Martina Navratilova has been accused of being “transphobic” after saying that some transgender women should not be allowed to compete against other women in sport.

The tennis star has criticised International Olympic Committee (IOC) guidelines, which say transgender athletes can compete as women if they reduce their testosterone levels.

Trans activists have accused her of being transphobic, but other prominent athletes including British Olympians Paula Radcliffe and Dame Kelly Holmes have also suggested that male-to-female trans athletes could have an unfair advantage over other women.

What do the rules say?

The IOC has allowed trans athletes to compete at the Olympics since 2004, but only people who had undergone surgery on their genitals.

New IOC guidelines came out in 2016. Female-to-male athletes can now compete without any restrictions. Male-to-female athletes no longer need to have reassignment surgery, but they do need to demonstrate lowered testosterone levels.

Controversially, the current guideline states that a male-to-female transgender athlete must show that her testosterone levels have been below 10 nmol/L for at least 12 months prior to her first competition.

That concentration – 10 nmol/L – is around the bottom of the range that clinicians consider normal for adult males, but is more than three times higher than the upper limit of the normal range for adult females – around 3 nmol/L.

Why is testosterone so important?

Both males and females naturally produce the hormone, but men generally have much higher levels.

Testosterone has been shown to profoundly influence the way boys’ bodies and brains develop in the womb, in early childhood and at puberty.

Higher testosterone has been linked with increased muscle mass, strength, production of red blood cells, competitiveness and more.

People who transition from male to female often take the main female sex hormone oestrogen as well as drugs that block the release of testosterone to reduce its “masculinising” effect on the body. The vast majority of people who make medical transitions do so after puberty.

Transgender women athletes who have not had their testicles removed might well have to take drugs that block the production of testosterone if they want to comply with IOC rules.

Does lowering testosterone cancel out the competitive advantage of people born male?

Hard data on the effects of lowering testosterone in athletes is very limited.

The Canadian scientist Joanna Harper, herself a transgender woman and runner, published a study in 2015 suggesting that male-to-female transgender athletes tended to run significantly slower after having hormone therapy to reduce testosterone, to the point where they had no advantage over other women.

The problem was that the sample size was just eight athletes. All of them were distance runners, and none were competing at international level.

A follow-up study tried to rectify some of these limitations, but again, the number of people tested was tiny.

The sample size problem is not an easy one for sports scientists to solve, since transgender people are a small minority of the population. The subset of those people who are likely to be elite athletes, and agree to take part in a study, is very small indeed.

In 2017, Stephane Bermon and Pierre-Yves Garnier took a different approach, focusing on links between testosterone and performance in non-transgender athletes.

They published a study in the British Journal of Sports Medicine looking at more than 2,000 blood tests from athletes at the 2011 and 2013 IAAF world athletics championships.

They concluded that elite female athletes with higher testosterone levels had an advantage of 1.8 to 4.5 per cent over women with low levels in five out of 21 athletic events.

The paper has been criticised for design flaws, but Bermon and Garnier published a follow-up with revised data which reaffirmed the original findings: there was a “very strong correlation” between testosterone levels and results obtained in the five events, and the link is very unlikely to be explained by chance.

The variations in testosterone between the female athletes were still mostly in the normal range for natal females, begging the question of what percentage advantage a transgender woman with hormone levels approaching the male range might have over her rivals.

Other intriguing questions remain. Why was there no link between higher testosterone and results in the male athletes? Could undetected doping have skewed the findings?

What about puberty?

There’s a whole other argument about fairness: does a transgender woman who transitions after puberty retain permanent physical advantages over other women?

Professor Alison Heather from New Zealand’s Univesity of Otago has led research into “muscle memory” and thinks that growing up male could give transgender athletes a lifelong edge.

Testosterone during growth gives men more muscle fibres called “myonuclei”. Even if a male athlete stops training for years, and their muscles shrink, increased numbers of these fibres mean the athlete can produce more force from their muscles.

She told FactCheck: “Muscle memory is a permanent thing. The extra nuclei that accumulates during hypertrophy have been shown to persist for 15 years.

“Therefore, the ability to regain muscle, or maintain muscle, that has accumulated during a prior male physiology, is a distinct advantage (for a transgender woman).”

There are other permanent advantages for biologically male children, she added.

Exposure to testosterone in the womb “drives masculinisation of the brain that includes a more aggressive and competitive nature”.

Higher testosterone levels after birth mean males have larger hearts and lungs, on average. Females have a wider pelvis, altering hip rotation and making them inherently slower.

And females’ tendons and ligaments tend to be looser, making them more prone to injury.

Professor Heather went on: “Males have longer and stronger bones from puberty. Longer allows for increased reach, etc, but also a wider articular surface, especially in the upper body which allows them to put down more skeletal muscle.

“Males are much stronger in upper and lower body strength because of their different musculoskeletal properties.

“All of this is not going to be reformatted by lowering testosterone to 10 nmol/L or 5 nmol/L.”

Level playing field?

A number of transgender activists and academics dispute Bermon and Garnier’s findings, insisting that research data does not support a relationship between an athlete’s current level of testosterone and performance.

Even if this is true, it’s not a complete answer to the accusation of unfairness, since there is scientific support for a legacy effect of being exposed to testosterone in early life and puberty.

Nevertheless some trans activists – like the leading Canadian cyclist and academic philosopher Dr Rachel McKinnon – think the requirement to suppress testosterone with drugs in order to compete in women’s sport should be scrapped altogether.

Dr McKinnon points out that out that athletes never compete on a completely level playing field: there will always be differences in genetics, socioeconomic status, access to training facilities and so on.

“Fairness cannot require the elimination of all significant competitive advantages,” she writes.

On the other side of the argument, sports scientist Stephane Bermon says the potential advantage from higher male sex hormones is so great that the limit for transgender women should be cut from 10 to 5nmol/L.

Joanna Harper has written: “Since I believe in both the vital importance of women’s sport and the rights of intersex and transgender women, then I am forced to consider a compromise position, one virtually identical to that espoused by the IAAF and the IOC.”

The debate from all sides about whether the current rules are fit for purpose will certainly rage on.