I joined a gym last week and noticed that a one song playing on the overhead television screen got everyone moving with particular vigour. 'Just say you feel the way that I feel / I'm feeling sexual, so we should be sexual', went the song by Neiked featuring female singer Dyo.

Nothing revolutionary there. But it struck me that not so long ago, it was only male singers who advertised their sexual desire quite so explicitly. Women were restricted to singing about love.

On that score, several years ago I heard an elderly relative impart some words of advice to my two daughters: 'Always remember, girls, men are after only one thing!' This came with an implied corollary – that women are not after that thing at all, and therefore have to keep men at bay.

At about that time I read The Female Brain by the American psychiatrist Louanne Brizendine, who tried to explain why it was that men were only after just one thing by claiming that the brain's hypothalamus, which she called its 'sex-related centre', was twice as big in male brains as in female brains.

But a little like Brizendine's most famous claim – that women use 20,000 words a day, and men a mere 7,000 – this one turned to dust. When I read further, I discovered the function of the hypothalamus had nothing to do with thoughts about sex and all to do with linking the nervous system to the endocrine system – and that men and women use the same average number of words a day.

It turned out that male and female brains are remarkably similar (scientists can't be sure which is which without further biographical information), and yet it is hard to dispel the feeling that what happens inside them differs hugely. One persistent shibboleth is that women enjoy sex less than men. But is this really true?

The academic psychologist Janet Shibley-Hyde investigated this in her meta-analysis of 46 studies of gender traits taken over a 20-year period. What she found was that the difference in what men and women said about their own sexual satisfaction was 'close to zero'.

She found only one significant gap between what men and women reported: frequency of masturbation. But this could be at least partly cultural because many cultures continue to regard male masturbation as far more acceptable than female.

The opposite view – that men always have sex on their minds, and would look for any opportunity to get it, while women have an inbuilt interest in keeping men at pikestaff length – is one of the staples of evolutionary psychologists. Their idea is that men evolved to spread their genes as widely as possible, and women to attract the best of the batch and keep then for life so that they can be reliable providers. Men are therefore naturally polygamous, and women, naturally monogamous.

A related claim is that men are 'hard-wired' to marry nubile younger women (better odds for spreading their genes) while women are 'hard-wired' to marry older, richer men (better providers). Yet research all over the world shows that the age gap in marriage reflects women's position in society rather than a biological imperative. When women's economic status improves, the gap narrows: in the US it fell from 4.1 years in 1890 to 1.7 years in 2007.

The Stanford evolutionary biologist Paul Erlich has long despaired of the claims made by genetic determinists. "If a male-female difference exists in the desire to have multiple mates, it does not necessarily need to have a genetic basis," he wrote.

"Even if women enjoy sexual variety as much or more than men, for thousands of years they have not needed to be rocket scientists to understand that they make a greater potential commitment per copulation than do men." He added: "Women, like men, evolved to be smart."

A German study found that only 28% of men would find sexual infidelity more worrying than emotional infidelity, and in Holland it was 23%

In some cultures, being smart has led women in the opposite direction – by passing on more of their genes through several partners. University of California anthropologist Dr Monique Borgerhoff Mulder studied the women of the hunter-gatherer-herder Pimbwe people of Tanzania for 15 years. She found that those women with multiple partners had the most children and the highest status and were most likely to prosper, while with men, the higher the nuptial count the lower the social ranking.

This social system would seem to contradict another staple of evolutionary psychology: that male jealousy concerns sexual infidelity (because if another man impregnates his woman, he can't pass his genes on) but female jealousy is all about emotional infidelity (if he falls in love with another woman, he may abandon her and her children).

Some US attitude studies have indeed tended in this direction, but the position is different in northern Europe. A German study found that only 28% of men would find sexual infidelity more worrying than emotional infidelity, and in Holland it was 23%. What this suggests is that in cultures with more relaxed attitudes to female sexuality, men are less threatened by their partners having quick flings with other men, and more worried about emotional liaisons that could threaten their relationships.

And yet it is hard to dispel the sense that it is mainly the men who are having the quick flings – a view reinforced by surveys published periodically, wherein men routinely claim to have had double the number of sexual partners as women.

But if we assume the numbers of heterosexual men and women are roughly the same, then the average number of sexual partners they have would also be roughly the same: if a man has a one-night-stand, or visits a prostitute, it is likely to be with a woman, which produces a tick in the box on both sides.

The real explanation for the impossible 2:1 ratio is simple: that despite the popularity of the 'feeling sexual' song, men continue to exaggerate their number of sexual partners, and women downplay theirs.

Gavin Evans's latest book, Mapreaders & Multitaskers: Men, Women, Nature, Nurture, is published by Thistle.