Population study of the Nephites and Mulekites

[_keithb]

Hi Zee,

Thank you for the clarifications. It seems like you have a good start to a study here.

The one thing that I would advise is that, if the simulations only take such a small amount of time, you might want to run a copious amount of those simulations -- say at least 10,000 or so, all with uncertainty in the inputs. By my calculations, that should take you less than a day of computer time. (10^5/10^2/24/60).

If you have access to an old computer that can crank away on this problem or a high performance computer at your work/university, you could run even more simulations.

Also, thanks for the article Beastie. It has been an interesting read so far; although, I am still not done with it.

[_zeezrom]

So Jaredites mixed with Mulekites? Where was I when we covered that in SS and Seminay?

Ok, then I will simply have to reduce the scope of the study to 200 years of the Lehi-Zoram-Ishmael clan.

[_MCB]

Yea, studying a limited window, such as before possible contact between the two peoples, will reduce the amount of random error.

Good work.

[_keithb]

After reading the article posted by Beastie, it gave me a few ideas.

One would be to compare your model, Zee, back to the simple exponential model of population growth that the authors of the study used: P(t) =P_o exp(rt). That way, you can check the r=rate required for various ending populations and see if the growth rates in your study are reasonable compared to those models.

Also, if the population growth rate was .04% historically, then I take back my comment about population statistics not being a good method of disproving the Book of Mormon. In fact, population would be one of the larger problems that I would see with the Book of Mormon in this case, particularly because we have a timeline of the populations that would have needed to be present at various stages in order for the text to be a factual account of history.

[Guest]

As I'm sure Kish would verify, life expectancy in Classical Rome was somewhere around 30 (partly due to the infant and child morality rates). If one made it past puberty, the estimated expectancy shot to just above 50. I'd expect that a small group of bronze-to-iron age pilgrims in a strange world wouldn't have any more favorable statistics.

[_Kishkumen]

As I'm sure Kish would verify, life expectancy in Classical Rome was somewhere around 30 (partly due to the infant and child morality rates). If one made it past puberty, the estimated expectancy shot to above 50. I'd expect that a small group of bronze-to-iron age pilgrims in a strange world wouldn't have any more favorable statistics.

Excellent point, Morley. Yes, the average life expectancy was lower, but did improve significantly once one survived past a certain age. I do not have the exact statistics at hand, however. Demography is not my thing.

[_MrStakhanovite]

Once again, Jaredite studies gets ignored in favor of one of the lesser disciplines.

[_Kishkumen]

Once again, Jaredite studies gets ignored in favor of one of the lesser disciplines.

Well said, Stak. The Jaredites are a grossly under-appreciated object of inquiry. It is my life's mission to rectify the situation.

[_beastie]

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.

I actually think the infant mortality rate should be higher. Childbirth, in and of itself, is very dangerous to mothers and infants. I found one source that says in ancient rome the infant mortality rate was 30 deaths per 100 pregnancies.

http://books.google.com/books?id=U8Muzx ... ld&f=false

[_zeezrom]

OK, this is a bigger job than I thought coming into this but I did find something interesting. I ran a simplified version of the model that only looks at Lehi's group from 600 BC to 500 BC. When I increase infant mortality and change adult survival possibilities, I get a fairly low probability of success for the group. A low infant mortality rate really hurts.

Here are my updated input assumptions:

Annual fertility rates
Age_______ chance of giving birth
1_______ 0
13_______ 10
14_______ 25
15_______ 80
16_______ 80
18_______ 80
30_______ 80
35_______ 75
40_______ 15
45_______ 2
50_______ 1
60_______ 0
100_______ 0

Infant mortality rate: 50%
Females have 5% higher chance of surviving each year than males.
Initial population does not include servants and unmentioned grandchildren and children.

I compared my results to a simple p = p0*exp(rt) model and look what I get after 100 years:

The results from my model are shown in blue, which represents the average of 10,000 simulations. The red line represents the simple exponential growth method. The results are a little misleading, however.

While on average, the results of my method show a higher ending population, it is actually quite rare that one of my single traces will exceed the exponential growth method. As an example, please see a plot showing the first 10 of the 10,000 realizations of my model:


Here is the cumulative probability distribution of the final population after 400 years:


Interestingly, there is only a 50% chance that anyone survives after 100 years.