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That parent in their turn may contribute to their offspring a blue eye allele, or a brown eye allele.
So there is a 50% probability that any given grandchild will be a heterozygote, and a 50% probability that they will be a homozygote.
If you have a background in biology, you know this is wrong, because there’s more to the story.
Recombination means that in fact you don’t invariably inherit intact copies of your grandparent’s chromosome.
But we live in the genomic age, and as you can see above we can measure the variation in genetic relationships among siblings today in an empirical sense.
The expectation, as we would expect, is 0.50, but there is variance around that expectation.
So “paternal” and “maternal” here is in reference from the parental generation, so there are two of each.
The ones inherited from the parental mother I’ve italicized.
I contrast this randomness among siblings to the hard & fast deterministic nature of of parent-child inheritance.
In the toy example above the eye color locus is on a chromosome. Each individual will inherit one copy of 15 from their parents.
But, there is no guarantee that each sibling will inherit the same copy from the generation of the grandparents. Below you see the four combinations possible in relation to the chromosomes inherited by an individual’s parents from their own parents.
That is the most general theory, without any direct reference to proximate biophysical details of inheritance.
Pure Mendelian abstraction as a formal model tells us that reproductive events are discrete sampling processes.
The outcome are as follows: Top-left cell: paternal grandfather’s chromosome maternal grandfather’s chromosome Top-right cell: paternal grandfather’s chromosome maternal grandmother’s chromosome Bottom-left cell: paternal grandmother’s chromosome maternal grandfather’s chromosome Bottom-right cell: paternal grandmother’s chromosome maternal grandfather’s chromosome As an example, if on chromosome 15 two siblings were characterized by the top-left cell, we might say that they were 100% “identical-by-descent” (IBD).