If two individuals can mate and produce fertile offspring does that make them the same species

That's the geneticist's definition, which is all but useless. It won't work for fossil forms nor for ones reproducing asexually. Sometimes, members of the same species cannot produce fertile offspring. Google "Rassenkreis" or "ring species" or consider a chihuahua and a great Dane. In contrast, some minnows are quite interfertile across generic lines.

BTW, rarely, mules are fertile, if they happen to be polyploid. Some people consider dogs and wolves to be the same species; some do not. Coyotes can breed with dogs too. I have never heard anyone consider lions and tigers to be the same species.

Nope. The most common definition of species for sexually reproducing organisms is called the biological species concept (BSC). It was first established by Ernst Mayer and Theo Dobzhansky in the 40's. The idea that members of different species can't produce fertile offspring is an oversimplification of the BSC.

In actuality, the BSC defines different species as possessing genetically based reproductive isolating mechanisms (RIMs) that prevent significant genetic interchange with populations outside the species. One example of such a RIM would be inability to produce fertile offspring, but there are many other less effective RIMs that can still work to prevent significant genetic interchange. For instance, different species could have different courtship rituals, or breeding areas, or breeding times, or pheromones. It's theoretically possible that humans and chimps might on rare occasions be able to produce fertile offspring together, but that wouldn't make them the same species, because the strong mate preferences of both species prevent significant genetic interchange. On the other hand, whereas chihuahuas and great Danes don't have significant genetic interchange directly between each other, each breed does have significant interchange with similar sized breeds, which then have significant interchange with other similar sized breeds, such that the entire group of dog breeds acts as a single ring species. http://en.wikipedia.org/wiki/Ring_specie… Eliminate all dog breeds except for chihuahuas and great Danes and suddenly you'd have two separate species of dog that didn't exchange genes to any significant degree.