The Problem with Species
Back at school you will learn that a species is a group of animals who are close enough on the evolutionary tree to be able to breed and have fertile offspring. So for instance a horse and a donkey are not the same species, because although they can produce a foal, which is called a mule (or a hinny depending on the genders of the parents), it will be infertile. This definition seems quite neat but I'm going to highlight some of the edge cases which make the definition of species just as fuzzy as everything else in Biology.
Firstly the relationship “can have fertile offspring with” is not associative. There exist animals where animal A can breed with B and B can with C, but A cannot with C. By definition this means that A and B are the same species, as are B and C, but A and C are different species. This tends to happen when there is a geographical divide large enough that A and C don't come in contact with each other, but the B population occasionally breeds with members on each end and is particularly common with migratory birds.
If the species covers a long enough distance then it can be that the ends loop around the world with the two incompatible ends meeting again at the same place. These are called ring species and we can see in the diagram below the layout of the Larus Gull where each subspecies can breed with the ones on either side, but 1 and 7 are too genetically removed.
Here is another example of ring species with Greenish Warblers where this time the ring is formed around the impassable mountains rather than the polar region:
New species form by initially having some natural variations in the population and then some sort of barrier comes which splits the group into two so that they no longer interbreed. Eventually the natural mutations will make enough cumulative changes so that the two halves cannot rejoin as one species even if they encounter each other again. This barrier could be another from a river to continental drift or simply a large distance between the group as above.
A similar edge case comes when considering evolution of a species through time. You are the same species as your parents. You are also the same species as your great great great grandparents. However you are not the same species as your ancestor going a million generations back. At what point are you not the same species? There must exist two ancestors of yourself, one further back than the other where they could have breed together and where you could have bred with the nearer of the two, but not with the other. This situation is similar to the first problem, but with the barrier to breeding (which drives divergent evolution) being time rather than space.
Yet another problem with this definition of a species is that there are many animals where we just aren't sure whether they would produce fertile offspring. If they aren't based in the same place, similar animals could well be able to breed and it is impractical for humans to introduce every feasible animal with every other feasible animal to check. In this way a statement of two animals being a single species is a hypothesis rather than a fact.
A final problem with species comes from trying to use the ability to produce fertile offspring together as a method of determining the same species on life that reproduces asexually. Clearly there should be subcategories similar to species with these fauna (especially as most species do reproduce asexually so they are very much the norm), but it is hard to come up with one which catches everything that we want and nothing that we don't. In doing research for this article I've come across a couple of dozen definitions and in practice biologists seemed to use whichever seems to fit with common sense. Deeply unsettling Biology, I'm not impressed.
The problem has been noted for a long time and I like this quote from biologist H. A. Nicholson, “No term is more difficult to define than “species,” and on no point are zoologists more divided than on what should be understood by this word” 1872.