Hand-reared for their colour and beauty, koi carp have become an iconic symbol of Japan that can sell for hundreds of thousands of dollars and even participate in fishy beauty contests.

The nation's koi carp were brought to the world's attention when visiting US President Donald Trump was snapped unceremoniously dumping the last of a box of feed into a palace pond in Tokyo.

But the  fish  have for decades been popular in Japan, where top breeders take their most prized specimens (known as "nishikigoi") to highly competitive "beauty parades."

At one such competition in Tokyo, judges in sharp suits, notebooks in hand, stride around tanks lined up along a pedestrian street where the valuable koi strut their stuff.

They come in all the colours of the rainbow: pearly white, bright red, cloudy-grey, dark blue, gleaming golden yellow. But it is the curvature of the fish that accounts
for 60% of the final score, explained competition organiser Isamu Hattori, who runs Japan's main association for breeders of koi carp. Colour and contrast make up another 30%, he says.

And the final 10%? "Hinkaku" -- a concept that is tricky to define and even harder to judge, best translated as the "presence" or "aura" of the  fish.

"'Hinkaku'. It's either there in the genes at birth, or it's not," mused Mikinori Kurikara, a koi breeder in Saitama, north of Tokyo, who says he can spot it in  fish  when they reach eight or nine months old.

"Put it this way, it's like looking after your own children every day. You care for your kids and want them to grow healthy. In the same way, you take care of these  fish, appreciate them and adore them," he says. At his farm, thousands of tiny "nishikigoi" (coloured carp) dart around deep basins of carefully purified water, meticulously divided by age and colour.

"It's a really delicate job, really difficult. Everything matters: the ground, the water quality, the  food," explained the 48-year-old, who took over the farm from his father and is training his son, half his age, in the subtle arts of koi breeding.

"We have many secrets," he adds mischievously. "But even if we let them slip, it wouldn't work. You have to be able to feel it." These days, any self-respecting traditional Japanese garden has plenty of colourful koi gracing its ponds, but it is a relatively recent tradition.

Around 200 years ago, villagers in the mountainous region around Niigata (in the north-west of Japan) started to practice genetic engineering without knowing what they were doing. For the first time, they began to cross-breed rare colourful carp, not for  food  but for pure aesthetical value.

The craze for nishikigoi gradually took over the whole of Japan and then spread into other parts of Asia.

Today, koi is big business and Japanese exports are booming -- 90% of domestic production is exported and sold at auction. In 2016, Japan exported a record 295 tonnes of koi carp, generating turnover of 3.5 billion yen ($31 million), an increase of almost 50% from 2007, according to Japan's agriculture ministry.

As for individual carp, "the prices have become insane," said carp association boss Hattori.  "Today, a two-year-old carp can sell for 30 million yen each ($265,000) whereas 10 years ago, two million yen was already a very good price," he says.

Like racehorse owners, many foreign owners leave their prized possessions
in their Japanese farms so they can compete in the most prestigious fishy pageants, which are only open to domestic rearers.