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OK, so as part of my job, I'm building a population based "aging chain" model. This actually is not my area of expertise but I'm helping an economist and social scientist build the model because I have background in dynamic systems simulation and they needed someone to help construct it. I have this model set up to simulate a population using some basic assumptions as multiple age groups are first born, they age, reproduce, and finally, die. I figured I might as well test my model on a real-world application. Why not Lehi's family tree? How much more "real-world" can you get? :)

So here is the summary of the model. Please note that this is only a draft and needs some work. I'm tired and have been sustained only by lots of Lady Gaga music, pears, and aged cheddar.

Basic Assumptions:

Ishmael: Ishmael, wife, 9 children + 9 servants + 10 grandchildren = 30 people
Zoram: Zoram, wife, 3 children, 3 servants = 8 people
Lehi: Lehi, wife, 4 daughters, 6 sons, 10 servants = 22

Total = 60 people in 600 BC

The following figure shows how I decided to distribute the 60 people.


Nephites met Mulekites in approx. 200 BC

Assume Mulekites were 60 people strong in 600 BC as well.

The largest number listed for the Nephite record is 230,000 thousand in Mormon 6:11-14

Assumed annual survival rates:

birth = 60%
2 years old = 90%
75 years old = 90%
100 years old = 0%

All years between these are linearly interpolated. So, there is a 60% chance of survival at birth, then a 90% chance of survival after age 1, and onward until 75 years of age. After age 75, the survival rate decreases rapidly to 0% at age 100. If the population rises above 1000 people, the survival at birth goes up 10%.

The way aging chains work is by grouping the population into age groups. In my case, I grouped them into each year from 1 to 100 years old. Using a starting birth rate, I have some number of 1 year olds that come out the other end of that group. Some of these (about 20%) die off. Then I go to the 2-yr olds and when they turn 3, I assume about 15% die off. I continue this process through all the age groups until age 100, when all remaining people die off.

It is assumed that males and females have equal survival rates.

The split of Lamanites from the Nephites is ignored.

Mortality rate increases during wars are ignored.

Mortality rate increases from desease is simulated using uncertainty sampling from a normal distribution applied to a reduction factor on each time step (each year). I auto-correlate uncertainty between the current and previous time steps. This means there is memory in the uncertainty correlation. So, if last year sustained a high mortality rate in 6-yr olds, it is very likely next year will see a similar situaltion.

Chances of females giving birth are shown in the table below:

Age_____% chance of giving birth
1______ 0
13_____ 10
14_____ 25
15_____ 100
16_____ 100
18_____ 100
30_____ 100
35_____ 75
40_____ 15
45_____ 2
50_____ 1
60_____ 0
100____ 0

Nephites-only population is simulated from year 600 BC to 200 BC. Mulekites-only are simulated for the same time period. All values are updated on an annual basis. On year 200 BC, I combine the two populations (for total Nephites + Mulekites) then continue with a combined population for another 200 years, for a total simulation time of 600 years (600 BC to 0 AD). I run the entire system model for 100 Monte Carlo realizations, where uncertainy is quantified, sampled, then propogated through the model. The end result is a probability distribution of the final, total population for Nephites (and Lamanites) and the Mulekites.

Here is a a plot showing the Nephite only probability history results(600 BC to 200 BC):


Here is a plot showing the Mulekite only probability history results (600 BC to 200 BC):


Sorry, I don't have a plot available for the combined population from 200 BC to 0 AD. I'm not currently saving those results and it would take some doing to get them and I'm tired.

Here is a graph showing the cumulative probability of the final population values:


To give you a better idea of what results I'm getting, I will tell you what the chances are that we might have seen 230,000 people in around 600 years after Nephi arrived on the continent (Mormon 6:11-14). There is a 11% that we would see at least 1,000,000 people, 19% chance that we would end up with at least 230,000 people, 26% chance of seeing at least 50,000 people, 66% chance of seeing at least 500 people. There is an 85% chance that the population would not survive due mainly to such low starting population.

To be honest, I'm surprised and a little skeptical of my results. I figured I was being fairly liberal with my survival rates and expected population to grow rapidly.

Stay tuned for updates as I work out the bugs.

Zee.

My comments and questions are in bold

zeezrom wrote:OK, so as part of my job, I'm building a population based "aging chain" model. This actually is not my area of expertise but I'm helping an economist and social scientist build the model because I have background in dynamic systems simulation and they needed someone to help construct it. I have this model set up to simulate a population using some basic assumptions as multiple age groups are first born, they age, reproduce, and finally, die. I figured I might as well test my model on a real-world application. Why not Lehi's family tree? How much more "real-world" can you get? :)

So here is the summary of the model. Please note that this is only a draft and needs some work. I'm tired and have been sustained only by lots of Lady Gaga music, pears, and aged cheddar.

Basic Assumptions:

Ishmael: Ishmael, wife, 9 children + 9 servants + 10 grandchildren = 30 people
Zoram: Zoram, wife, 3 children, 3 servants = 8 people
Lehi: Lehi, wife, 4 daughters, 6 sons, 10 servants = 22

How did you generate the initial assumptions for the number of people in the population? The estimates seem reasonable -- especially given the indirect textual evidence from the Book of Mormon -- but I am just curious how you picked those numbers.

Total = 60 people in 600 BC

The following figure shows how I decided to distribute the 60 people.



Nephites met Mulekites in approx. 200 BC

Assume Mulekites were 60 people strong in 600 BC as well.

The largest number listed for the Nephite record is 230,000 thousand in Mormon 6:11-14

Assumed annual survival rates:

Something is wrong with the numbers below. Did you possibly mislabel this section? There shouldn't be a 100% survival rate at 100 years old.

birth = 80%
6 years old = 90%
25 years old = 90%
65 years old = 85%
75 years old = 85%
100 years old = 100%

All years between these are linearly interpolated. So, there is an 80% chance of survival at birth, then a slightly higher chance of survival at age 1 (around 80.5%), and onward until 25 years of age. If the population rises above 200 people, the survival at birth goes up 10%.

Why would the survival rate go up 10% if the population exceeds 200? Just from looking at the Wikipedia article on this, it seems like the historical infant mortality rate for the U.S. population in 1850 was above 20%, and the population there was much higher than 200.

The way aging chains work is by grouping the population into age groups. In my case, I grouped them into each year from 1 to 100 years old. Using a starting birth rate, I have some number of 1 year olds that come out the other end of that group. Some of these (about 20%) die off. Then I go to the 2-yr olds and when they turn 3, I assume about 15% die off. I continue this process through all the age groups until age 100, when all remaining people die off.

It is assumed that males and females have equal survival rates.

The split of Lamanites from the Nephites is ignored.

Mortality rate increases during wars are ignored.

I don't really understand the first sentence of the following paragraph.

Mortality rate increases from desease is simulated using uncertainty sampling from a normal distribution applied to a reduction factor on each time step (each year). Chances of females giving birth are shown in the table below:

I don't understand this table. Would this be the chance of one female giving birth at a given age (say 15)? While the number was likely high in an era without condoms, surely it's not 100%

Age_____% chance of giving birth
1______ 0
13_____ 10
14_____ 25
15_____ 100
16_____ 100
18_____ 100
30_____ 100
35_____ 75
40_____ 15
45_____ 2
50_____ 1
60_____ 0
100____ 0

Nephites-only population is simulated from year 600 BC to 200 BC. Mulekites-only are simulated for the same time period. All values are updated on an annual basis. On year 200 BC, I combine the two populations (for total Nephites + Mulekites) then continue with a combined population for another 200 years, for a total simulation time of 600 years (600 BC to 0 AD). I run the entire system model for 100 Monte Carlo realizations, where uncertainy is quantified, sampled, then propogated through the model. The end result is a probability distribution of the final, total population for Nephites (and Lamanites) and the Mulekites.

It's somewhat ambiguous to me where in your simulations the Monte Carlo aspect of it fits in. Did you have uncertainty in the initial ages of the population, the mortality and birth rates, or in all of those variables simultaneously? What were the upper and lower bounds on your uncertainty for each stage? For example, if a girl in the initial population distribution was modeled as having a median age of 15, what are the upper/lower bounds on her age? What distribution did you use for your ages in this case?

Also, is 100 runs of your simulation enough to generate meaningful statistics about your final population distribution? How many computer hours did it take to run the simulations 100 times?


What does "p" stand for on the y-axis of the plots below?

Here is a a plot showing the Nephite only probability history results(600 BC to 200 BC):


Here is a plot showing the Mulekite only probability history results (600 BC to 200 BC):


Sorry, I don't have a plot available for the combined population from 200 BC to 0 AD. I'm not currently saving those results and it would take some doing to get them and I'm tired.

This graph doesn't seem clear to me. Perhaps you could try a semi-log plot along the x-axis for a better result?

Here is a table of the final population probability Distribution:


To give you a better idea of what results I'm getting, I will tell you what the chances are that we might have seen 230,000 people in around 600 years after Nephi arrived on the continent. There is a 1% that we would see 1,000,000 people, 3% chance that we would end up with 230,000 people, 5% chance of seeing 50,000 people, 35% chance of seeing 500 people. There is a 50% chance that the population would not survive due mainly to such low starting population.

To be honest, I'm surprised and a little skeptical of my results. I figured I was being fairly liberal with my survival rates and expected population to grow rapidly.


Stay tuned for updates as I work out the bugs.

Zee.

That's a good study Zee. I will be interested to see how it turns out. What are you going to use the model for in the end? Are you planning to publish the data?

On a side note, I don't think that the population statistics are a super effective way to disprove the claims of the Book of Mormon (especially since there are much better ways of doing it). naïvely, I would expect that a small starting population to have likely died out (as you stated above), but, given a best case scenario for population growth and survival, I couldn't rule out the chances of the population exploding, like you noted in some simulations above.

John Kunich did similar research. His essay is found in New Approaches to the Book of Mormon and can be read here:

http://signaturebookslibrary.org/?p=10200

This is one of the issues that has resulted in apologists postulating that the Nephites immediately were subsumed within a larger, pre-existing host culture. The unnamed "others".

Zeezrom,

This seems like an excellent start. Making adjustments for combat mortality would be justified, especially when specific battles or times of conflict are mentioned. In primitive societies, the loss of an individual who produced food, whether through agriculture or hunting / gathering, did not bode well for that individual's offspring.

The Signature Books article cited by Beastie above has a nice compilation of Book of Mormon battles and reported battle losses, where available, as well as a discussion about the ways in which the reported battle losses help inform theoverall population numbers at different points in the Book of Mormon (imagined) history.

You have shown that the chances of an initial population of a few hundred being able to eventually produce hundreds of thousands or millions of offspring are very small. And accomplishing this feat while their genetic markers disappear without a trace would be a miracle.

The Lemba Jews of Africa, whose male ancestors are believed to have migrated from Yemen to Africa approximately 2,500 years ago, were able to establish a viable population descended from some 50 male priests. Clearly this was possible because there was already a relatively large and established population in the area from which the males took wives.

DNA evidence unambiguously traces the descendants of these original group of male priests back to Yemen, and from there to Judea. Most of the members of the tribe still carry genetic markers associated with the Cohanim, clearly establishing them as being of Jewish descent. After 2,500 years, although mainly Christian and Muslim, the Lemba still maintain and practice a remarkable number of traditional Jewish customs and rituals, including the use of the Star of David on grave markers..

For faithful Mormons -

The Book of Mormon records that soon after their arrival in the Americas, the descendants of Lehi 'multiplied exceedingly and spread upon the face of the land' (Jarom 1:8). By about 46 BC, after which time they had joined with the Mulekites, they had multiplied until they 'covered the face of the whole earth, from the sea south to the sea north, from the sea west to the sea east (Hel. 3:8).

-and not a Star of David or any other trace of Jewish culture or Semitic DNA anywhere to be found.

As your work shows, yet again - not very likely.

Thanks for the comments! I will review.

In the meantime, let me say that I think my birth survival might be unreasonably high while survival rates thereafter are too low.

Oh, and my goal is not to prove the Book of Mormon false. I just like to see what the possibilities may have been.

Regarding the question of what I plan to use this model for- eventually, we will be using this model for population studies in various locations where water supplies are a concern. I haven't mentioned migrations but that will be part of the future models we are doing.

The others were the Jaredites, and there were many of them. The story of the Jaredite destruction is greatly exaggerated in keeping with the literary device, common in antiquity and the medieval period, of epic inflation. The Lamanites were the first group to intermarry with the Jaredites, but eventually the entire population was mixed. In fact, Lamanite only later became a distinct ethnic group, long after the intermarriage began, and in the end the term simply referred to those who were by tradition identified as descendants of the early mixed marriages, plus those Jaredites and others culturally and religiously aligned with them, as opposed to the Nephite minority. Distinctions of ethnicity thus later depended more on cultural and religious markers. Obviously, the cultural distinctions were barely visible, although Nephite literature greatly exaggerated them.

To elucidate on Kish's theories:

The Jaredites who were concerned about the violence and depravity of the Jaredite civilization silently left and settled in other areas. They became the Mulekites, who gradually intermarried with the Nephites (and Lamanites). This happened in such a subtle and quiet manner that it was not noted in the Book of Mormon, axcept in the sealed portion, to which we no longer have any access. It is too bad that they denied their Jaredite ancestry, because they might have learned from thier ancestors' mistakes. It is also too bad that the Book of Mormon, as we currently have it, places Ether at the last, when we should have it at the beginning.

OK, I modifed the assumptions. See my OP with updated results. Now I will look at Beastie's reference and add the possibility for wars.

KeithB,

Here are my responses to your questions:

How did you generate the initial assumptions for the number of people in the population? The estimates seem reasonable -- especially given the indirect textual evidence from the Book of Mormon -- but I am just curious how you picked those numbers.

We are pretty sure about children but the servants, daughters, and grandchildren is up in the air. I felt I should take a liberal approach to counting the people we aren't sure of. You made me think of something! I should really apply uncertainty to the initial population because we just aren't sure. maybe I could say it ranges somewhere between 30 and 60 people?

Something is wrong with the numbers below. Did you possibly mislabel this section? There shouldn't be a 100% survival rate at 100 years old.

Fixed the typo.

Why would the survival rate go up 10% if the population exceeds 200? Just from looking at the Wikipedia article on this, it seems like the historical infant mortality rate for the U.S. population in 1850 was above 20%, and the population there was much higher than 200.

I'm being liberal again in my assumptions. I did change my infant mortality rate as you see in the updated OP but I didn't go to 20%. Wow, that is really low! I will do a sensitivity test on infant mortality rates and see. Thanks! I also changed the threshold for increasing infant survival rate to 1000 people. I assume that babies are more likely to survive if there is a larger community.

I don't really understand the first sentence of the following paragraph.

Mortality rate increases from desease is simulated using uncertainty sampling from a normal distribution applied to a reduction factor on each time step (each year). Chances of females giving birth are shown in the table below:

On average, the survival rate might be 90% but I have applied uncertainty that causes that survival rate to fluctuate over time. I added a little more information to the OP.

I don't understand this table. Would this be the chance of one female giving birth at a given age (say 15)? While the number was likely high in an era without condoms, surely it's not 100%

This is the likelihood that a female will give birth to a new child within that year. You know, you are right about that not being correct. I should reduce those numbers. Note that I *do* apply uncertainty to the birth rates. Thanks!

It's somewhat ambiguous to me where in your simulations the Monte Carlo aspect of it fits in. Did you have uncertainty in the initial ages of the population, the mortality and birth rates, or in all of those variables simultaneously? What were the upper and lower bounds on your uncertainty for each stage? For example, if a girl in the initial population distribution was modeled as having a median age of 15, what are the upper/lower bounds on her age? What distribution did you use for your ages in this case?

Ah, good questions. Uncertainty is put into mortality rates and birth rates. Uncertainty is applied on each year with correlations between them. Regarding initial population - I haven't yet applied uncertainty to initial conditions but I will soon. Thanks!

Also, is 100 runs of your simulation enough to generate meaningful statistics about your final population distribution? How many computer hours did it take to run the simulations 100 times?

No, it is not enough. I should propbably do 1000, and plan to do that later. It takes about 1 minute to do 100 on my 5 core, 8gb machine. Adding wars will slow it a little more. Adding Lamanite splits and migrations would make it even longer.

What does "p" stand for on the y-axis of the plots below?

person

zeezrom wrote:.
This is the likelihood that a female will give birth to a new child within that year. You know, you are right about that not being correct. I should reduce those numbers. Note that I *do* apply uncertainty to the birth rates. Thanks!

Birthrate needs to be recalculated. 9 months pregnancy plus six+ months of nursing= 15+ months. I think 90% survival rate of newborns should be accurate in an area where there is minimal contagious disease.

You will come to the inescapable conclusion of having to calculate Jaredite influence. And that is impossible because of the sealed portion.