I am reading a book called "Sapiens" and it tells the story of humankind. So far most of it has been about neanderthals and the other species of humans who existed at the same time. Eventually, all but one species went extinct and homo sapiens (us) made it to the top of the food chain.
These species, such as neanderthals and homo erectus, existed two million years ago.
What is the Orthodox explanation of this?
Back to the OP - according to Orthodox Tradition, Neanderthals...<complete the sentence>
There really isn't any Orthodox Tradition concerning Neanderthals. Someone floated the idea of the Nephilim earlier, but I think that is a stretch, and is more of a proof text attempt at reconciliation. Science has asserted a relationship between "modern" humans and what they define as our cousins and/or ancestors. Maybe, maybe not - but either way there is no theological reason to protest the idea that thing A, through a process of "natural selection" became thing B. Put a pin in that.
The age of the earth and/or universe always seems to be a sticking point in debates on evolution. I suggest we treat it as a completely separate issue. There are really only 2 choice - the earth very young (7500 year or so) or the earth is very, very old. The idea that the earth is young is based solely on the first creation narrative, coupled with the genealogies in scripture. There is zero observed physical evidence that would support this theory. The idea that the earth is very, very old is based on a multitude of physical evidence from every discipline of science, but does this contradict scripture and/or Tradition? Absolutely not. Knowing what we know now, I think it's actually an abuse of scripture to argue otherwise. The Young Earth counting methodology that use scripture to arrive at a number is answering a question that had never been asked. In other words, Genesis never intended to offer a scientific data point when it said, so-and-so begat so-and-so in their 150th year.
But what about the fall? Well, that actually is not part of the 6 day narrative. The 6 day narrative has multiple purposes and subjects, but the fall is not one of them. The story of the fall, or perhaps more appropriately, Man's relationship to God, Woman & creation, we must look to the 2nd creation narrative in Genesis - which give NO time data, and even mixes things up significantly from the 1st narrative. What if we used this narrative to date the earth? Wouldn't that be silly since it's obviously not the point? In any case, this is where we find the story of the fall. So WHEN did the fall happen? Difficult to say - in terms of "timelines" it seems to contradict even the 6 day narrative, yet some seem to hang their hat on this inflection point in history as the reason an "old" earth doesn't hold up to Tradition.
So back to evolution - I find no reason to doubt that earth is very, very old, so the time element is there. At a minimum, we must admit that it's plausible. But is it true? I don't know. I have my doubts honestly. There are many questions that still need to be answered. Maybe those answers will support evolution, maybe they will lead somewhere new - either way, I don't see how denying the theory outright, based on bad theology, is helpful.