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Analysis of Molecular Variance (AMOVA)

The Analysis of Molecular Variance, or AMOVA, was originally described in Excoffier et al. 1992 and is now a common method in the population genetics toolkit. The method compares within-population and across-population variance in allele frequencies to derive a metric of genetic differentiation. It has also been extended to calculate pairwise FSTF_{ST}, which is the default method for pairwisefst() since PopGen.jl v0.10. What makes this method great is that it can explore hierarchical population structure. That is, you can see if there is significant structure as a result of (e.g.) localities nested in regions, or localities nested in regions nested in years, etc. Sadly, hierarchical structure is not yet supported, because I need time to figure out the proper math for it. Help is always appreciated!

AMOVA​

You can perform an AMOVA using the amova function:

amova(data::PopData; hierarchy::String, missing_cutoff::Union{Nothing,Float64} = 0.05)

Arguments​

  • data: A PopData object

Keyword Arguments​

  • hierarchy: A String of what metadata column has the grouping type you would like to use. This is likely the popultion column in sampleinfo, since heirarchical clustering is not yet supported. The heirarchy API is very likely to change once that feature is implemented.
  • missing_cutoff: A threshold to use for filtering out missing data. The default is 0.05, meaning remove loci with greater than 5% missing data. It accepts nothing to indicate you want all data kept.

The result is of type AMOVAResult, which allows it to be nicely printed as a familiar AMOVA/ANOVA table. You can easily access the fields of the result using dot-indexing, e.g. result.SS. Note that sigma-squared uses fancy characters, which will require Julia's built-in ASCII character rendering: \sigma<tab>\^2<tab>, where <tab> is the tab key on your keyboard.

struct AMOVAResult
    source::Vector{String}
    df::Vector{Int}
    SS::Vector{Float64}
    MS::Vector{Float64}
    σ²::Vector{Float64}
    FST::Float64
end

example​

julia> cats = @nancycats;

julia> julia> amova(cats, hierarchy = "population")
[ Info: removing 2 loci with >5.0% missing data
Analysis of Molecular Variance
─────────────────────────────────────────────────────────
            Source   DF        SS      MS      σ²     FST
─────────────────────────────────────────────────────────
             Total  236  753.7099  8.8930  0.4409  0.1369
 Among populations   16       142  2.7792  2.7792        
Within populations  220       611                        
─────────────────────────────────────────────────────────