# Is being able to interbreed and produce fertile offspring a transitive relation in biology?

Being able to interbreed and produce fertile offspring is one criterion to decide whether two populations are of different species.

Are there 3 populations A, B, C such that A and B are able to interbreed and produce fertile offspring, B and C are able to interbreed and produce fertile offspring however A and C are not able to interbreed and do not produce fertile offspring?

• @worldsmithhelper: Would you be interested in the general answer on populations or in an answer about species? Commented Mar 28, 2022 at 1:10
• If there exists such populations A, B, C examples with references would be awesome. If there are multiple "reason or mechanisms" for such tripplets of populations emerging examples of each mechanism with some elaboration on the mechanism would be appreciated. If there exists species tripplets A, B, C (and since every species is a population) they are welcome to. It doesn't have to be exactly triplets either quintuples or a continous spatially distributed population which has this property also works. If there is a strong reason or argument why this can't work that would also be accepted. Commented Mar 28, 2022 at 1:24
• A useful example may be modern dogs, you have the chihuahua-great Dane problem, they can't interbreed without human intervention. and that is just breeds of the same species.
– John
Commented Mar 29, 2022 at 0:23

## The ring species conundrum

As commented above, in essence this is the classic case study of ring species, and reading up on it will completely answer your question. A case of ring species is visualizable geographically (area A, area B, area C, and 'variant species' graduating across).

## 'Transitive', jargon and the idea of transition

Sure, something's transitive if A is B, and B is C, and it follows that A is C. But species are not transitive sets (of numbers). It's a bit along the lines of 'mixing'. Say, by analogy, if water dissolves soap, and soap dissolves fat, it does not mean that water dissolves fat. I wouldn't use mathematical terminology in biology (i.e. I would also not call species intransitive or nontransitive, it would not be helpful) but I would rather focus on the concept and word "transition". Lineages evolve and diverge gradually, some remain extant and co-exist with- and sometimes without interbreeding. I think lineages you can talk about in a very robust manner in the long term. The 'species' category is more about 'binning', deciding which section or degree of branching of the lineage you want to consider a unit.

## Imagine the concept phylogenetically

Extant (currently living) canines are a nice example. Those similar can interbreed naturally, those dissimilar cannot realistically or even physically or genetically interbreed. Chihuahuas and wolfhounds or Great Danes could be construed as different species with our classical definition of species, because they truly do not interbreed. Yet they are widely and scientifically today considered the same species! You can surmise that there is difficulty with this classical concept of using 'species', when used stringently and in a strictly categorical fashion... let's consider it from another point of view...

## Imagine the concept though time

If one's ancestors 5 generations back could interbreed with ancestors 10 generations ago, we could 'define' them as a species. Perhaps even those 5 and 1,000 generations back. What about 10,000? What about 100,000? 100,000,000,000? You see, every generation can interbreed with the next, yet at some point we choose to categorize them as different species. You have to understand that we define biological species not because there is such a real thing as a species boundary, but only because it helps us think about things by chunking them arbitrarily together. The concept of species is useful, but not objectively a feature in reality.

I would also refer you to my previous answer on what the definition of a species is and why it's always been problematic. I think that will help with a more complete understanding.

• If you want to give a short summary what one is supposed to get from ring species i can accept the answer. As is the answer doesn't really answer the question but points to resources which do. Commented Mar 28, 2022 at 13:45
• @worldsmithhelper An example may be to look up the classic example the Larus gulls. what we learned is these classical species definitions fall apart in light of modern genetics. they are useful tools of simplification not accurate representations of reality.
– John
Commented Mar 29, 2022 at 0:20
• @worldsmithhelper I believe I've answered your question. Can elaborate when I find some time to spare... but as mentioned, ring species case studies are just an iteration (manifestation) of your abstract question. You asked for an example. There are many to find in ring species, and entire books have been written on this motif. Consider my mentioning ring species as simply grounding the question prior to expanding your understanding of the species concept. I rather think it more suitable to address your (mis)conception that there is such an immutable, exclusive identity such as 'species'!
– S Pr
Commented Apr 1, 2022 at 16:10