I'm familiar with the concept of hybrid infertility, but my question is: Are ALL hybrids infertile, or is it just so extremely unlikely that the chances are basically nil that they can actually produce a viable sperm/egg?
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The whole problem is based upon your definition of hybrid and therefore your definition of species. If a hybrid is the offspring of two individuals belonging to different species and if we define species based on reproductive isolation, then a hybrid can, by definition, not be fertile.
However, we often call two lineages as being two different species even if they can reproduce. To get into more difficulties we could differentiate between pre-zygotic and post-zygotic reproductive isolation assisted reproduction.
You should definitely have a look at the post How could humans have interbred with Neanderthals if we're a different species? for a discussion on the concept of species.
In practice we often call two lineages as different species even though they are not reproductively isolated. In such cases, yes hybrids are fertile. In fact, hybrid can even have a very high fitness, a phenomenon called heterosis (aka. hybrid vigour). A historically important example is one described by Darwin in The Variation of Animals and Plants under Domestication; the hybrids between the common pheasant and domestic fowl are larger nd more resistant than both parents.
Note also, Haldane's rule that states
if in a species hybrid only one sex is inviable or sterile, that sex is more likely to be the heterogametic sex. This is for example the case of the Yakalo (hybrid of yak and bison).
There are also cases where the hybrids are reproductively isolated from both parent species and end up creating a third species. This is called hybrid speciation.