Hexp calcuation is erroneous

[zkamvar]

The problem:

After re-reading Nei (1978), I realized that my implementation of Hexp is:

N/(N - 1) * 1 - sum(p^2)

Where N is the number of allelic states and p is the vector of allele frequencies. Nei's definition is:

kn/(kn - 1) * 1 - sum(p^2)

Where n is the number of observed samples at a locus and k is the ploidy (to account for dosage).

User-facing impacts:

• poppr()
• locus_table()

What needs to be fixed:

• internal function locus_table_pegas()

Impacts after fix:

• Polyploids - Because the calculation is dependent on ploidy, this means that it would inappropriate to calculate this for polyploids due to ambiguous dosage.
• locus_table(type = "genotype") - Hexp will change to unbiased simpson's index.

Unfortunately, I might have to wait until just before August to submit this patch, lest I anger our CRAN overlords.

[zkamvar]

To ensure that things are working correctly, I will write a test based on the example presented in Kosman (2003).

[zkamvar]

Currently, the strategy is:

If it's polyploid, change to unbiased Simpson's index over alleles:

(n/(n - 1)) * 1 - sum(pi^2)

This way a measure can actually be reached instead of having complaints of missing data in the result.

Currenlty, locus table will report a different column name, and poppr probably should as well.

Now, I just need to fix the documentation:

• adjust documentation in locus_table()
• adjust documentation in poppr()
• adjust documentation in vignette (that was wrong anyways 😩)

[zkamvar]

The new column name for poppr and locus_table is Mu.

[zkamvar]

Scratch that, reverse it.

The calculation will be

(n/(n - 1)) * 1 - sum(p^2)

where n is the number of observed alleles. This will impact polyploids and mixed ploidy populations by increasing diversity, but it's better than using kN, which would increase it even more.