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Men with an eye for younger ladies, and women who prefer a more mature man, are not just obeying cultural stereotypes: both have evolved to appreciate an age gap when it comes to sex and marriage, scientists have found.

Both men and women have more children when the father is a few years older than the mother, according to research suggesting that natural selection has driven each gender’s age preferences in mutually compatible ways.

Men are most reproductively successful with a partner who is six years younger than they are, while women have most children if they choose a father who is four years older, a study in Austria has shown.

One of Britain’s most successful and famously fertile marriages falls squarely in the middle of this age range. The Queen, 81, is four years and ten months younger than the Duke of Edinburgh, and they have four children – more than double the British average.

Couples in which the man is much older, however, do not have an advantage. Women whose partners are ten years older have on average the same number of children as those with spouses five years younger.

The results offer the strongest evidence yet that the combination of an older man and a younger women has evolved to become the norm for heterosexual couples across the vast majority of human cultures that have been studied because it carries a reproductive advantage.

In England and Wales, 26 per cent of marriages involve a younger man, against 48 per cent where the man is between a day and five years older, and 26 per cent where he is six or more years older. Other societies show similar trends, and while the size of average age gaps often differ, the older-male norm does not. The global average is for men to prefer a partner who is 2.66 years younger than them, and for women to prefer a partner who is 3.42 years older.

Similar patterns have been observed in marriage records all over the world. This cultural uniformity has long led scientists to suspect that evolution is involved, and that age differences have historically promoted the birth and survival of more children. The usual explanation given is that men have an in-built preference for partners who are visibly fertile, which is enhanced by youth, while women seek resources and status, which tend to increase with a man’s age.

While such ideas make theoretical sense, however, research had not previously established any reproductive advantage in the real world for men who choose younger wives and girlfriends or for women who take older mates.

The new study by Martin Fieder and Susanne Huber, of the University of Vienna, has found such evidence for the first time, by examining a database of more than 10,000 Swedish men and women. All the participants had had children, and had kept the same partner from the birth of the first child to the birth of the last one. Details of the research are published in the journal Biology Letters.

For men, the average number of children increased as the age of their partners decreased, peaking at an age gap of 5.92 years, before declining again with larger differences. There was a similar finding for women. The average number of children rose as their partners grew older than them, peaking at a gap of 3.97 years before declining again. The differing figures for men and women are possible because the sample does not include both partners from each relationship.

When women were older than their partners, the curve was sharper still: the number of children declined steeply with each extra year of age difference. Much of this is probably attributable to the way in which female fertility declines at a much earlier age. A woman ten years older than her partner is likely to be starting a family when her fertility is waning, which will not always apply to a much older man.

The results show a clear gain in evolutionary “fitness”, the birth of extra children, when men are a few years older than women. The scientists said: “These findings may account for the phenomenon that whereas men typically prefer and mate with women younger than themselves, women usually desire and mate with men older than them, We conclude that the age preference for the partner increases individual fitness of both men and women, and may thus be an evolutionarily acquired trait.”

The study also found that when people have children first with one partner and then with another, the second partner tends to be younger than the first for both men and women. This may reflect a preference for younger partners to compensate for one’s own declining fertility, the scientists suggested

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