Some of them rely on odd-looking sperm instead to boost their chances of fathering offspring.

The sperm of the Norway rat, for instance, have tiny hook-shaped heads that allow them to link together in their hundreds, forming a mega-sperm with several hundred tails that can power towards the eggs faster than single sperm. This gives the sperm a vital edge in the race to reach the egg before a rival’s sperm does.

Other rats play dirty. They have developed deliberately malformed ‘kamikaze’ sperm, which seem to linger behind as their peers race to the egg. These sperm are thought by some scientists to join together and form a tangled mess that ensnares the sperm of rival males - although the idea is controversial.

Even the semen that carries the sperm can help boost a male’s chances of mating success.

In many mammals - including humans - seminal fluid contains a chemical that encourages the female brain to release ovulation-inducing hormones. This may help to guarantee that there is an egg waiting for the sperm at the end of their swim. It might also help males to fertilise a female before she can mate with a rival.

Mind-bending semen seems to offer a clear advantage in the fight among males for paternity rights.

Females may not be particularly happy about being manipulated like this, though. “When we first discovered ovulation-inducing factor, we thought it may send a shiver up the spine of every woman using the "rhythm method" of contraception,” says Gregg Adams at the University of Saskatchewan in Saskatoon, Canada - although he thinks it’s unlikely that female mammals have evolved counter-adaptations to avoid this male control.

Female mammals certainly have evolved strategies to cope with other forms of male sexual control, though.

This gender conflict stems from the fact that males and females tend to have different goals in mind during mating season. It’s a quantity versus quality clash.

Males are generally keen to breed with as many females as they can: a female, in contrast, may be more interested in exploring the field and mating only with the very best males she can find. To boost their chances of getting their way, both males and females sometimes make use of some bizarrely adapted genitalia.

Gender wars

Things aren’t going well for one Argentine lake drake. His attempts to impress the female ducks with his plumage and courtship displays have failed. As yet another dissatisfied female swims away, the male instinctively reacts: in the blink of an eye he explosively releases his 40-centimetre-long penis, uses it to lasso the female and forces himself on her.

Male ducks have become notorious on the internet for what is, in our eyes, some pretty unpleasant sexual behaviour. They provide a perfect example of how the antagonistic battle of the sexes has led to some truly peculiar sexual organs - particularly because in the case of ducks, the vagina is no less bizarre than the penis.

The long duck penis is corkscrew shaped, twisting in an anti-clockwise manner. The duck vagina twists in the opposite direction, preventing the duck penis from reaching deep inside the female.

Patricia Brennan at the University of Massachusetts Amherst thinks female ducks may have evolved such a vagina to increase their level of control during the breeding season. Female ducks may tighten their vaginal muscles to thwart an unwanted male, but relax them during sex with a preferred male, making it easier for his penis to bypass the barriers and deposit sperm near to the egg. But she concedes that it won’t be easy to prove the idea. “I need a transparent duck!” she says.

Sexual conflict has probably also had a hand in shaping the strange sexual organs of the bat bug.

This close relation of the bed bug has mating habits that make even the Argentine lake duck’s look relatively tame. Males ignore the female vagina when they want to mate. Instead, they use their short, sharp penis to stab the female, injecting sperm directly into her body cavity. A female that has the misfortune to receive too much male attention can find herself at serious risk of death from the penis-inflicted wounds.

Females have responded to this aggressive male sexual behaviour by developing a special defensive structure - an area on the abdomen where the hard scaly skin is replaced by soft spongy tissue that males find easier to stab. This abdominal area focuses the attention of the male bat bug’s penis stabs. The spongy tissue is also packed full of immune cells, helping the females to avoid nasty infections that the males may pass on during sex.

But what looks like a win for both genders has actually backfired on the male bat bugs.

Females have basically endorsed the male habit of penis stabbing, and as a result males have begun enthusiastically stabbing any bat bug that strays too near – even other males.

This has become such a problem for males that they, too, have had to adapt. Some of them now sport female-like areas of spongy tissue, but the male versions are subtly different in a way that other males can apparently distinguish: male bat bugs with spongy tissue usually suffer penis-related injuries.

The final twist in this complicated tale is that females, in turn, are now taking tips from the males: the spongy tissue of some females has taken on the masculine form - a move that allows the females to masquerade as males and avoid too many penis-related injuries.

Sexual conflict has clearly helped shape some of the strangest sexual organs in the animal kingdom.

But it hasn't shaped all of them. Eberhard has looked at hundreds of insect species, and discovered something interesting: the genitalia are as complex in species that don’t resort to conflict during mating as they are in species that do. There must be one missing factor that has shaped the sexual organs.