In perhaps the most jubilant message of national science week geneticist Steve Jones has announced that we are living in a utopia - of a genetic kind.

"The great engine of evolutionary progress has come to a halt in a siding," Professor Jones told the Royal Society on Tuesday. Evolution, which has the power to eliminate individual humans through a cut-throat army of mutations, natural selection and random change, has lost 94 per cent of its force. "If you're worried about what the genetic utopia might be like, you shouldn't because you're living in it now," he said.

The great operator of evolution is mutation - as our genes copy themselves to produce the genes of the next generation they make errors which lead to new characteristics in our offspring. Mutations cause the variation essential for evolution but they can cause disease, so we fear carcinogens - things that increase mutation rates. But Professor Jones, who works at University College, London, said our man-made chemicals and radiation are "trivial" carcinogens compared to natural sources which we do not fear.

A rational person would have less fear of pesticides such as PCBs, which, given our annual exposure to them, are 100,000 times less carcinogenic than lettuce. "Humans have been exposed to lettuce for a lot longer than DDT," he said.

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In fact, the most dangerous mutagen of all is old age because as men get older they produce sperm with more mutations, so they are much more likely to produce children with damaging mutations. Sixty-year-olds are ten times more likely to father children with dwarfism than 20-year-olds, for example.

But there is good news here as well, said Professor Jones. "Many people think that the age of parents is going up - but that isn't true. People are delaying pregnancy - but people complete their families very quickly. The number of older parents is dropping enormously. That is going to reduce the net mutation rate to the lowest it has ever been." The good news went on: natural selection, the great filter of evolution, which kills off people with certain mutations, so that only beneficial mutations survive, has stopped operating in humans, he said.

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But natural selection has another prong, which people still fear. Sexual selection means that men who father more children fill the next generation with more of their genes than those who father fewer children. "In primitive societies there are massive differences in sexual success," he said. The most fecund male was a medieval North Moroccan who fathered 888 children. Many men would have fathered none. But fecundity, too, is losing its power. There is a worldwide trend towards having two children.

That leaves the third great evolutionary power, evolution by accident (genetic drift) which happens in a community as some lines die out and others intermarry. This powerful and rapid force is over, he said. Inbreeding has vanished with increasing mobility: "without doubt the most important event in human evolution was the invention of the bicycle".