The Mathematical Reason You should have 9 Kids

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In this post I propose a curious genetic question that can be modeled with a remarkably simple answer. If you have children, what is the probability that every allele in your genome is present in at least one of your children? In other words, if you have children, what is the probability that your entire genome has been replicated in the next generation?

Note: I do not believe there is a correct number of children to have. This blog post is just for fun. An organism’s biological purpose is not to replicate its genome. Rather, an organism’s biological purpose is simply to reproduce.
For an explanation of biological purpose, I invite you to read Debunking the Selfish Gene by T. K. Van Allen.

As a human, you have two sex chromosomes XY or XX, and you have 22 homologous pairs of autosomal chromosomes (autosomes) numbered 1 through 22. Your child receives 23 chromosomes from you and 23 chromosomes from the other parent. The manner in which each chromosome is transmitted to your child is independent of the manner in which the other chromosomes are transmitted to your child. Each autosome has a roughly probability of being transmitted as a crossover of your own homologous autosome pair during cellular meiosis. And each autosome has a roughly probability of being transmitted as an identical copy of 1 of your 2 corresponding homologs during cellular meiosis.


In this image, chromosomes of different size correspond to differently numbered chromosomes. Chromosomes of the same size and different single colors correspond to homologs of the same numbered chromosome. The H-shaped things are two chromatids attached at a centromere, and the 1-shaped things are lone chromatids. Dual-colored chromatids were generated by a crossover event during meiosis I. The end result of meiosis is 4 gamete cells. A single gamete cell from each of 2 parents fuse to form the zygote.
Source: Wikimedia Commons

Because chromosomes are transmitted independently, the probability that all of your autosome pairs are replicated into your children is just the probability that one of your autosome pairs is replicated into your children, raised to the power of 22.

(see the rest of the post in the link)