Walk into a bookshop and you cannot avoid the apocalyptic claim that Darwinism is about to crumble to the ground. But ask almost any biologist and you will be told that Darwinism has never been so solid. The gulf between the biologists' version and the popular version is huge.

Yes, biologists are squabbling, but their subtle arguments are misheard on the other side. They agree that today's creatures arose by evolution from one single-celled ancestor. They agree that the best way of explaining how it happened is by combining Darwin's theory of evolution by natural selection with Mendel's discovery of the laws of inheritance to make the synthesis of Neo-Darwinism, achieved in the 1930s. They have refined their knowledge with this century's dramatic discoveries in genetics to form the theory they use today.

This Neo-Darwinism proposes a two-stage mechanism. First, each organism is born with a genetic blueprint that contains random genetic mutations. These cause slight differences in physical characteristics. Second comes natural selection: when these organisms come up against their environment some will be better adapted to surviving (and reproducing) than others and so will pass their mutations on to the next generation. Thus, those genes will gradually increase in the population.

Biologists such as Steven Rose are unhappy at Neo-Darwinism's insistence that there is only one level of selection - the gene. He says it is necessary to consider multiple levels of selection, from genes through individuals, to populations. But while most biologists agree about evolution and randomly mutating genes, some say natural selection cannot be the only motor for evolution.

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Some see a greater role for natural catastrophes in explaining big leaps in evolution which, they argue, must have occurred. A disaster that obliterated many species would wipe out a lot of genes and leave others supreme, sending evolution off in a different direction. Others back "neutral drift". This happens if a small group from a species colonises a place from which there is no going back - an island, for example. Their genes - odd mutations and all - are suddenly the only ones and are unlikely to be representative of the population on the mainland. They survived not because they were better adapted to the environment but perhaps because they got caught up on some flotsam. Another motor for evolution is molecular drive. Some genes can force themselves on to the next generation more powerfully than others, leading to a shift in genetic make-up caused by the genes themselves rather than by natural selection.

For a different objection, see Brian Goodwin, right. Another famous objection is from Stephen Jay Gould: why concoct elaborate how-the-elephant-got-its-trunk stories to explain every "adaptation"? Could characteristics not just have arisen perhaps as side-effects of other adaptations?

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But these divisions do not cut Neo-Darwinism at its roots; they add to it. Pursue such arguments into the more controversial area of sociobiology and they can fuel its critics. Goodwin's ideas demote genes and promote the developmental stages of organisms as explanations of human behaviour, says Tim Ingold, anthropology professor at Manchester University. Similarly, if historical contingencies are an evolutionary force then they could rival natural selection as shapers of human culture. And a distaste for Just So Stories in biology can spawn distaste for the argument that language evolved by natural selection- perhaps it was just a side-effect of having a large brain.

Back at the bookshop, the diatribes against Darwinism have been on sale all century. It is a science that will not settle, says John Durant, professor of the public understanding of science at Imperial College. "How many scientific theories do you know which are called 'ism'? Does it sound like a movement that you join or is it accepted scientific theory?" People always want to pull down "big theories" particularly if they are counterintuitive, as Darwinism is, he says. "But what's going on within biology is a rather subtler debate".