# Inheritance percentiles

I am aware that the average DNA contribution from each grandparent is 25%, while the possible range is 0%-50%. I found a source citing 18%-32% as the "normal" range but this was undefined. I assume it must be referring to a percentile based on the distribution in a Gaussian curve.

After searching in vain for a chart showing "normal" ranges for each level of consanguinity (sibling, grandparent/aunt, great-grandparent/cousin etc.), I started doing the calculations myself on an Excel spreadsheet... and soon went back to searching. Surely this information is available somewhere, and there must be generally accepted norms. The math formulas are well established.

Where should I look to find the results summarized in a compact format?

I want to first know, essentially, the statistical results of flipping 23 identical immutable coins to represent the various generational probabilities. The facts that the chromosomes are not identical, and that recombination is more likely at certain loci on certain chromosomes, are to be considered later as adjustments to the non-biological math.

I will pursue a statistical answer elsewhere if I can get the "biological" answer as to what percentile is accepted as the "normal" range. (The 25% average for grandparents has a vanishingly small probability of actually occurring, as it would require enough recombination to equal an inheritance of 11.5 chromosomes from each grandparent.)

• Good question +1. The actual probability distribution will depends upon the recombination rate and the number of chromosomes. Are you talking about the human genome only? The distribution in recombination rate might matter too but that would make things too complex for a simple calculations so anyone giving it a shot would probably want to assume constant recombination rate. Sexual chromosomes might also make things more complicated. Sep 18, 2019 at 17:45
• For your edit, that part is now a (fairly trivial) statistical question involving the binomial distribution with p=0.5 and n=23. Sep 18, 2019 at 23:49
• I have seen a spreadsheet with percentiles with real data. I cannot recall where it was, but that resource exists. Mar 1 at 5:23

Setting up the binomial distribution:

For generation F1 each parent (F0) has a 50% chance of contribution the chromosome (under your simplified model), i.e. p=0.5, n=46 for the binomial distribution. I assume that when you say the 'normal' range you are looking for the mean +- 1 standard deviation? For p=0.5, n=46: mean=23 with standard deviation=3.39116 which helps define: Pr(20≤X≤26)=0.698. So in about 70% of cases a child will inherit 20-26 of their chromosomes from one parent.

For generation F2 each grandparent has a 25% probability of contributing a chromosome so we use p=0.25, n=46 which gives: mean = 11.5, standard deviation=2.93684 Pr(9≤X≤14)=0.6936. So in about 70% of cases a grandparent will have contributed 9-14 chromosomes.