Among mammals, rabbits are famously big breeders. They have been regarded as symbols of fertility since antiquity, admired for their ability to produce vast numbers of baby bunnies.

A couple of adaptations earn them this reputation: they are sexually active at just 3-4 months old and females can get pregnant as soon as they have given birth.

This means rabbits can produce multiple litters, of up to seven babies, through the breeding season.

But the season is really key. In Europe, rabbits only breed in spring and summer, limiting the number of offspring. However, in Australia and New Zealand, where European rabbits have been introduced, they can breed year-round in some areas raising as many as seven litters.

Unsurprisingly, rabbits are considered pests in these countries. In fact, pest status is often linked to breeding habits and can be a useful starting point for identifying the world's most fertile animals.

Every spring the Great Barrier Reef turns tides pink in a mass spawning event

For instance, Australia also suffers from overwhelming plagues of mice.

With an abundance of food and the right environmental conditions, mouse mothers have an average litter of six every month, which can themselves begin breeding the following month. Plague densities can peak at 2,700 mice per hectare in grain stores.

If those numbers are not extreme enough for you, consider "the greatest sex show on Earth".

Every spring the Great Barrier Reef turns tides pink in a mass spawning event. Instead of physically mating, corals synchronise the release of their sperm and eggs to boost the chances of fertilisation across the full extent of a reef.

"I do not think that anyone has really ever tried to count how many eggs an individual coral produces," says Dr Mary Hagedorn of the Smithsonian Conservation Biology Institute, who leads research at a pioneering coral fertility clinic in Hawaii. "Most people describe it as massive numbers of eggs produced during a spawn and that could mean many millions of eggs produced by an individual coral."

What at first glance appears to be superb virility is actually a risky strategy

Millions of eggs might sound like a lot, but time is against the corals. "Corals have some of the most restricted reproductive patterns in the animal kingdom," says Hagedorn. "For most corals, they only produce male and female gametes for 2 days per year."

What's more, most of the young die. "Even though corals produce massive numbers of offspring, the result is more-or-less the same as for other groups of animals: one or possibly two offspring are produced that grow to maturity," says Hagedorn.

So what at first glance appears to be superb virility is actually a risky strategy. Hagedorn warns that bleaching events, which stress the corals and their symbiotic algae, have a dramatic impact on future generations.

Elsewhere in the ocean, there swims a giant that was formerly recognised by Guinness World Records as the most fertile backboned animal: the ocean sunfish.

Their Latin name "Mola mola" means "millstone", and it is apt: these round, grey fish can measure 10 feet (3m) across and weigh up to 2 tonnes. Affectionately known as "swimming heads" for their large bodies and relatively small fins, they are often found basking in the sunlight near the surface of the ocean.

A newly-born summer female already contains the embryo of the next generation, like a tiny Russian doll

Sunfish are egg-carrying champions. Females can release an estimated 300 million into the water at a time. In Japanese waters, they are thought to spawn from August to October, suggesting they are multiple spawners.

"Large, mature ocean sunfish have a solitary life in the open ocean where finding mates is likely a challenge, so producing lots of eggs in multiple spawning events may increase chances of fertilisation and by multiple males," says Dr David Sims of the Marine Biological Association in Plymouth, UK.

As with the corals, only a few of their eggs will develop into mature adults – or the world's oceans would be a flapping mass of sunfish and not much else. "We think they produce so many because the chance of fertilisation of eggs and subsequent survival of larvae is so low," says Sims.

If we want to find some truly stunning rates of reproduction, we need to look at smaller animals: specifically, insects.

Cabbage aphids are familiar to any gardener as prolific pests.

In the spring, females turn out 5-10 genetic copies of themselves a day. This continues through the summer when the daughters gain wings to help spread the family further.

A single aphid could spawn enough descendants to cover the Earth in a layer of aphids 149km deep within a year

Under the microscope, a newly-born summer female already contains the embryo of the next generation, like a tiny Russian doll. In autumn, the females finally produce some males, allowing for mating and some healthy shuffling of genes.

"Individually aphids are unremarkable in this regard, producing only 50 or so offspring. Many insects produce very many more," says Dr Richard Harrington, head of the long-running Rothamsted Insect Survey. "However, combine that with their very short generation time – a week or even less under ideal conditions – and they may well be the insect reproductive champions."

In perfect conditions, Harrington has estimated that a single aphid could spawn enough descendants to cover the Earth in a layer of aphids 149km deep within a year. In reality, mortality is high for the insects because they are preyed on by ladybirds, lacewings and a variety of birds.

But there are some insects that spend their entire lives reproducing. The queens of social ant colonies have workers to do everything else for them, and they may be the most successful reproducers of all.

At the head of a colony of African driver ants sits a monarch that can produce an estimated 3-4 million eggs a month. That may well be the record.

"However, it is important to note that although they produce the most per queen, many other species are not limited to a single queen and thus can achieve even greater levels of colony fecundity," says Thomas O'Shea-Wheller of the University of Bristol in the UK.

For instance, Argentine ants live in "polygyne" colonies with thousands of queens, which means their populations are truly spectacular. The largest of these mega-colonies stretches for 6,000km (3,700 miles) along the Mediterranean coast. Like the antipodean mice, they are considered pests.

In an odd twist, in their native Spain European rabbits are now considered "near threatened", due to disease, habitat loss and hunting pressure. Perhaps we should change the saying to "breeding like ants".