To satisfy our palate (and dietary needs, historically) we started to use many animals, some of which we now keep in extremely high numbers (estimates of 1 billion to 1.4 billion of cattle alone). What would these numbers be had we chosen different animals to exploit or refrained from doing so? Do we have any idea of what the size of populations of these animals would be without our intervention? I am asking mainly about farm animals such as cattle, chickens. Since these are usually rather domesticated, the answers can be about numbers of their closest relatives in the wild.
Subsequently, in a hypothetical vegan world where we do not exploit animals anymore and we do not keep them on farms or anywhere else, what are the numbers we should look to gradually reduce these populations to?