# Provides descriptive stats and plots to diagnose potential problems with Hardy-Weinberg proportions

`gl.diagnostics.hwe.Rd`

Different causes may be responsible for lack of Hardy-Weinberg proportions. This function helps diagnose potential problems.

## Usage

```
gl.diagnostics.hwe(
x,
alpha_val = 0.05,
bins = 20,
stdErr = TRUE,
colors_hist = two_colors,
colors_barplot = two_colors_contrast,
plot_theme = theme_dartR(),
save2tmp = FALSE,
n.cores = "auto",
verbose = NULL
)
```

## Arguments

- x
Name of the genlight object containing the SNP data [required].

- alpha_val
Level of significance for testing [default 0.05].

- bins
Number of bins to display in histograms [default 20].

- stdErr
Whether standard errors for Fis and Fst should be computed (default: TRUE)

- colors_hist
List of two color names for the borders and fill of the histogram [default two_colors].

- colors_barplot
Vector with two color names for the observed and expected number of significant HWE tests [default two_colors_contrast].

- plot_theme
User specified theme [default theme_dartR()].

- save2tmp
If TRUE, saves any ggplots and listings to the session temporary directory (tempdir) [default FALSE].

- n.cores
The number of cores to use. If "auto", it will use all but one available cores [default "auto"].

- verbose
Verbosity: 0, silent or fatal errors; 1, begin and end; 2, progress log ; 3, progress and results summary; 5, full report [default NULL, unless specified using gl.set.verbosity].

## Value

A list with the table with the summary of the HWE tests and (if stdErr=TRUE) a named vector with the StdErrFis and StdErrFst.

## Details

This function initially runs `gl.report.hwe`

and reports
the ternary plots. The remaining outputs follow the recommendations from
Waples
(2015) paper and De Meeûs 2018. These include:

A histogram with the distribution of p-values of the HWE tests. The distribution should be roughly uniform across equal-sized bins.

A bar plot with observed and expected (null expectation) number of significant HWE tests for the same locus in multiple populations (that is, the x-axis shows whether a locus results significant in 1, 2, ..., n populations. The y axis is the count of these occurrences. The zero value on x-axis shows the number of non-significant tests). If HWE tests are significant by chance alone, observed and expected number of HWE tests should have roughly a similar distribution.

A scatter plot with a linear regression between Fst and Fis, averaged across subpopulations. De Meeûs 2018 suggests that in the case of Null alleles, a strong positive relationship is expected (together with the Fis standard error much larger than the Fst standard error, see below).

**Note**, this is not the scatter plot that Waples 2015 presents in his paper. In the lower right corner of the plot, the Pearson correlation coefficient is reported.The Fis and Fst (averaged over loci and subpopulations) standard errors are also printed on screen and reported in the returned list (if

`stdErr=TRUE`

). These are computed with the Jackknife method over loci (See De Meeûs 2007 for details on how this is computed) and it may take some time for these computations to complete. De Meeûs 2018 suggests that under a global significant heterozygosity deficit:- if the correlation between Fis and Fst is strongly positive, and StdErrFis >> StdErrFst, Null alleles are likely to be the cause.

- if the correlation between Fis and Fst is ~0 or mildly positive, and StdErrFis > StdErrFst, Wahlund may be the cause.

- if the correlation between Fis and Fst is ~0, and StdErrFis ~ StdErrFst, selfing or sib mating could to be the cause.

It is important to realise that these statistics only suggest a pattern (pointers). Their absence is not conclusive evidence of the absence of the problem, as their presence does not confirm the cause of the problem.

A table where the number of observed and expected significant HWE tests are reported by each population, indicating whether these are due to heterozygosity excess or deficiency. These can be used to have a clue of potential problems (e.g. deficiency might be due to a Wahlund effect, presence of null alleles or non-random sampling; excess might be due to sex linkage or different selection between sexes, demographic changes or small Ne. See Table 1 in Wapples 2015). The last two columns of the table generated by this function report chisquare values and their associated p-values. Chisquare is computed following Fisher's procedure for a global test (Fisher 1970). This basically tests whether there is at least one test that is truly significant in the series of tests conducted (De Meeûs et al 2009).

## References

de Meeûs, T., McCoy, K.D., Prugnolle, F., Chevillon, C., Durand, P., Hurtrez-Boussès, S., Renaud, F., 2007. Population genetics and molecular epidemiology or how to “débusquer la bête”. Infection, Genetics and Evolution 7, 308-332.

De Meeûs, T., Guégan, J.-F., Teriokhin, A.T., 2009. MultiTest V.1.2, a program to binomially combine independent tests and performance comparison with other related methods on proportional data. BMC Bioinformatics 10, 443-443.

De Meeûs, T., 2018. Revisiting FIS, FST, Wahlund Effects, and Null Alleles. Journal of Heredity 109, 446-456.

Fisher, R., 1970. Statistical methods for research workers Edinburgh: Oliver and Boyd.

Waples, R. S. (2015). Testing for Hardy–Weinberg proportions: have we lost the plot?. Journal of heredity, 106(1), 1-19.

## Author

Custodian: Carlo Pacioni -- Post to https://groups.google.com/d/forum/dartr

## Examples

```
if (FALSE) {
require("dartR.data")
res <- gl.diagnostics.hwe(x = gl.filter.allna(platypus.gl[,1:50]),
stdErr=FALSE, n.cores=1)
}
```