Animal reproduction when resources are scarce
This is actually a comment, but was not allowed to comment. 

I think what you're interested is more in population dynamics and I think what you're really asking about is more in line with what system of  differential equations explains a network of animals and how their populations grow and decrease with the amount of resources and the species population. 

I think the problem is that, there's actually no good model, because there are so many factors which seem to contribute to shifts. 

@ MIT this year, they had a visiting prof from Tufts give a talk on this, and they're working on models, to try and describe this, and even HE- the prof said, yeah, it gets complicated even for two species. 

I would recommend, that if you have time to read up on this?

https://sites.tufts.edu/hening/publications/ &lt;--- a link to his publications

https://arxiv.org/abs/1710.01220

Also, this is probably more a question for the mathematics stack.