Why do they need "16 female, 7 male" to re-establish Zion?

Question

So, re-reading this:

After which, you will be required to select from the Matrix 23 individuals - 16 female, 7 male - to rebuild Zion.

It got me thinking - why exactly this ratio (and why exactly on that scale)?

Is it based on some out-of-universe scientific research for optimal seed population? Was there some in-universe explanation for the peculiar non-1-to-1 ratio?

I am fine with out-of-universe answers, but would prefer those backed by specific data (or in-universe answers based on canon material, or words from franchise workers), as opposed to pure unfounded guesses.

Answer 1

This wouldn't work for an actual population of humans. First, there is a concept in population biology called Minimum Viable Population Size. You typically need hundreds of organisms to survive. In a sheltered environment like Zion, the number could probably be reduced, but reducing it to 23 individuals (one per chromosome?!) would be a really bad idea because of how drastically it would curtail genetic diversity.

For example, the Major Histocompatibility Locus is a crucial protein involved in immune response. There are thousands of variants:

The most diverse loci, namely HLA-A, HLA-B, and HLA-DRB1, have roughly 1000, 1600, and 870 known alleles, respectively.

With only 23 individuals, the maximum number of variants (alleles) is 46--two per individual. The vast majority of our diversity would be lost, and we would consequently become hyper-vulnerable to various pathogens.

So I don't know what the in-universe explanation might be, but if it was supposed to be an out-of-universe explanation, it's wrong.

Answer 2

I think you are forgetting, that Zion survives not only by generations of people, who are free of the matrix, but also by those that are freed from it.

Average spaceship crew in the Matrix consisted of 8 people. This might mean that 23 means the number of people needed to operate two ships and get some more people out of the matrix to get the civilization really going, with the rest operating controls in the city.

Theory may also be calculated by the machines giving the minimum number of individuals needed to operate a society (minimum being the chosen amount to prolong the people numbers growth to delay the next war). The decision might also be based by previous experiences, since this being not the first time the machines claim to have done this.

Answer 3

The Matrix makes tons of references to Religion. Genesis 7:16

Those that entered, male and female of all flesh, entered as God had commanded him; and the LORD closed it behind him

Maybe it has nothing to do with genetics like we would like it to be?

Answer 4

Since no one answered why 7 males and 16 females yet, I'll leave here my guess.

The 23 freed humans would need guidance of some sort, when fresh out of the Matrix, much like Neo needed. It is likely the One would go with them to rebuild Zion, and provide some guidance in this new world.

If you add the One gender (male in the case we witness) to the numbers, that leaves 8 males for 16 females, leaving two females for each male. This could ease repopulation, accounting for pregnancy downtime of each female. That sounds exactly like the thinking of a machine to me.

I'll add to that, that genetic diversity is completely irrelevant. There would still be plenty of diversity if you take into account the people connected to the Matrix - whom the zionists could free and procreate with.

Answer 5

7:16, men:women. Each man could impregnate each woman once, resulting in 7*16 children over the course of at most a decade (Since pregnancy takes 40 weeks plus recuperation, and each woman would get pregnant seven times).

Now, you have 112 children, gender not yet known. This is where math gets a little out of hand. You now need to calculate how many potential mates each of these children will have.

Assuming we ignore gender here, every child has 15 half-siblings by their father (one man and 16 women), and 6 by their mother. That means each kid has an unlikely maximum of 91 potential mates, and a more likely 45-ish.

After that, the math gets really nutty and I lose my mind, however, you could probably still have a rather steady population rise if you avoided screwing your half-siblings...