Best Nikon lens for low-light wildlife photography?

I'm going on a safari soon and need a good telephoto lens for my Nikon D3100. I was going to go with the basic 55-200mm, but the maximum aperture is only 4, and on the 55-300mm it's 4.5. The animals are out early in the morning and late at night, so the light won't be great. I've heard that for low-light wildlife photography you need at least an aperture of 2.8, but the 70-200mm f/2.8 VS and VSII are both really expensive. Do I really need the f/2.8? Also, will 200mm of zoom be enough?

As a rule, the longer lenses with a fast aperture are indeed expensive.

That being said, some of Nikon's older 80-200 f2.8 zooms are no longer that expensive, certainly relative to the newest 70-200s. I've seen them on sale here (in Japan) for around 50,000 yen, which is around five hundred US dollars or slightly under. The downside is that, if I recall, many of them don't have VR, which is definitely something you can use in these kinds of shooting situations.

Anything longer than that while maintaining a fast aperture and you're into selling your house territory. There's a manual focus 500mm lens at f/4, and as 500mm lenses go it's not expensive (but as lenses go in general, it is). The writer of this piece recommends the 80-400 instead and puts his case well.

http://www.johncaz.net/blog/nikkor-500mm-f4-p-if-ed

As for focal length, it's hard to say how much zoom you'll need because we (and presumably you) don't yet know how close you will be getting to the animals. Nick Brandt shot his animal pictures with a standard lens, but then again he's not your average shooter and he had a lot of time to wait for the right opportunity.

You could put a teleconverter on an 80-200 2.8, but then you're down a stop or more and it's essentially the same as having the slower zooms you named above.

You might well get some good advice by asking the organisers of the safari. They are bound to get this kind of question a lot, and they will know how close you're going to get to the animals.

For wildlife you need a tele zoom, unless it is very tame wildlife. And you need f2.8 for low light, and zoom range around 80mm to 200mm. Older lenses of that spec are apparently not too expensive, see answer above. For some shy wildlife you might need longer than 200mm, but you have pixels to spare in your D3100, so you can crop a bit.

If you know anyone with a lens around those focal lenghts (even if not f2.8), try to borrow it for a few days to help you get your ideas sorted.

A compromise is the 70-200 f/4. It's still expensive (apx $1500), and it's a stellar performer. My friend used this lens on a safari and it worked well. The animals are generally vehicle tame, so the 200mm focal length was enough for the large critters. If you're doing a wilder type safari (camping in the bush), a longer lens is necessary along with a sturdy tripod. You'll see plenty animals in decent light. After all, there's only 30 to 60 minutes of low light shooting where a faster lens is needed. In the morning, you'll go from dark to full daylight where you'll have plenty opportunity to shoot with slower lenses.
Take decent binoculars, 8x42 or 10x42 (Carson ED glass seems to work well).
Uncropped image from Madikwe. We got pretty close.