# Ternary Plots

### Ayush Noori | EduSTEM Advanced Biology

## Background

A ternary plot is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. In population genetics, it is often called a de Finetti diagram.

Please see the HardyWeinberg package vignette here.

## Setup

Load the requisite libraries.

```
if(!require(HardyWeinberg)){
install.packages("HardyWeinberg")
library(HardyWeinberg)
}
```

Set the working directory to where you would like your output data to result.

```
dir = "<insert appropriate directory address here>"
setwd(dir)
```

## Plotting

AA, AB, and BB are homozygous dominant, heterozygous, and homozygous recessive respectively (i.e. bi-allelic markers). Each row in the column is a different marker or SNP.

Draw random SNPs from a population that is in Hardy-Weinberg Equilibrium.

```
set.seed(123)
m = 100 # number of markers
n = 100 # sample size
dat = HWData(n,m)
out = HWTernaryPlot(dat, 100, region=1, vertex.cex=2, signifcolour=TRUE)
```

In this ternary plot, the center parabola represents the ratio p^2+2pq+p^2, or the Hardy-Weinberg Equilibrium. Red loci differ from the ratio by more than a certain p-value, therefore are considered to NOT be in Hardy-Weinberg Equilibrium.

For more information, please see Hardy-Weinberg Equilibrium and the Ternary Plot by Graffelman and Camarena.

With these courses, we hope to further our mission to make high-quality STEMX education accessible for all. For questions or support, please feel free to reach out to me at anooristudent@outlook.com.

Best Regards,

Ayush Noori

*EduSTEM Boston Chapter Founder*

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