so, i've seen some videos about rabbit-squirrel hybrids. i have an interest in this.
something i noticed living in ottawa was that the urban rabbit population was increasing. of course, wild rabbit populations are known to increase and decrease wildly due to predation, but it's hard to see what kind of predation would exist in downtown ottawa. coyotes (and incresaingly coywolves, actually) are known to exist in the suburbs, but there are many serious barriers to moving right into downtown. who knows, though. these animals are shy and good at being evasive. yet, even if there were a few wild coyotes, i couldn't imagine them acting as a check on the rabbit population.
rabbits and squirrels would occupy similar niches in an urban setting. they're also mildly related (i'll get to this in a second). so, we have a situation where i believe hybridization would be more likely than competition, if it is indeed possible.
now, the only way to know if it's possible is to check. i haven't been able to find anything useful with a quick google search and would suspect that such a targeted breeding program would be considered useless. nothing could be gained except a more hardy nuisance species. well, that's exactly the possible evolutionary advantage, though. about the only realistic proof of such an idea would be to find a specimen and test it. it also falls under the category of questions that cannot be effectively disproven, not even with tests.
one of the arguments against this will no doubt be to point out that they exist in different orders, but this is a bad argument. it's circular. species are indeed partially defined by their inability to mate outside their boundaries, but we're learning that the methods used by naturalists (number of teeth, or bone structure) are not remotely conclusive regarding the question of genetic compatibility. all kinds of animals that have been defined as different species are in fact genetically similar enough to mate. rather than argue that they're in different orders (because they look different) and therefore cannot mate, we need to carry out experiments to determine if their differences in physical appearance actually provide enough of a genetic difference to justify putting them in different orders. this process of updating linnaeus to a genetic basis is an ongoing process that in many ways is still in it's infancy.
the tree of life has many pending revisions.
it's currently understood that lagomorphs and rodents are cladistically closely related. that is to say that rabbits and squirrels, while in different orders based on physical traits, are considered to share a relatively recent ancestor. certainly, rabbits and rodents are more closely related to each other than they are to other animals. of all the other mammals, rodents provide the most likely cross-order hybrid potential to rabbits. we simply cannot know until we experiment, or until we find a specimen in the wild.
one clue, though, is chromosome count - and this is actually quite promising. rabbits are at 44, while rodents are at 40. this provides an intermediate point of 42. while it would be most likely if they had a shared number of chromosomes (cat hybrids are possible due to a shared 38 chromosomes across the different subspecies), the second best is an even split. an example of this kind of intermediate argument comes in whale/dolphin hybrids, where everything gets split - chromosomes, teeth number and other features.
i'm not wiling to say it's possible until i see a specimen, but if such a thing were presented i would definitely want to present it as evidence of my alternate theory of evolution. i'm certainly not willing to write it off offhand. the shared common ancestor is too recent, regardless of what the aristotlians classified them as.
i want to clarify the can't disprove thing, because i over-simplified. what i meant was that just taking a few rabbits and trying to cross them with squirrels and seeing it fail isn't rigourous enough to disprove the possibility.
now, if the precise genetic incompatibility could be isolated, and if it could then be proven that this incompatibility is constant throughout one or both genomes, then that's conclusive. then you could say that they're incompatible due to whatever genetic component that is characteristic of all rabbits and/or all squirrels.
otherwise, there's the lingering doubt that this population of rabbits or that population of squirrels has some kind of mutation beyond the shared ancestor that prevents mating. and, in full generalization, it couldn't be anything other than a mutation that would prevent mating - because they share a common ancestor.
so, you need to get into a lot of details before you can rule this out. what you'd want to do is find the most archaic representations of both species to test. and what that even means is difficult to determine without mapping out all the mutations in the first place.
i'm not an expert on rodent or rabbit dna, so maybe that work is further along than i realize. but my oversimplification stands, until the genomes of both species - and the mutations that led to them as distinct species - are fully understood in concrete, quantifiable terms.
it's not as simple as just taking random variables. it's the exception to the rule, the negation of the probability, that is what is being sought, here, to disprove the claim.
it's not just theology that runs into the unicorn problem. it's an issue within science itself.
there's even the bizarre possibility of rabbits back mutating to a more primal state. i mean, fins have become legs have become fins, and there's some suggestion that this has to do with turning things off and on.
if rabbits and squirrels live within close quarters, could rabbits even return to a "genetic memory" in order to breed with squirrels? i'm being teleological. but the epigenetics just might....
regardless, all it would take would be a handful of viable individuals to conceivably create the material to allow for a back-crossing, at which point all linneaen hell then breaks loose.