In thousands of years temperatures in the India - Asia area rise and cause a mass migration from African animals due to less competition for food in new areas. This causes the food chain to get jumbled from the over saturation of apex predators. This causes a need for tigers to further evolve to compete with the new threats to their prey and territory in a way that avoids them, and not directly compete. I imagine they do this by evolving new camouflage to blend in to this new, hotter environment and helping to hide away from pack animals which propose a threat. The camouflage may not be enough to survive, so along with a new greyer, more woodlands-esque camo they may evolve to be bigger and benefit from this in a cave bear type situation where they can scare away pack animals from their already dead food.
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