How closely are siblings related?

A child inherits half each parents genes, and for any individual gene a sibling can either inherit the same or the other allele. Averaged out over the genome, siblings have the same allele for about half the genes.

But genes don’t assort independently of each other, genes are found on chromosomes and due to this inheritance of gene variants is lumpy, a parent has a pair of each chromosome and siblings either get the same chromosome or each gets one of the parent’s pair. This happens randomly for each of the twenty-three pairs of human chromosomes. If humans had only two chromosomes then one forth of the time two siblings would inherit the same pair (out of the four) and be genetically identical. Because humans have twenty-three chromosomes this is vanishingly unlikely. But while on average two siblings have the same gene variant half the time, there is actually a distribution centered at 50%, and siblings can inherit more or less than 50% of same alleles. So how likely are siblings to be 30% or 40% related?

Here’s what the distribution looks like. There are a few more wrinkles to consider. First off, the chromosomes recombine before they assort, so each chromosome a child inherits is a combination of the parents chromosomes. It turns out that in humans, recombination happens more than once per chromosome, about thirty-three times (The Human Genome Project
By Necia Grant Cooper, p31
). I include this in my model. I don’t consider the chance that a parent will have two copies of the same allele for a gene, or how recombination is more likely at particular places along a chromosome, or that genes are clumped together in certain chromosomal regions. Here’s the distribution I find:

% in common Chance of happening
0.33 0.02
0.35 0.15
0.38 0.77 =
0.40 3.03 ==
0.42 8.85 ======
0.45 21.14 ============
0.47 39.23 ==================
0.50 60.27 =====================
0.53 78.68 ==================
0.55 91.05 ============
0.57 97.17 ======
0.60 99.25 ==
0.62 99.85 =
0.65 99.98
0.68 100.00
0.72 100.00

So two siblings have a 3% chance of inheriting 40% or less of the same gene variants from their two parents. The curve is slightly broader if inheritance from only one parent is considered. In that case, two siblings have a 9% chance of inheriting 40% or less of the same gene variants, and a 1% chance of only having 33% or less of their gene variants in common.

So siblings don't always share half their gene variants, but rather have a modest chance or being a bit more or a bit less related.

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