In Avatar: The Last Airbender, Appa was the only known living sky bison. But in The Legend of Korra, we saw Tenzin had one:
Is this Appa or was the sky bison species somehow resurrected?
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At first I thought this (Tenzin's Sky Bison) was Appa. However, after some research I found this quote, on the Avatar wikia:
During San Diego Comic-Con, it was revealed that Avatar Aang found a whole new herd of sky bison. The new subspecies has a few differences, for example: old bison had four transversed strips plus the last one, that lies at the end of the tail, whereas the new species has more strips that are thinner. The new bison also have brown fur on their ears instead of white.
These differences are noticeable when you compare the tail markings to Appa:
Tenzin's Sky Bison is called Oogi.
Per the Avatar Wiki page for Appa,
Due to Appa being a male and the implications of Appa being the last sky bison, it was speculated that the species would become extinct upon his death. However, it is mentioned that a flock of sky bison was discovered after the War.
Possibly not all sky bison were domesticated. There were likely wild herds of bison living in the mountains or out roaming the wilderness. The bison at the Air Temples were all destroyed save Appa.
However Firelord Sozin lacked the manpower to track and destroy every last flying bison or he may have been unaware other bison existed. So the wild herds were safe.
Aang encountered a surviving herd on an island during his travels and brought them to the Air Temple. He discovered a new breed of bison with brown ears not white.
This flying bison is named Oogi and its a descendant of the herd. Numerous other bison live on the island. Healthy colonies of flying bison also live at the Air Temples where the acolytes look after them and other bison live in the wilderness around the temples.
I never thought this bison was Appa. The Avatar has a strong spiritual bond with their animal guide and the guide normally dies alongside or soon after the Avatar.
Avatar Roku had a dragon called Fang that chose to die at his side in the volcanic eruption. I reckon Appa would die with Aang or soon after him.
Shortly after the war ended, Avatar Aang found a lost herd of flying bison on an island near the Earth Kingdom. These were a new type of bison with brown ears not white ones, and different markings on their tail.
He likely tamed the bison and then drove them to Air Temple Island so the flying bison Tenzin has, Oogi, is a descendant of one of those bison.
There was also a new type of lemur there called the ring tailed flying lemur with orange eyes and black rings all down their tail. These are the new lemurs that fly around the island where Tenzin and his family live.
That animal is a different bison called Oogi. Appa likely died alongside or around the time that Aang passed away. He is dead by the time of Avatar Korra
The Avatar shares a deep emotional or spiritual bond with their animal guide. Avatar Roku had a dragon called Fang that chose to die at his side rather than flee to safety. Avatar Wan had his own cat deer, Mula, who accompanied him faithfully during his journey.
It's highly possibly not all the flying bison were domesticated but that wild sky bison roamed the mountains or lived in the wilderness around the Eastern Air Temple.
These bison survived the purges of the Air Nomads but the domestic bison were all killed. Firelord Sozin lacked the manpower to track and destroy any remaining bison
Avatar Aang discovered a surviving flock of sky bison on an island some years after the war. These bison were likely to have been feral after years of surviving alone.
He must have tamed the herd before driving them to Air Temple Island. Oogi is a descendant of the herd. He also discovered a new breed of flying lemurbat called the ring tailed flying lemurbat with black rings on their tails.
These are the lemurs seen on the island. Tenzin has a son called Meelo who adopts a lemur and names the animal Poki. It's similar to Momo.
I think that when the series of Avatar: The Last Airbender ended, Aang found a cave full of sky bison when he got older. But there wasn't an episode to show him finding the sky bison, and when The Legend of Korra started there was Oogi.
I just think Tenzin had not found the sky bison yet in The Legend of Korra.