I read er... listened to "time" by stephen baxter, i found the "Carter Catastrophe" pretty interesting, you see it happen all the time in nature, except maybe for cockroaches, which apparently never die out. I'm just going to forget about the hysteria and note a couple possible holes in the theory, first of all, it just cites population, not other important factors like technology level, area occupied etc. Secondly, you can say you have sufficient data, but really, is looking at a few samples of data over 100 or so years going to suffice, we may have accurate data for humans at least, but for the animals you're comparing us to you may not have enough samples for the comparison.
For the theory, if u suspended ur disbelief long enough, it does make sense if you think about it a certain way, first of all, all species are terminated on a distinct timeline, no exceptions even cockroaches, mosquitos, and fruit flies, which we wish were all dead now.

Otherwise the theory makes sense, but as history has shown us, the worst thing that happens with isolated populations is they all die (easter island) which we have a lot of, Or the government collapses and a lot of people die, but not all.