It's very random. The first few months are devoid of the more difficult races, but after 10 months or so, all races participate.
As for actual ratios, they vary by mission. For example, the alien terror mission (after above-mentioned month 10 as an arbitrary cutoff) can feature any race, with more popular races being 2 to 3 times more likely. The chance for Reptoids on a terror mission is average, and for Cerebreals it's small, but it can vary between other missions.