Creation Moment 6/24/2017 - Biblical Population modeling

And God blessed them, and God said unto them, Be fruitful, and multiply....

Genesis 1:28

"The Bible presents several historical scenarios in which the human population grew from very small numbers. These include the initial populating of the world starting with Adam and Eve and the repopulating of the earth from three founding couples after Noah’s Flood. There were also multiple small-scale duplications of these events within the many post-Babel populations, including the growth of the Hebrew nation from Jacob and his twelve sons. Most modern commentators on the subject of biblical demographics have assumed a smooth increase in the population over time, but small populations do not tend to grow in an algebraic manner. We wanted to analyze many different biblical scenarios, so we created a population modelling program in the C# programming language that could handle multiple variables like age of maturation, minimum child spacing, and age of menopause, as well as probabilities like polygamy, twinning rates, and a variable risk of death according to age. We were able to demonstrate that the current world population and the

size of the Exodus population are easy to account for under most parameter settings. The size of the antediluvian and Babel populations, however, remain unknown.

While we do not know what environmental challenges the antediluvian and immediate post-diluvian populations faced, human populations have the ability to grow quite quickly. Based on numerous examples from recent history, we expect the early post-Creation and post-Flood generations would have experienced a rapid population increase, under a wide range of potential conditions, but what rate of growth is reasonable?

The standard exponential model of population growth is as follows:
N = N₀e ^kt where N = the population size at time t, N₀ is the population size at time 0, and k = the growth rate. Importantly, this formula should only be applied to large populations. While it is true that the human population only needed to average a 0.464% growth rate (k) to go from 6 (N₀) to 7 billion (N) people in the c. 4,500 years (t) since the Flood, the growth of small populations is stochastic by nature. One reason for this is the fact that random births and deaths have a much greater effect in a population of, for example, 10 individuals than they do in a population of 10,000 individuals.

Another reason is the unpredictable availability of members of the opposite sex in very small populations. Consider a biblical model starting with Adam and Eve. The population size at 100 years could be drastically different if they had children in the order boy-girl-boy-girl-boy-girl versus a scenario where they had a series of boys (or a series of girls) in the early years. Thus, it is impossible to predict or accurately model the growth of small populations with the exponential growth formula.
Modern genetic data indicate the human population has exploded over the past several thousand years. But that is only considering the size of the population. In fact, excess population has had a significant factor throughout much of world history. For example, various Greek colonies were founded across the Mediterranean and Black Sea regions by young people looking for space.
Likewise, the invasions of the Germanic tribes into Roman Europe in the waning years of that empire

were driven in part by population expansion.

Biblically, the entire human race descends from just two people, Adam and Eve. Growing to unknown numbers over the first one and a half millennia, the population then went through an extreme but short bottleneck when only eight people survived Noah’s Flood. From the three sons of Noah (and their three wives), the population grew again to unknown numbers before being subdivided at the Tower of Babel, whereupon each of the resulting subpopulations followed an independent, and complex, growth trajectory.
Those three demographic expansion events need to be addressed mathematically to see if they comport to reality. An additional population expansion mentioned in the Bible is that of the Israelites.

Even though we attempted to be as comprehensive as possible, there were several areas where we simply had to make assumptions. For example, we assume a rate of twinning of 1 in 89 births. This ratio changes over time and across cultures but since it is less than 2% of all births, it should have but a small effect on population growth.
Likewise, there is no available data for ancient maternal mortality when carrying twins, and ancient mortality rates should be higher than today, so we simply doubled the set maternal mortality rate for twins. We did not even consider triplets, for they are several orders of magnitude more rare and the maternal death rates in these cases were extreme for times more than 100 years ago.

.....the effect of polygamy (polygyny). A small percentage of men were allowed up to a maximum of five wives (details in Methods). On average, most model runs experienced a boost of approximately 4% over baseline (i.e. they were growing at 104% the rate of a non-polygamous model with the same parameter settings).
Near the edge of population survivability, polygyny enabled some populations to experience more growth, on average, due to the fact that unwed women were more rare.

The date of the Tower of Babel event is unknown. From context, it appears the timing has something to do with a man named Peleg, whose name means ‘division’ (Gen 10:25). He was born c. 101 years after the Flood and lived until c. 340 years after the Flood (Gen 11).
If the division of people occurred only 100 years after the Flood, there would not be many people in the world. However, the data behind the growth rates calculated indicate that under some scenarios it is possible to obtain a population size greater than 1,000 individuals in that much time.

We modelled various scenarios that started with a single founding couple. As before, it was simple to obtain significant numbers in a short amount of time. However, we know very little about the age of maturation (minimum CBA), minimum or average child spacing, etc., of antediluvian women.
Therefore, there are too many unknown variables and there is no way to estimate the antediluvian population size. It could have been in the billions. Or it could have been a few thousand. We cannot know.

There are two main factors that influence population growth the most: minimum CBA and minimum child spacing. This makes sense in that a population will grow most quickly when people marry young and have children close together. This also means, however, that the maximum CBA is far less relevant. Furthermore, since the people who reproduce earliest will have a higher percent representation in the future population, genetics should be driving all populations towards faster reproduction, by default. Early maturation is thus a mathematical certainty, given a population with individuals that have a range of maturation ages. This alone could explain the population-wide drop-off in lifespan after the Flood. While it is true that individual mutation count should increase over time, contributing to a decline in lifespan, it is also true that the ones who reproduce the fastest will outnumber those who do not. In the end, maximum lifespan does not matter.

In fact, the relative individual impact on the future population size of any two people is simply the ratio of inverse population sizes when each person was born, which can be reduced to a simple ratio of the relative times when they were born:
(1/N₀e ^kt1) / (1/N₀e ^kt2) = t₂/t₁ The only caveat is that people who lived a long time may not have matured as young as modern people, so the minimum CBA might come into play to a greater degree than we illustrate here. Yet, the average generation span for the first seven generations born after the Flood is 31.4 years, and there is no reason to suspect these are all oldest children. Interestingly, the modern average human generation time is approximately 30 years.

This brings up another interesting point; kingship has historically been conferred on the eldest sons. Thus, one might expect a long line of kings to experience more generations on average per century than the rest of the population.
Thus, when Jacob met Pharaoh, he asked him how old he was, as if he was surprised to have met such an old man (Gen 47:8). Jacob was but 12 generations removed from Noah and was the grandson of Abraham, who had met another Pharaoh approximately 200 years earlier. How many generations

after the Flood was the Pharaoh of Jacob’s day, and how many generations was he removed from the Pharaoh who knew Abraham two centuries prior?
The subject of how many generations removed were the modelled people from the starting ancestors is fascinating.
We included this calculation for the sake of curiosity. In each run, there were always people with very long lines going back to the founding couple (essentially equal to the length of run/minimum CBA) and at the same time people with very short lines in their family tree (due to the fact that very old men could still father children with younger wives). There are modern analogues to the Abraham-Pharaoh scenario, so this should really be no surprise.

Concerning the Egyptian sojourn, we started with 12 couples with no children, but Gen 46:27 indicates that Jacob’s sons had already started reproducing before he moved to Egypt.
Also, Jacob brought household servants with him to Egypt (Gen 12:16, Gen 14:14, and Gen 46:1 “all that he had”), who might have occasionally married into the family. This is especially true of the women, but the male servants were also circumcised (Gen 17:13), meaning they were at least tangentially part of the Covenant.
Could long-standing, multigenerational, faithful, God-fearing, male family servants have married into the family as time progressed? This is likely, especially since many of them would eventually have Jacob as an ancestor, for obvious reasons.

In conclusion, it is relatively easy to explain the modern world population, starting with the six Flood survivors, in c. 4,500 years. The number of people alive at the Tower of Babel event is more difficult to determine, but could easily have been in the thousands, or even tens of thousands, under certain conditions.
The long/short sojourn debate cannot be answered with demographic data, but there is no reason to reject the short sojourn from numerical data alone. And, it is impossible to estimate the number of people alive at the Flood, for we simply do not have the necessary demographic data." CMI