1) Population in this meaning is singular: animal population IS... 2) I would say : "determined". However, I would change the sentence in this way: "According to zoologists, animal population growth at a given time is determined by food supplies".

I read examples of population both with singular and with plural verbs, but I'm uncertain about when to use singular or plural verbs. As for govern, it should be seen if native speakers use that combination of words. That's why I proposed another verb. It doesn't matter whether a certain word have a meaning that suits a sentence, if native speakers doesn't use it in that way, it doesn't sound natural. I think you should ask a native speaker, possibly a tutor or a teacher, about both "population" and "govern".