DISCUSSION
The genealogy in Exodus chapter six always puzzled me. The count of Jacob’s descendants was 70 when they entered Egypt (Genesis 46:26), and the men numbered 600,000 when they exited Egypt (Exodus 12:37). But in Exodus 6:16-20, there are only two generations from Kohath (who is counted in the 70 immigrants in Genesis chapter 46) to his grandson Moses, who led the 600,000 out of Egypt. How can a population grow from 70 to 600,000 in just two generations? I decided to develop a population growth model to see if this is plausible.
I’ll begin the explanation with considering who is included in those counts. The original 70 did not include women who had married into Jacob’s family – the only woman who was included in that count was Dinah, Jacob’s daughter. Maybe Jacob’s wife Leah was counted too – see Genesis 46:8-15. But that is a minor detail when you consider that nothing is said of the number wives Jacob’s 12 sons had, nor do we know how many of Jacob’s listed 52 grandsons had wives too. We do know from Genesis chapter 46 that two of those grandsons already had sons themselves when the family moved to Egypt. I chose 85 for the total count for when the family moved to Egypt.
The 600,000 who exited Egypt are explicitly described as men only –not including women and children. The verse that follows that figure says “Many other people went up with them”, which begs the question – are these others included in the count? Two years later a census was taken at Mount Sinai. This census counted the military aged men (20 years and older) from the tribes and the total came to 603,550. But that count deliberately left out the Levite clan. The count of all Levite males over one month old came to 22,273. While this makes the 600,000 figure look like a rounded number, it’s clear that the figure refers to only Jacob’s descendants. It’s difficult at this point to estimate how many children to add to the 600,000 to get to a grand total at the time of the Exodus, but the total number of Jacob’s descendants including women and children could have easily been more than 1.5 million. The numbers problem looks even tougher.
Fortunately, there’s a mitigating factor to the challenge of explaining the rapid growth in numbers of Israel. Two generations for the period of growth is not the rule. For one thing, Moses was 80 years old when in the Exodus, so that’s enough time to add two generations to the count. Also, while Moses was separated from Jacob by four generations; his older brother, Aaron, married a woman (Elisheba) who was six generations from Jacob. So the number of generations between Jacob’s arrival and the Exodus is ambiguous. What really counts is the number of years elapsed.
Nominally, Israel was in Egypt for 400 years (Genesis 15:13). But this is full of caveats. Read http://www.bibleinsight.com/crn1p5.html to see how confusing this gets. To keep this simple, I’m going to put an upper and lower limit on the time the people of Israel were in Egypt. I’m going to work with the endpoint of that 400 years landing on the Exodus, when Moses was eighty years old.
The upper bound on that period comes from the short genealogy for Moses in Exodus 6:16-20 which says his father lived 137 years and his grandfather Kohath (who was one of Jacob’s grandchildren who was among the immigrants) lived 133 years. So if Kohath was a newborn then, and Moses’ father, Amram, was born right when Kohath died, and then Moses was born right when Amram died, then the total time in Egypt would amount to 137 + 133 + 80 = 350 years.
The lower bound on that period starts the 400 year period when Abraham left Ur of the Chaldeans. From Genesis chapter 12, we know Abraham was 75 years old then. Using the ages of the patriarchs given in the Genesis record, we can calculate that 215 years had elapsed when Jacob and his family went to Egypt. So the lower limit would be 185 years.
THE MODEL
The model I developed is definitely an amateur model. No probability distribution curves were used and the variables such as survival rates and birth rates are assumed to be constant. It works by using a year-by-year calculation of the total population. What I did was divide the population into three cohorts: children, adults, and elders. The age boundaries between the groups is defined by the age range over which women give birth. Within that range, both men and women are counted as adults; before that age range, they’re counted as children; and after, they’re counted as elders. People are born into childhood, and “graduate” into adulthood and later graduate into elderhood. Deaths among children are calculated by dividing their total number by the length of childhood in years, and then multiplying by the mortality rate (100% minus survival rate percentage). Adult deaths and elder deaths are calculated in the same way, except the mortality rate for elders is 100%. Annual births are calculated by taking the number of female adults (half of the adult count) divided by the span of adulthood in years, and then multiplying by the birth rate expressed as births per woman.
I initialized the model with the birth of the 12 sons of Jacob –one born each year over 12 years- along with the assumed birth of their wives. Jacob, Leah, Rachel, Bilhah, and Zilpah are not included. T he 12 sons and their wives are then allowed to propagate normally through the model, but without any fatalities until they become elders.
The model in Excel format can be downloaded here: PopGrowth.xls. Sheet 3 gives you the opportunity to play with the numbers and see the results. Sheet 2 has data for some different birth rates and Sheet 1 is where the year-by-year calculations are performed.
RESULTS
If the childhood and adulthood survival rates were set at 98%, life span set at 80 years, and adulthood set from 20 to 35 years, the birth rate would have to be about 10 births per woman to make the 185 year limit. Nearly three-quarters of the population would be under 20 years old and the total Exodus population would have been 4.4 million.
Using the same numbers and adjusting only the birth rate, it would require about 4.5 births per woman to make the 350 year limit. About half the population would be children and the total Exodus population have been 2.5 million.
From the World Bank, the annual world population growth rate has slipped below 1.2%. It was above 2% in the early 70’s. The annual growth rate in Egypt for the 185 year period is nearly 6%, and the growth rate for the 350 year period is almost 3%. A birth rate of 4.5 per woman (the rate for a 350 period in Egypt) is not unheard of. There are 27 countries listed by World Bank that have rates that equal or exceed this rate; the highest being Niger with a rate of 7.0 births per woman. But infant survival rates in these countries are below 96% – meaning that infancy (not childhood) fatalities are 4% and above; much higher than the 2% rate used in my model. Some of these countries lose close to 8% of their babies. The birth rate of 10 per woman appears to be outlandish in comparison, but I’ve met people who have grown up with a dozen siblings. But then again, could you imagine living in a place where families of that size is the norm and 73% of the population is 20 and under? But after all, I don’t think Moses was kidding around when he wrote in Exodus 1:7: “….. the Israelites were fruitful and multiplied greatly and became exceedingly numerous, so that the land was filled with them.”