Why do they? When you get back to a singularity, you are outside of time. Time does not exist. Evolution does not deal with events before the big bang and the start of wordly time.
Yeah, it really does. Biological evolution is a consequence of the evolution of matter, is it not?
I used the word "singulartiy" not in the sense you're referring to, from the standpoint of Physics. I was using it in the sense of causes and first cause being unique and unrepeatable.
A species, being unique, can only evolve or be created once. It is a singular event.
Confirmation or "proof" of scientific hypotheses depends on the repetition of experimental results. It is the nature of some hypotheses to be outside the realm of experimentation, and I think Evolution is one. Small scale experimental standards of scientific proof aren't really applicable to issues of vast time scales such as evolution or cosmology.
That's why I suggested the phrase "Postulate of Evolution" above. "Big Bang Postulate" would be another.
A species, being unique, can only evolve or be created once. It is a singular event. I'd like to suggest that, like many who argue about this issue, you are struggling with a false picture about speciation.
Fixed speciation, with long-fangled latinate names is a manifestation of the zoologist's desire to organize things into neat little boxes. We do not, in fact, think that species suddenly give rise to each other in a single generation, through a single remarkable event that needs an extra-ordinary explanation. Fixed species are just a set of still photo slices of an everchanging phenomena. And in fact, we have current examples of the sliding speciation scale. Such as Herring Gulls. Pick any 3 points on the continuous scale that species with names represent a still-life of, and you could get relative speciation unrelated to the naming conventions.
That is, A could mate successfully with B, but not with C, and C with B, but not with A. And none of this may be relevant to actual named species on the scale.
No great leaps required here, so speculation about odds against--or lack of capacity to determine odds against--is off-subject.