Language is a rather tricky thing to study. Sure, we can look at the anatomy and infer our ancestors spoke; but figuring out what they said is next to impossible. Until they started making a note of it themselves we can't really make any conclusions about it.
Researchers have tried to circumvent this issue by treating language as you would any other biological object and applying evolutionary principles to it. These results have been pretty successful; although we keep running into a brick wall: we can only study what we can examine, and we can only examine modern language. Thus our ability to look at the evolution of language before a few thousand years ago just vanishes.
All of this raises the question: how much can we learn from this approach? Is it even possible to look at the "evolution" of modern language and study it's origin? To study this a team recently conducted one of the largest language studies ever, examining the phoneme (i.e. noises that make up a language) variation of more than 2,000 languages. Their goal: compare language evolution to genetic evolution to see how far back we can go.
The results
The results of this investigation were both fascinating and frustrating. On the one hand, they revealed some interesting ways in which language and biological evolution are similar. However, they also discovered that there were enough differences between the two to mask "early" language evolution. No figuring out what cave men spoke, sorry.
And what were those key differences? Well, it's mostly the fact that language evolves a lot faster than genes; rapidly hiding the evolutionary "signal" from before. But perhaps more importantly, that linguistic evolution can take place without the addition of outsiders. An isolated genetic population will typically decrease in diversity (mutation not being enough to counteract the effect of people dying off), but their language will show no such decrease. In fact, it will often increase in variety, relative to similar languages. If anything, being surrounded by people will slow down language variation.
But what of those similarities between language and genes? Most of them you could probably guess, being linked to geography. The closer two groups are together, the more similar their genes and language will be. Nothing too shocking here.
Conclusion
Over short time frames, applying evolution to language isn't an awful approach. However, over time the differences discussed above add up; to the point where any old evolutionary signal is completely lost. The study, for example, found no trace of that out of Africa migration which dominates our genetic lineage.
References
Creanza, N., Ruhlen, M., Pemberton, T. J., Rosenberg, N. A., Feldman, M. W., & Ramachandran, S. (2015). A comparison of worldwide phonemic and genetic variation in human populations. Proceedings of the National Academy of Sciences, 201424033.
