but there are some points that simply have to be wrong, and deserve some investigation.
Mathematical models are interesting. In the mid 70's I did research on mathematical models for predicting weather patterns based on observed data points of the atmosphere over the Pacific ocean. It was a great model. But it didn't work because it couldn't account for too many variations. Resolving that problem was so computationally complex that by the time you arrived at a solution, the weather you were trying to predict would have already occurred.
If a mathematical model showed that the common ancestor to all humans lived between 3000 BC and 1000 AD it is missing a key factor in the equations. That key factor it a practical accounting for observed history and human behavior.
Between 3000BC and 1000AD significantly large population of humans lived in South and North America. Most of these had no interbreeding with Europeans, Africans, or Asians until the last 500 years. These cultures were not really open to the potential of wholesale interbreeding until the last 100 years or so, once tribal life had been completely obliterated and the vast majority became assimilated into the modern society. Even so, there are still populations in the Amazon and Eskimo tribes that are isolated from interbreeding.
While a mathematical model can use number progression to show that the DNA can freely pass among the species, it won't account for families that would not allow their daughters to mix with outsiders. Any accounting for this social resistance to biological propagation is a guess, because quality data simply does not exist to properly measure this. Its the same problem I had with weather prediction, a lack of quality data on which to do the math.
In regards to African birds not being able to mate with South American birds, that is simply not the case on the whole or in the large. Cross species propagation has been repeatedly observed of this nature. African bees have militarized passive honey bees. Mallard ducks are inter-breeding with Hawaiian and New Zealand species of duck that are unique, and threatening to make that unique species extinct. There are many, many examples of this.
national geographic articleI could very well be wrong, because I am not doing the math, and am not familiar with the models that are being touted, or how much peer review they have gone through. But it sure seems to me that there is some dry labbing going on here, and the math nurds are not giving due consideration of how hard it is for a smelly, lilly white Calvinist with a penchant for calling a native Americans blaspheming savages to get laid by the same. Since most of the ones that did accomplish the feat did so at the point of a gun, the natural reaction for the tribes would be to move their daughters and wives further away from contact. But how does that calculate in a differential equation or an enumeration model?