It seems to me that China still has this kind of diversity somehow. Going to a large Chinese supermarket is dizzying in the variety of vegetables, dried fungus, seaweed, spices, etc. on display. I wish I knew more about it, and how they maintained that diverse food culture.
Mann's 1491 suggests this may be a myth, as passenger pigeon remains are nearly non-existent in native refuse piles, so they don't seem to have been a normal part of their diet (at least, before contact). Rather, he paints both their incredible abundance and subsequent demise as consequences of contact with Europe: the boom in the passenger pigeon population may have been a sign of an ecosystem experiencing a catastrophe, resulting from large areas of cultivated land falling out of use as entire cities were depopulated by disease, causing a temporary but enormous increase in easy, available calories for animals positioned to take advantage of it, and of course their decline and extinction is entirely a post-contact event.
[EDIT] I misread you as having written that the native people contributed to the demise of the pigeons, but I think the info's still broadly relevant so I'll let the post stand.
My ex-wife is Chinese and I might be able to assist a bit.
China is a massive country and each province has their own "special dishes".
For the Chinese out there reading this - you can guess where she's from when i tell you their speciality is "Guìlín mǐfěn"
Anyhow, when you go to a large Chinese grocery store in North America you are looking at the fruits, vegetables, etc from a large number of provinces.
So if someone from Guangxi goes there for Hot Peppers they can find it. If someone else is looking to make Peking duck can find what they need as well.
Back in China, someone from Guangxi wouldn't be making a lot of Peking duck...
Hope this helps?