Version française

The border between species and races seem increasingly slim.

We can refer to Wikipedia (which I think is the most appropriate modern tool and the easiest way to check for everyone – even if my references are in French with bad translation):
The most commonly cited definition is that of the biological concept of the species stated by Ernst Mayr (1942): “Species are groups of natural populations, actually or potentially inter-fertile, which are genetically isolated from other such groups” . In this definition, it was then added that this species must be able to produce viable and fertile offspring. Thus, the species is the largest unit of population in which gene flow is possible in natural conditions, individuals of a same species are genetically isolated from other equivalent sets of reproductive point of view.

http://fr.wikipedia.org/wiki/Espèce

The definition of race, or subspecies, is:
In a given species, a subspecies is a group of individuals who are isolated (for geographical, ecological, anatomical or organoleptic reason) and changing out the genetic current of indicated species. After a while, this group of individuals take specific characteristics that set it apart from the reference species. These characters may be new (after a mutation, for example) or the setting of a variable characteristic in the referred species. Subspecies are often able to reproduce between them, because their differences are not (yet) sufficiently marked to constitute a reproductive barrier.

http://fr.wikipedia.org/wiki/Sous-espèce

If the difference between species and subspecies seems to be cross-fertilization, it will go against some property acquired knowledge.
Species do not mix naturally, but may do so under domestication, or under coercion. Coercion caused by human, or a lack of choice.

We can observe the fertility of their hybrids.

a. The case of Grolar or Pizzly

An example is the recent case of mixing between polar and grizzly bears, two different species of bears. These bears hybrids were mixed in nature because the grizzlies move into the territory of polar bears due to melting ice. If we follow the strict sense is the definition of the species, these hybrids would be sterile. If all cases are obviously not studied, there is evidence for the fertility of these, at least in the fertility of female hybrids, which is also easier to check (bear cub: successful breeding).
The first second-generation hybrid has been identified by DNA testing in April 2010. Here is an excerpt from the article by CBC News, 30 April 2010
(To read the entire article please refer to the link that follows.)

Bear shot in N.W.T. was grizzly-polar hybrid
Could be first 2nd generation hybrid found in wild

Last Updated: Friday, April 30, 2010 | 6:53 PM CT CBC News

« Biologists in the Northwest Territories have confirmed that an unusual-looking bear shot earlier this month near Ulukhaktok, N.W.T., was a rare hybrid grizzly-polar bear. »
(…)
« Wildlife DNA analysis shows the bear was a second-generation hybrid, officials with the N.W.T. Environment and Natural Resources Department said in a news release Friday.
The bear was the result of a female grizzly-polar hybrid mating with a male grizzly bear, according to the department. »

http://www.cbc.ca/news/canada/north/story/2010/04/30/nwt-grolar-bear.html?ref=rss

Best known, breeding of pig and wild boar also called in french « cochonglier » or « sanglochon »; the mixture of dog and wolf, which even gave the race of dog or Czechoslovak wolf-dog or saarlos wolf-dog.

Then, pigs and wild boars, if the definition is taken literally, species or races? Dog and wolf, species or races? Many examples can be added to that.

b. The case of Tiglon or Tigon and Liger.

An astonishing example and particularly interesting to our study is the mixture of the tiger and the lion.
The tigon is an artificial hybrid from the crossing of a male tiger and lioness.
The liger is the artificial hybrid from the crossing of a male lion and a female tigress.

The liger and the tiglon are very different products but they are relatively fixed:
By size, Tiglon do not exceed his parents. It may have dark spots (lion genes) and streaks. His mane is shorter than that of the lion.
The liger is the largest of all cats. It can weigh over 400 kg, that is to say the weight of its two parents together (!). Its fur is light brown with eyespots and his mane is short.
We will consider later the reasons for these major differences, and their consequences, as this example will follow us throughout this chapter. Let us talk about their fertility:

Quote from Wikipedia. Keyword: Liger
The fertility of hybrid big cat females is well documented across a number of different hybrids. This is in accordance with Haldane’s rule: in hybrids of animals whose sex is determined by sex chromosomes, if one sex is absent, rare or sterile, it is the heterogametic sex (the one with two different sex chromosomes e.g. X and Y).
According to Wild Cats of the World (1975) by C. A. W. Guggisberg, ligers and tiglons were long thought to be sterile: In 1943, a fifteen-year-old hybrid between a lion and an ‘Island’ tiger was successfully mated with a lion at the Munich Hellabrunn Zoo. The female cub, though of delicate health, was raised to adulthood.[8]

http://en.wikipedia.org/wiki/Liger

These hybrids can be fertile, but once again, only the females are, the males remaining in an intermediate state of development, which does not lead them to a fertile puberty. The female liger or tiglon can therefore not be crossed with a male liger or tiglon (which would make these hybrids new species), but with a tiger or a lion.

We note with these examples, that the boundary between species and race seems very thin, and that mixing between species are often against nature (not instinctive, but forced by human, lack of choice, or domestication) but possible in some cases. Hybrids from these crosses are, either totally or relatively fertile (cochonglier, Czechoslovak wolf-dog or saarlos wolf-dog) or half fertile (only the female is, and can breed with a male from a specie which it is derived).
This is not essential for our study, so we’ll do a small note, but still say that the track of the chromosomes seems to be better to explain why a mix is fertile, infertile or sterile. In general, the hybrids will be anyway less fertile than their parents.