Unlike lions, leopards, and bears, tigers appear relatively rarely in Roman art, with the tigress seen more frequently than her male counterpart. - Cleveland Art Museum
Apparently, the emperor Titus was the first ruler to introduce tigers to the crowds in the Flavian Amphitheater (Colosseum), among the 9,000 beasts killed over the course of its 100 day inauguration. I found a reference to the book "Rome beyond the Empire" by Mortimer Wheeler published in 1954 that describes Roman trading posts around the coast of India and how a Greek merchant sailed as far as the Bay of Bengal about 60 CE. Perhaps he established some trading relationships that resulted in the acquisition of those tigers.
"The Scriptores Historiae Augustae explicitly praised the emperor Antonius Pius for his munificence in staging a games featuring ‘all the animals of the whole earth,’ and it seems such claims were scarcely an exaggeration: lions, rhinos, crocodiles, hippos, cheetahs, rhinoceroses, monkeys and elephants were all transported from Africa to the capital. Tigers, leopards, panthers, and cheetahs made the perilous journey from Asia, whilst bears were captured and taken to Rome from the highlands of Scotland..." - Lions and Tigers and Bears, Oh My! Wild animals in the Colosseum, througheternity.com
Elephants were actually the first animal used for a public spectacle in Rome in 251 BCE when 142 elephants appeared in a victory celebration of the Roman legions over Carthaginians riding the beasts. Sadly, the animals were slaughtered afterwards.
"With the passage of the centuries things got a lot more sophisticated. In 186 B.C. the Roman consul and general Marcus Fulvius Nobilior staged the first known example of lions and panthers being hunted down in the arena for sport, and his innovation caused a sensation. Such venationes quickly became a staple of the Roman games, known as ludi circenses, and in 46 BC Julius Caesar built a dedicated wooden amphitheater where such spectacles could be staged." - Lions and Tigers and Bears, Oh My! Wild animals in the Colosseum, througheternity.com
The result of all of this carnage? Hippos disappeared from the Nile and lions no longer roamed through Mesopotamia, whilst the north African elephant, aurochs, European wild horses, great Auks and Eurasian lynxes were all wiped out entirely.
Read more about it: https://www.througheternity.com/en/blog/history/wild-animals-in-the-colosseum.html#
Image: Roman mosaic of Tigress and cubs, 300s CE, estern Roman Empire, now in the collections of the Cleveland Art Museum, image courtesy of the museum.