Fun fact: When Cicero was governor over part of Anatolia, a friend wrote to him to request some panthers. Cicero wrote back to regretfully inform him that panthers had been driven out of the province by overhunting.
Rather than seeing this as a negative function of the endless lust of the Roman people for bloodsport, the Romans saw it in largely positive terms. Lacking the full modern conception of ecosystems, the Romans simply saw such creatures as untameable animals which competed with human beings for precious and limited food resources - and endangered humans besides. It was basically a win to see a province depopulated of such noxious creatures! After all, it's not like human effort can drive entire species to permanent and worldwide extinction, right...?