| MadSci Network: Genetics |
When you cross two organisms to make a "new" organism, the new organism is called a hybrid. Hybrids can be formed by cross breeding two different breeds, races, variants, or species. The nature of the hybrid can be used to determine the relationship of the two parents: if the hybrid is able to reproduce, then the parents were both members of the same species; if the hybrid is sterile (unable to reproduce), then the parents were members of different species.
The first type of hybrid, the crossbreed, is very common. If you cross a broccoli (Brassica oleracea) with a cauliflower (Brassica oleracea) you get a "broccoflower" which can be planted, grown, and harvested just like its parents. Similarly, if you cross a Cocker Spaniel (Canis familiaris) with a Poodle (Canis familiaris), you get a "Cockerpoo", one of the more common mutt breeds in america. Since both parents belong to the same species, the offspring belong to that species, i.e. all dogs are very closely related, no matter how different they look.
The second type of hybrid, the true hybrid, is much less common, because it is unusual for two different species to be closely enough related. The example you gave is a good one: a mule is the offspring of a male donkey (Equus asinus) and a female horse (Equus caballus); all mules are sterile, so the only way to make more mules is to cross more horses and donkeys. If you cross a female donkey and a male horse, you get a hinny, which is also sterile. There are also some hybrid plants, like hybrid roses, which can only be reproduced from clippings of the original plant and don't produce viable seeds.
In both cases, the two organisms crossed must be very closely related to produce any offspring. Generally this means that they must at least be in the same genus, although often that is not even enough. In the same way, crossing animals from different genera will not produce offspring, and certainly crossbreeding an animal and a plant is impossible.