<p>Simulating genotypes with realistic correlation structures is indeed not so simple, and there's quite a few papers dedicated entirely to that (e.g. <a href="https://bmcgenet.biomedcentral.com/articles/10.1186/s12863-015-0173-4" rel="noreferrer">https://bmcgenet.biomedcentral.com/articles/10.1186/s12863-015-0173-4</a>). Also, DEPICT (<a href="https://data.broadinstitute.org/mpg/depict/index.html" rel="noreferrer">https://data.broadinstitute.org/mpg/depict/index.html</a>) comes with a number of simulated GWASs to generate the nulls, so that's a simple way to obtain some ready-made fake data.</p>

<p>On the other hand, indepedent SNPs <em>should</em> behave as draws from $Binomial(2, MAF)$. Note that the standard QC procedure of filtering out genotypes that deviate from Hardy-Weinberg equilibrium is just a goodness-of-fit test against $Binomial(2, \hat{MAF})$. If you employ this filter, some LD-pruning, and still get different results, consider posting more details about the discrepancies you see - that would be indeed unexpected.</p>

CC BY-SA 3.0
2017-09-01T15:11:44.927Z
Thanks. I agree that independent SNPs behave as draws from Binomial. I think the discrepancies I observe is mainly on a population level.
Haohan Wang
CC BY-SA 3.0
2017-09-01T10:03:37.913Z
2017-09-01T10:03:37.913Z
juod
<p>I found that several papers describe SNPs as a binomial distribution with the probability of "success" equals to minor allele frequency. </p>

<p>However, in my experiments, when I generate SNP array following this distribution, the simulation results behave very differently from the SNP array generated following the random mating procedures. I feel like there is some missing information about the description of a binomial distribution. </p>

<p>I wonder what will be a better mathematical description of the SNP array data? Besides a direct answer, any thoughts, or any suggestion of papers are also highly welcome. </p>

<p><strong>EDIT:</strong></p>

<p>Thanks for these suggestions, after reading relevant materials, I think what I observe is about the Hardy-Weinberg equilibrium affected by evolutionary influences like mutation and migration. I will continue to look and list findings here if I find anything interesting. Please feel free to suggest some mathematical descriptions.  </p>

<p>Also thanks for the suggestion of tools. They look very helpful, but I really hope to understand some mathematics behind it. </p>

CC BY-SA 3.0
2017-09-01T05:43:01.377Z
Are you familiar with linkage disequilibrium and Hardy-Weinberg equilibrium? Looking up review papers on those might give more insights.
gringer
CC BY-SA 3.0
2017-09-02T09:00:50.337Z
Re the edit: given the very low mutation rates in eukaryotes, mutation effect on HWE in SNPs should be negligible - or at least, much lower than the effect of genotyping errors.
juod
<r><snp>
What will be an appropriate mathematical distribution for SNP data?
# What will be an appropriate mathematical distribution for SNP data?

(Asked by: username_0 on 2017-09-01)

I found that several papers describe SNPs as a binomial distribution with the probability of "success" equals to minor allele frequency.

However, in my experiments, when I generate SNP array following this distribution, the simulation results behave very differently from the SNP array generated following the random mating procedures. I feel like there is some missing information about the description of a binomial distribution.

I wonder what will be a better mathematical description of the SNP array data? Besides a direct answer, any thoughts, or any suggestion of papers are also highly welcome.

**EDIT:**

Thanks for these suggestions, after reading relevant materials, I think what I observe is about the Hardy-Weinberg equilibrium affected by evolutionary influences like mutation and migration. I will continue to look and list findings here if I find anything interesting. Please feel free to suggest some mathematical descriptions.

Also thanks for the suggestion of tools. They look very helpful, but I really hope to understand some mathematics behind it.

**Tags:** r, snp
> **Comments:**
> **username_1**: Are you familiar with linkage disequilibrium and Hardy-Weinberg equilibrium? Looking up review papers on those might give more insights.  
> **username_2**: Re the edit: given the very low mutation rates in eukaryotes, mutation effect on HWE in SNPs should be negligible - or at least, much lower than the effect of genotyping errors.  

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## 1 answers

### Answer by username_2 on 2017-09-01. Score: 6

Simulating genotypes with realistic correlation structures is indeed not so simple, and there's quite a few papers dedicated entirely to that (e.g. <https://bmcgenet.biomedcentral.com/articles/10.1186/s12863-015-0173-4>). Also, DEPICT (<https://data.broadinstitute.org/mpg/depict/index.html>) comes with a number of simulated GWASs to generate the nulls, so that's a simple way to obtain some ready-made fake data.

On the other hand, indepedent SNPs *should* behave as draws from $Binomial(2, MAF)$. Note that the standard QC procedure of filtering out genotypes that deviate from Hardy-Weinberg equilibrium is just a goodness-of-fit test against $Binomial(2, \hat{MAF})$. If you employ this filter, some LD-pruning, and still get different results, consider posting more details about the discrepancies you see - that would be indeed unexpected.

> **Comments:**
> **username_0**: Thanks. I agree that independent SNPs behave as draws from Binomial. I think the discrepancies I observe is mainly on a population level.  

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