This vignette introduces how to use *SimPhe*, an R package dedicated to simulate multiple phenotyes based on genotyping data. The main feature of this package is the possibility to take genetic epistatic effects, not only additive-additive interaction but also additive-dominance and dominance-dominance, heritability and multiple phenotypes into account. Moreover, we provide a variety of convenient functions, including suggestion for set the variation of random variable according to user specified genetic effects and flexible support for input formats, as well as output formats. It also supports the input of plink formats.

First, we show how easy to get phenotype(s) by using *sim.phe*. Before running *sim.phe*, we need specify the parameter file and genotype file for simulation. After installing *SimPhe*, these two toy files exist in package folder. To get the path, type

```
# get file path of simulation parameters
# (two shared SNP pairs and one independent SNP pair for each phenotype)
fpar.path <- system.file("extdata", "simupars.txt", package="SimPhe")
# get file path of genotype file: rows are individuals and columns are SNPs
fgeno.path <- system.file("extdata", "10SNP.txt", package="SimPhe")
```

Then simulate the phenotypes as designed in the parameter file after loading package:

```
# simulate phenotype(s)
phe <- sim.phe(sim.pars = fpar.path,
fgeno = fgeno.path,
ftype = "snp.head",
seed = 123,
fwrite = FALSE)
```

In the parameter file, we conduct two phenotypes contrbituted by two common SNP pairs with epistatic effects and one independent SNP pair with epistatic effects, the example of simulation parameters, same as the example file, is also included in *SimPhe*. Users could touch it by typing *genepars*.

```
## $P1mean
## mean
## 1 10
##
## $P1main
## SNP additive dominance
## 1 SNP01 4.0 2.0
## 2 SNP02 2.5 1.5
## 3 SNP03 5.5 1.8
## 4 SNP04 -2.5 1.0
## 5 SNP05 8.5 9.8
## 6 SNP06 8.7 8.4
##
## $P1epistasis
## SNPA SNPB additive_additive additive_dominance dominance_additive
## 1 SNP01 SNP02 10.0 2.0 2.8
## 2 SNP03 SNP04 8.0 3.0 3.5
## 3 SNP05 SNP06 20.5 20.6 20.4
## dominance_dominance
## 1 1.8
## 2 2.5
## 3 10.2
##
## $P1heritability
## heritability
## 1 0.6
##
## $P2mean
## mean
## 1 20
##
## $P2main
## SNP additive dominance
## 1 SNP01 8.0 2.0
## 2 SNP02 4.5 1.8
## 3 SNP03 6.5 1.5
## 4 SNP04 -3.5 -1.2
## 5 SNP07 10.4 8.6
## 6 SNP08 12.3 11.9
##
## $P2epistasis
## SNPA SNPB additive_additive additive_dominance dominance_additive
## 1 SNP01 SNP02 15.0 4.0 3.0
## 2 SNP03 SNP04 12.0 5.0 3.5
## 3 SNP07 SNP08 21.5 20.9 20.5
## dominance_dominance
## 1 2.0
## 2 2.5
## 3 20.3
```

Phenotype 1 has been set with certain heritability but phenotype 2 has not. We will show whether the heritability of the simulated phenotype 1 is same as the set. *SimPhe* includes the coefficients and the allele frequencies for simulating phenotype 1: *gene.coef* and *allele.freq*, which is extracted from the simulation parameters.

```
## $epi.par1
## SNPA SNPB additiveA dominanceA additiveB dominanceB additive_additive
## 1 SNP01 SNP02 4 2 2.5 1.5 10
## additive_dominance dominance_additive dominance_dominance
## 1 2 2.8 1.8
##
## $epi.par2
## SNPA SNPB additiveA dominanceA additiveB dominanceB additive_additive
## 1 SNP03 SNP04 5.5 1.8 -2.5 1 8
## additive_dominance dominance_additive dominance_dominance
## 1 3 3.5 2.5
##
## $epi.par3
## SNPA SNPB additiveA dominanceA additiveB dominanceB additive_additive
## 1 SNP05 SNP06 8.5 9.8 8.7 8.4 20.5
## additive_dominance dominance_additive dominance_dominance
## 1 20.6 20.4 10.2
```

```
## SNP major.frequency minor.frequency
## 1 SNP05 0.6447673 0.3552327
## 2 SNP01 0.7238366 0.2761634
## 3 SNP03 0.7394188 0.2605812
## 4 SNP06 0.7334176 0.2665824
## 5 SNP02 0.6433986 0.3566014
## 6 SNP04 0.6581386 0.3418614
```

```
# calculate genetic variance
genevar <- calc.gene.var(gene.coefficients, allele.freq)
# the variance of simulated phenotype 1
phe1var <- var(phe[, "p1"])
# heritability of simulated phenotype 1
simuht <- genevar / phe1var
simuht
```

`## [1] 0.6297038`

The result is not the exactly 0.6 due to the (pseudo)random numbers generated in R. To get phenotype 2 with a specific heritability, for example, 0.45, we could proceed as:

```
# get regression coefficients settings for phenotype 2
genecoef <- get.gene.coef(main.pars = specify.pars(genetic.pars = genepars,
effect.type = "main",
phe.index = 2),
epi.pars = specify.pars(genetic.pars = genepars,
effect.type = "epistasis",
phe.index = 2))
# get genotype data
genotype <- read.geno(fname = fgeno.path, ftype = "snp.head")
# get allele frequencies of the SNPs set for phenotype 2
freq2 <- get.freq(geno = genotype,
epi.pars = specify.pars(genetic.pars = genepars,
effect.type = "epistasis",
phe.index = 2))
# get noise variation
exp.noise.var <- get.noise.var(gene.coef = genecoef,
freq = freq2,
heritability = 0.45)
```

Then when simulating a phenotype, just give this value as argument *noise.var* to function *sim.phe*. It will generate a phenotype which has a heritability close to 0.45.

As we mentioned earlier in this article, buiding the correlation by setting the shared interactive SNP pairs cannot be controlled. We can take a look at the correlation between the simulated phenotype 1 and phenotype 2:

```
##
## Pearson's product-moment correlation
##
## data: phe[, "p1"] and phe[, "p2"]
## t = 2.2112, df = 98, p-value = 0.02935
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.0225377 0.3973936
## sample estimates:
## cor
## 0.2179908
```

According to the result of correlation test, the two simulated phenotypes are significantly correlated but the correlation coefficient is small and the amount cannot easily be predicted. To get a certain amount or higher correlation, we can conduct correlation by applying the correlation matrix to two independent variables. For two phenotypes, if we set different SNP pairs for each, we assume these two phenotypes are independent. Here we give another parameter file to but same genotype file to the arguments in *sim.phe*, *fgenetic.pars* and *fgeno*:

```
# get file path of simulation parameters
# (different SNP pairs for each phenotype)
fpar.path <- system.file("extdata", "sep_simupars.txt", package="SimPhe")
# simulate phenotype(s)
indphe <- sim.phe(sim.pars = fpar.path,
fgeno = fgeno.path,
ftype = "snp.head",
seed = 123,
fwrite = FALSE)
```

We can test the correlation between initial phenotypes with seperated SNP pairs settings:

```
##
## Pearson's product-moment correlation
##
## data: indphe[, "p1"] and indphe[, "p2"]
## t = -0.094853, df = 98, p-value = 0.9246
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2056123 0.1871892
## sample estimates:
## cor
## -0.009581143
```

Apparently, these two phenotypes are not related. We could continue our work on coverting them to be correlated. First, conduct a correlation matrix:

```
## [,1] [,2]
## [1,] 1.0 0.6
## [2,] 0.6 1.0
```

Before applying correlation matrix to simulated phenotypes, we would like to know what the data looks like:

```
## p1 p2
## 20.18028 33.24045
```

```
## p1 p2
## 20.05408 17.92715
```

Then we can build correlation between the two initial phenotypes:

Now let’s test the correlation between the two new phenotypes and see if there is anything difference:

```
## p1 p2
## 20.18028 33.24045
```

```
## p1 p2
## 20.05408 17.84452
```

```
##
## Pearson's product-moment correlation
##
## data: corphe[, "p1"] and corphe[, "p2"]
## t = 7.3301, df = 98, p-value = 6.615e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4514244 0.7086646
## sample estimates:
## cor
## 0.5950781
```

Obviously, there is no significant difference on means and standard deviations between the initial phenotypes and the new phenotypes.

Cockerham, C. Clark, and Bruce Spencer Weir. 1977. “Quadratic Analyses of Reciprocal Crosses.” *Biometrics* 33 (1). JSTOR: 187–203. https://doi.org/10.2307/2529312.

Kao, Chen-Hung, and Zhao-Bang Zeng. 2002. “Modeling Epistasis of Quantitative Trait Loci Using Cockerham’s Model.” *Genetics* 160 (3). Genetics Society of America: 1243–61. https://doi.org/10.1534/genetics.104.035857.