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## Sibling Lotto! | DNA Science

#### # of trials

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Type of Sharing # on Last Run % on Last Run Avg. % Across Trials
Total IBD
HIR
IBD1
IBD2 (FIR)

IBD: identical-by-descent; HIR: half-identical regions; FIR: fully-identical regions. This model represents autosomal DNA only.

If you want to calculate the percentages from the counts on your own, you can count the checkmarks. For the amount of total IBD sharing, count all green checkmarks. For the amount of FIR DNA, count the green checkmarks only on rows with two checkmarks. For IBD1 DNA, you would count the number of checkmarks on rows in which there’s only one. HIR is calculated by counting the rows that have any check marks or by adding IBD1 and half of the FIRs. To get the percentage from the last trial, divide any of those counts by the number of “circles” that a person has (eight).

If you run enough trials, you’ll see that the averages converge towards 50% total IBD, 37.5% HIR, 25% IBD1, and 25% FIR.

How many times do you have to run one trial in order to get all average values?

The inherited DNA from parents shown here is random. There are only a few rules for this model. One is that a circle in a given sibling row has to come from the same parent row, i.e. a sibling gets their row one circle from row one of a parent. Another is that a sibling’s left column comes from their father and their right column comes from their mother. The only other rule is that each circle in a sibling’s rows and columns has an equal chance of coming from the applicable parent’s maternal or paternal column, i.e. a circle in a sibling’s first first column has a 50% chance of being from their father’s paternal column and a 50% of coming from their father’s maternal column.

Since this model is simplified to the fewest number of circles (four per column) possible to allow for the possibility of a trial run with the same average values of shared DNA seen in real sibling pairs, we will see extreme examples far more often than in real life. For example, we will often see sibling pairs who share no FIR or 50% or more FIR. And we’ll sometimes see sibling pairs who share no DNA or who share at least half-identical DNA over the whole length of the genome. Conclusions can’t be drawn from the variability shown in the table; only from the averages if enough trials were done. The variability is high because of the low number of circles that were used (four) per column of the genome. Using more circles would decrease the variability.

We can now see why fully-identical regions need to be counted twice rather than once in order to calculate total IBD sharing: When there are matching circles on both the left and the right, you wouldn’t count just the left side (paternal) circles as a match but not the right side (maternal) circles. Another way to say it is that, for rows with two checkmarks, you would want to add both checkmarks to get total IBD sharing. Sometimes centiMorgans are reported as HIR values, which are the IBD1 values plus only one copy of the IBD2 DNA. It’s sometimes fine to do it that way, but it’s important to remember that that isn’t the total amount of IBD sharing.

This tool is designed to help people understand the types of IBD sharing in the simplest way possible. Developing an understanding of this tool will show that a concept that most people find complicated is actually very simple. I’ve seen a lot of questions from people who were trying to understand the averages of IBD sharing between full-siblings. Even some influential people in the genetic genealogy community have asked me multiple times to explain how to obtain these averages. At those times I always wanted to be able to point to graphics like those above for an average case, but none were available.

This is probably the silliest genetic genealogy tool I’ve made, so I have no doubt it will be the most popular. If you're interested in more serious work, check out the most accurate and advanced relationship predictions available:

To read more about shared DNA between full-siblings, please see this article. I hope you enjoy the new tool! Feel free to share it with those looking for a learning aid about DNA randomness and averages of shared DNA. Tool released 10 Jul. 2022.