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There are many definitions of "species" which usually take the form

Two individuals are of the same species if ...

An implied (rarely made explicit) property of any sensible species definition is that the relation "is the same species as" should be an equivalence relation (the reason why this is sensible is that only such a relation partitions the set of all individuals into equivalence classes, that is, separate species). In particular, it should be transitive, that is

If A and B are of the same species, and B and C are of the same species, then it follows that A and C are also of the same species.


It appears to me that all species definitions in use violate that property.


Example

Are the Chihuahua enter image description here and the Great Dane enter image description here of the same species?

Not according to the "biological" species definition, which states:

Two individuals are of the same species if and only if they can produce fertile offspring.

Since that is (presumably) not true of Chihuahua and Great Dane, according to that definition, the two dog breeds are not of the same species.

However...

Let us say that the Chihuahua can produce fertile offspring with the Dachshund...

enter image description here

... and the Dachshund with the Golden Retriever...

enter image description here

... and that at last with the Great Dane as desired.

Then, if we assume transitivity, Chihuahua and Great Dane are of the same species - contradiction!


Another Example

Are the Chimpanzee enter image description here and the White Oak enter image description here of the same species?

Intuitively, they are of course not, the very idea seems ridiculous. Sure enough, with the definition (a variation of the "genetic" species definition)

Two individuals are of the same species if and only if their genome differs in less than 0.5% of base pairs.

the two are indeed not of the same species.

However, we can again construct a "chain" of intermediate individuals, each of which is similar enough to its predecessor to satisfy the definition, eventually connecting Ape and Tree and violating transitivity again.


My question to biologists: How is this problem resolved in practice? Are there any species definitions that preserve transitivity?

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    $\begingroup$ Does the criterion "produce viable offspring" include physical reasons? I'm assuming that the Chihuahua and the Great Dane could produce viable offspring by artificial insemination. Since species is a genetic term this is what matters. Otherwise you might say that a Great Dane in the USA and a Great Dane in Europe are different species because they cannot mate (due to physical separation). $\endgroup$
    – Alan Boyd
    Commented Nov 2, 2013 at 12:57
  • $\begingroup$ @AlanBoyd: Interesting question, I don't know the answer. It is, however, irrelevant to the presented problem of transitivity, which would still apply when more remotely related individuals are chosen (and also applies to other species definitions, such as genetic similarity). $\endgroup$
    – user4810
    Commented Nov 2, 2013 at 13:03
  • $\begingroup$ Added another example using a different commonly used type of species definition. $\endgroup$
    – user4810
    Commented Nov 2, 2013 at 13:14
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    $\begingroup$ I'm not convinced that you could form a chain of connectivity between a plant and a mammal using the criterion of 0.5% sequence divergence. In fact if you started with a human you would fail at the first hurdle (approximately 1% difference from human to chimp at the most conservative estimate). $\endgroup$
    – Alan Boyd
    Commented Nov 2, 2013 at 14:28
  • $\begingroup$ I think there could be a viable question in here, but you've started with some false equivalencies. The answer to your questions is clearly "yes" as it's been shown that both statements you took to be false are indeed true. $\endgroup$
    – Amory
    Commented Nov 2, 2013 at 14:49

2 Answers 2

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I am pretty sure you cannot jump from an oak tree to an ape with whatever common definition of species you're using. But this is some kind of practical implication of your question.

The concept of species was already being used by Aristotle and was kept up to now although the grouping of living things into species might not be a clever thing to do. I don't think there is any non-arbitrary, logical way of making groups out of living organisms. Here is a podcast (It is in French, sorry!) that is interesting for those wanting to learn about how the concept of species evolved.

The case you describe is called Ring species. There has been lots of discussion in philosophy about the concept of species. The concept of species is unclear and if accurately defined, then in practice we don't really follow this definition to improve efficiency in how we name lineages. The term lineage has a much more rigorous meaning and is often of greater usefulness.

Ensatina eschscholtzii (a salamander; see DeVitt et al. 2011 and other articles from the same group) is a classic example of ring species.

You should definitely have a look at the post How could humans have interbred with Neanderthals if we're a different species? which discuss the concept of species. Some other sources of info include:

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    $\begingroup$ "Species" is a human rule-of-thumb, often useful but having indefinite boundaries and not a thing that actually exists. See this short section of the Wikipedia article mentioned above for a good summary. $\endgroup$
    – mgkrebbs
    Commented Nov 2, 2013 at 19:20
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Membership of nominal species is certainly an equivalence relation. For instance, membership of Canis familiaris, or domestic dog. Dogs are not wolves, and wolves are not dogs. But all domestic dogs are the same species. But of course, some taxonomists recognize the dog as a subspecies of the wolf, as in Canis lupus familiaris. In that case, dogs and wolves are members of the same species. So it just depends on whose definition you are using.

Reproductive compatibility is not an equivalence relation, as you correctly note with respect to Great Danes and Chihuahas. It is not always transitive.

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