The solution to this contradiction involves two simple observations of the record given in the book of Genesis. First, the generations close to the flood had longer lifespans than we do today. And second, these generations had higher birth rates than we do today. When we combine these two observations, we can easily see the possibility that the population at the time of Abraham would be significantly higher than just 136 individuals, but the Bible actually gives us enough information to make some very reasonable estimates of just how much larger.
Genesis 9:28 tells us that Noah lived 350 years after the flood, so he was still alive at the time of Abraham's sojourn in Egypt (Abraham was still under 100 at that time - Genesis 21:5). According to Genesis 11, Shem lived 502 years after the flood. In fact, all the firstborn sons from Shem to Abraham were still alive at the time of Abraham's birth. This statement is limited to the firstborn only because they are the only ones for whom the Bible gives us the length of their lives. It is therefore not improbable to conclude that most of the other sons enjoyed similar lifespans, nor is there any reason to assume that this length of life was limited to the generations of Shem. Japheth, Ham, and their sons most likely were alive at the time of Abraham as well.
Now, of course, most skeptics claim that the long life spans recorded in Genesis are fictitious, but that claim does not take into account the fact that these life spans correspond to an exponential decay curve that would be very difficult to fabricate. This fact has been documented in several papers, but an excellent overview of it can be found on Dr. J. Wile’s blog post “Patriarch Age and Genetics.”
Higher Birth Rate
There are 70 descendents of Japheth, Shem, and Ham mentioned by name in Genesis 10. Arphaxad and Salah each have only one of their sons mentioned, but we know from Genesis 11 that they each bore at least two giving us a minimum listing of 72 sons in Genesis 10. There are 14 fathers listed in this chapter which would give us an average of 5.14 sons per father. If we assume 1:1 ratio between sons and daughters, then this would give us an average of 10.28 children per father. This may seem a bit excessive until we consider that Abraham, who did not begin fathering children until he was 100 years old, is recorded as having at least 8 sons (Genesis 25:1-6).
Putting it all Together
There are 9 generations listed for the line of Shem in Genesis 11. If we assume that there were no deaths within the first 250 years, and if we assume that each man fathered 5 sons, then we can calculate the size of Shem’s family by 5 times itself 9 times. This gives us a total of 1,953,125 male descendents of Shem at the time of Abraham. If we do the same for Japheth and Ham, we arrive at 5,859,375 males. Then, if we assume a 1;1 male to female ratio, we arrive at a world population estimate of 11,718,750 people at the time of Abraham. 11 million people would be more than enough to account for the heavy population which is apparent in the Genesis account.