I'll explain it how it was taught to me. I don't really like analogies but this one works on a simple level.
Think of Sapiens as Europeans in the 1600's, and Neanderthals as Native Americans of the same century.
The replacement (or Out of Africa) theory, which is what's widely accepted in paleoanthropolgy, is similar to what happened in early America. Europeans migrated from their home continent and replaced the Natives as the dominant population at their new "home". This replacement happened in part through disease and superior technology that allowed them to better adapt to their environment.
The analogy to the continuity hypothesis goes like this: Europeans migrated to America, and the decline of the Native population is explained primarily by an interbreeding of the Natives and the Europeans, with the Native traits gradually recessing--but not going extinct--to the dominant European traits. So instead of one population group replacing another through adaptive dominance like the above theory, this hypothesis explains the decline of the Native populations through the two groups having a ton of sex with each other, and this influencing the genetics in a way that's unique from the old location.
These two models don't need to be a dichotomy though. We know that Europeans virtually wiped out the Native population through disease and technology, but we also know that some Europeans were having sex in wigwams. It's a matter of scale, and the difference between the two models is how far they tip in either direction.
Why I say the continuity hypothesis is not complete junk science, like Intelligent Design, is for a few reasons. One, is that there's a small but still existent presence of genetic contributions from now-extinct population groups. I think the high number is about 15%?
Also, our DNA extraction technology is constantly improving, same with our carbon dating methods, to give us a less muddy picture of data than we've had before... and this recent data has shown Neanderthal contributions to non-African modern human genes to be a non-zero number.
My position is in line with what the science strongly suggests: that a wave of homo sapiens sapiens migrated from the Horn of Africa area, and over the course of a reallyfuckinglongtime we spread across the entire globe, being the fittest and best brand of humans at adapting to the local environments--better than the local populations. And this doesn't preclude some interbreeding between the migrants and the natives--although the DNA evidence doesn't support this being the primary reason for our conquest of the planet.
Plus, the longer a population group exists, the more genetic diversity they'll develop. So the population group with the most genetic diversity would be the one that's been around the longest. Modern African populations have the most genetic diversity than any other population on the planet, so...
And finally (I'm almost done), I think that there's not enough data to make a definitive conclusion about how much any interbreeding from back then effects our different human cultures today.
The racial supremacists don't care about the ambiguity of our current knowledge in this area--they overplay any possible effects of any interbeeding that took place areallyfuckinglongtimeago, and downplay the effects of cultural and behavioral reinforcements that happened because of the tens and tens of thousands of years of geographic isolation between population groups.
There have been some finds in south I think, China, that appear to be a combination of Sapiens and Erectus traits... we don't know yet, but as of right now it's possible that East Asian populations today may have a larger amount of genetic influence from their ancient locals than other population groups on the globe.
Hope this helps.
/sore fingers
