboriginals, Chinese, New Guineans, Inuits, and all – form one relatively close group of cousins. Some Africans belong in this close group. But other Africans don't. According to this analysis, the most parsimonious tree looks like this: [some Africans [other Africans [yet other Africans [yet other Africans and everybody else]]]]. They therefore concluded that the grand ancestress of all of us lived in Africa: “African Eve.” As I have said, this conclusion is controversial. Others have claimed that equally parsimonious trees can be found in which the outermost branches occur outside Africa. They also claim that the Berkeley group obtained the particular results they did partly because of the order in which their computer looked at the possible trees. Obviously, order of looking ought not to matter. Probably most experts would still put their money on Mitochondrial Eve's being African, but they wouldn't do so with any great confidence.

The second conclusion of the Berkeley group is less controversial. No matter where Mitochondrial Eve lived, they were able to estimate when. It is known how fast mitochondrial DNA evolves; you can therefore put an approximate date on each of the branch points on the tree of divergence of mitochondrial DNA. And the branch point that unites all womankind – the birth date of Mitochondrial Eve – is between a hundred fifty thousand and a quarter of a million years ago. {53}

Whether Mitochondrial Eve was an African or not, it is important to avoid a possible confusion with another sense in which it is undoubtedly true that our ancestors came out of Africa. Mitochondrial Eve is a recent ancestor of all modern humans. She was a member of the species Homo sapiens. Fossils of much earlier hominids, Homo erectus, have been found outside as well as inside Africa. The fossils of ancestors even more remote than Homo erectus, such as Homo habilis and various species of Australopithecus (including a newly discovered one more than four million years old), have been found only in Africa. So if we are the descendants of an African diaspora within the last quarter of a million years, it is the second African diaspora. There was an earlier exodus, perhaps a million and a half years ago, when Homo erectus meandered out of Africa to colonize parts of the Middle East and Asia. The African Eve theory is claiming not that these earlier Asians didn't exist but that they leave no surviving descendants. Whichever way you look at it, we are all, if you go back two million years, Africans. The African Eve theory is claiming in addition that we surviving humans are all Africans if you go back only a few hundred thousand years. It would be possible, if new evidence supported it, to trace all modern mitochondrial DNA back to an ancestress outside Africa (“Asian Eve,” say) while at the same time agreeing that our more remote ancestors are to be found only in Africa.