Is capacity to breed transitive?

Chihuahuas can mate with Spaniels and produce fertile offspring.
Spaniels can mate with Dobermans (Dobermen?) and produce fertile offspring.

As it happens, Chihuahuas can mate with Dobermans and produce fertile offspring. But is this really “as it happens”, or is it inevitable? Is it theoretically possible for members of Population A to produce fertile offspring with members of Population B, and for Population B to produce fertile offspring with Population C, but for Population A to be unable to produce fertile offspring with Population C? And if it is theoretically possible, are there known examples of the phenomenon?

Yes it is possible, and does occur. One way it happens is with what are called “Ring Species” Ring species - Wikipedia - A can breed with B, B with C, C with D, but not A with D; amusingly, Larry Niven has the ring species phenomenon occur on the Ringworld.

Domestic dog breeds (such as those mentioned in the OP) are all the same species, Canis familiaris. Breed ≠ species. So for this example, AFAIK, all domestic dog breeds can produce fertile offspring with any other domestic dog breed. It is a bit counterintuitive but that’s what selective breeding will do for you.

Ed McMahon joke:
Q: How did the Chihuahua mate with the Great Dane?
A: Someone put him up to it.
<rim shot>

Yeah, I’m aware of this… what I was wondering about was the adequacy of using the ability to breed as a definition for species. (That’s what I learned a long time ago: two organisms are of the same species if they’re capable of breeding and producing fertile offspring.) If that definition is correct, the “Ring Species” that Andy mentioned shouldn’t be possible… since an organism can belong to one and only one species, if B’s ability to breed with both A and C implies that both A and C are members of the same species as B, then A and C are members of the same species as each other and should be able to breed. Since we have counterexamples, obviously using breeding capacity as a proxy for species is inadequate. (Thanks, Andy, for that Wiki link… very useful and interesting.)

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Domestic dog breeds (such as those mentioned in the OP) are all the same species, Canis familiaris. Breed ≠ species. …

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I noticed that the OP used the term “population”, but you make a good point.

Out of curiosity, are there naturally occuring species that show the wide diversity seen in domesticated animals like the dog?

Considering it was an Ed McMahon joke I assumed the punch line was going to involve alcohol.

It is a good first approximation. If a creature can produce fertile offspring with another creature, then those two belong to the same species.

Unfortunately, nature is a lot sloppier than scientists would like, and the exceptions which probe the rule can give us all greater insight into how the world really works.

Sorry about the coding errors, I missed the edit window.

Nitpick: Canis lupus familiaris. Modern taxonomical practice is to not recognize domesticated animals as being separate species, but instead a subspecies of their most recent wild ancestor. I think this is because the most commonly used definition of “species” is based on breeding behavior in the wild, but one can’t really say anything about the behavior of dogs “in the wild”.

This is a very common misunderstanding of what the Biological Species Concept means. The real definition is that species are those which do not regularly produce fertile hybrids in nature in places where they co-occur. (More precisely, species are groups of organisms which are genetically isolated from other such groups, that is, there is little or no gene flow between them.)

There are many examples of perfectly good species which produce fully fertile offspring with other species in certain circumstances (especially in captivity) - many species of ducks do so, as do all members of the genus Canis (dogs, wolves, coyotes, and jackals). In the wild, behavioral or habitat differences keep them from interbreeding and hence genetically isolated.

Of course, this definition breaks down for species that do not overlap in distribution. The practice is that taxonomists in these cases regard two forms as being different if they differ as much as other species of the same group that do overlap in range. This is necessarily somewhat subjective.

Nature is, of course, much messier in practice than in theory, and whatever species definition you use you will always have some ambiguous cases. Fortunately situations like ring species are very rare.

Yep. Gene flow is the key. Although you can’t get genetic information directly from a mastiff population into a chihuahua population, you can get it there by going through intermediates, over several generations. Thus they still share the same pool of genetic information.

In ring species, one would have to look at the extent of gene flow through the ring. If the terminal species are able to exchange genes via the intermediate populations, it would be be reasonable to classify them as members of the same species, even though they do not interbreed directly.

Glad to help - Ring species are a good example (in my non-biologist’s opinion) of speciation in progress, and thus useful for explaining to someone how one species becomes two (or more)

This kind of boundary problem demonstrates that species aren’t really a inherent group of nature (contrasted to molecules or atoms or quarks) but are instead a convenience for scientists. Lifeforms can be grouped at many different levels and the boundaries will always be fuzzy. Where the lines are drawn depends on what the scientist wants to work with.

Right; as it is genes can flow throughout the entire ring, so they can all be considered one species, but if something happened to wipe out the populations in the middle, gene flow between the ends would be halted, and so you’d then have two species.

Of course, it’s an illustration of the fact that “nature is messy”, that two populations can go from being the same species to different species without anything actually happening to the two populations in question.