However, the larger this male reproductive organ is in one fish species then the bigger the brain in later generations of females.

That's the conclusion of a study into eastern mosquitofish by researchers at Stockholm University and the Australian National University.

The gonopodium, a modified anal fin, is used to deposit sperm in the female eastern mosquitofish (Gambusia holbrooki). The species bear their young internally, as do sharks and rays: this group is known as "live-bearing fish".

The researchers selected groups of male fish based on gonopodium size and mated them with female fish. They did this, they said, "to mimic the selection pressures in environments favouring different levels of male coercion success".

Previous studies have shown that "males with a longer gonopodium had higher reproductive success".

In some fish species, such as the guppy, males use two mating tactics: courtship and coercion. However, the male eastern mosquitofish has just one tactic: they force females to mate.

According to the study, "males usually sneak up to females, attempting up to a thousand forced copulations per day".

The researchers measured brain size in 90 females and 90 males after eight generations from an original population of mosquitofish collected in Sydney.

In the group bred from male fish with larger gonopodium, female fish had on average a 6.5 per cent heavier brain. Male brain size was unaffected.

The researchers speculate that "a larger brain might allow females to better predict their environment, detect males earlier and/or have faster reactions to more successfully evade males".

This, they suggest, might even allow the females to exert mate choice "by escaping the mating attempts of certain males".

As to why there was no change detected in male brain size, the study said: "Male cognitive skills do not play a prominent role in determining the outcome of forced mating attempts."

This fish species is known locally as the eastern gambusia, said Mark McGrouther, head of the ichthyology collection at the Australian Museum.

"They are a pest in Australian waters," he said. "They were deliberately introduced in the 1920s from the US in the mistaken belief they'd be better at eating mosquito larvae than native species."

Mr McGrouther said they are aggressive and "internal fertilisation allows them to breed quickly and outcompete native species".

Clelia Gasparini is a post-doctoral researcher at the University of Western Australia's centre for evolutionary biology. She is unconnected to this study but has studied gonopodium in guppy fish.

Dr Gasparini said the study shows that "experimental evolution of longer gonopodium results in females having a larger brain, [which is] important for their cognitive ability to avoid males' mating attempts".

Rob Brooks is a evolutionary biologist at the University of NSW. ​He said in all likelihood the "genes that influence those traits [longer gonopodium in males and larger brain size in females] are associated".

The study, published on Wednesday, concludes that gonopodium length is not evidence of a "cognitive arms race" between the sexes. Instead it argues female cognition evolves in response to sexual conflict favouring male genital size evolution.

"The acquisition of better cognitive abilities via increased brain size may enable females to exert greater control over the paternity of their offspring," the study said.

And, as ever with these studies, anthropomorphism is futile.