Taint is the mechanism that causes tier jumps in breeding and can also be used for tier skipping.
For starters, the offspring resulting from the breeding of two critters that are linked on the breeding chart, found here, will be tainted. "Linked" is a reference to two critters that will eventually make a critter of the next tier when bred. For instance, a wolf and moth that are bred together will create a tainted wolf or a tainted moth, with this offspring being tainted towards becoming a spider.
To remove taint from a critter, you must breed said critter with a critter that it is not linked, such as a tainted moth with a bird or a lizard. If the result is the same species as the tainted parent, then it is still tainted. However, if the resulting critter is species of the untainted parent, then the new critter is not tainted.
Unpredictability of Taint
A critter whose bloodline is tainted with too many species can cause abnormal offspring to develop. For example, it has been reported that two crocodiles have made a hydra. This is usually caused by the carelessness of the user to eliminate the taint by breeding with an unlinked critter. Exactly how to control such a tainted critter is unknown, but based on this theory, it is hypothesized that it is possible to create any different species of critter from another by correct tainting.