Pairwise F-Statistics

Background

Originating with Wright's $F$ fixation index (inbreeding coefficient), $F$ has since evolved into a whole slew of statistics used to describe the differentiation/divergence within or between groups. As you may have seen from summary(), there are a common group of these indices ($F_{IS}$, $F_{IT}$, and $F_{ST}$) that compare the $F$ at various hierarchical levels. The notation is pretty straightforward: $I$ is for individuals, $T$ is the total, and $S$ is for subpopulations.

F-statistic	Compares	Against
$F_{IS}$	Individual	Subpopulation
$F_{IT}$	Individual	Total
$F_{ST}$	Subpopulation	Total

Often, we are interested in pairwise $F_{ST}$, which is a type of coefficient that helps us infer how panmictic (fully mixed) two groups of interest are. A colloquial way of phrasing that is "how much genetic mixing is there between these two groups?". The value of $F_{ST}$ (and its derivatives) should typically range between 0 and 1 and can be interpreted like so:

$F_{ST}$ value	Interpretation
0	the two groups are completely panmictic
1	the two groups are completely isolated

However, it's not a linear relationship, and Wright considered 0.125 as the cutoff for when to determine populations as divergent.

$F_{ST}$ isn't everything

An important caveat to always consider is that $F_{ST}$ is just one tool to help us understand trends and not the entire picture. The genetic data we collect is just a snapshot in current time and populations can be completely isolated but still have near-zero $F_{ST}$ values for a number of reasons (slow divergence time, recent introgression, etc.). Significance testing helps add context to observed $F_{ST}$ values.

Pairwise FST

pairwisefst(data::PopData; method::Function, by::String = "global", iterations::Int64)

Calculate pairwise $F_{ST}$ between populations in a PopData object. Set iterations to a value greater than 0 to perform a single-tailed permutation test to obtain P-values of statistical significance. Use by = "locus" to perform a locus-by-locus FST for population pairs (iterations and significance testing ignored). `WeirCockerham is not yet implmented for by-locus $F_{ST}$.

custom output type

The returned object for is a custom PairwiseFST type with the fields results (stores the dataframe of $F_{ST}$ values) and method (a string of which method was used to calculate it). This was done to define a custom show method to make the results a little nicer, and so you never lose track of which method was used for the calculation. If you want to access the dataframe directly, you will need to do so with varname.results where varname is whatever you named the output.

Arguments

• data::PopData: a PopData object you wish to perform the calculation on

Keyword Arguments

• method::Function: which $F_{ST}$ calculation method you would like to use
  • Hudson: the Hudson et al. (1992) method (only for biallelic data)
  • WeirCockerham: the Weir & Cockerham (1984) method (default)
  • Nei: Nei (1987) genetic distance method
• by::String: perfrom a "global" pairwise $F_{ST}$ or "locus" for locus-by-locus (ignores significance testing)
• iterations::Int64: the number of iterations for signficance testing (default: 0)

Examples

without significance testing

julia> sharks = @gulfsharks ;

julia> pairwisefst(sharks, method = WeirCockerham)
Pairwise FST: WeirCockerham
                CapeCanaveral  Georgia   SouthCarolina  FloridaKeys  MideastGulf  NortheastGulf  SoutheastGulf 
───────────────────────────────────────────────────────────────────────────────────────────────────────────────
 CapeCanaveral        0.0       0.0            0.0          0.0          0.0            0.0                0.0
       Georgia        0.00081   0.0            0.0          0.0          0.0            0.0                0.0
 SouthCarolina       -0.0003   -0.00076        0.0          0.0          0.0            0.0                0.0
   FloridaKeys        0.00282   0.00202        0.00204      0.0          0.0            0.0                0.0
   MideastGulf        0.00423   0.00354        0.00329      0.00042      0.0            0.0                0.0
 NortheastGulf        0.00264   0.00147        0.00146     -7.0e-5      -0.00023        0.0                0.0
 SoutheastGulf        0.00312   0.00222        0.00191     -3.0e-5       0.00079        0.00118            0.0

with significance testing

julia> sharks = @gulfsharks ;

julia> pairwisefst(sharks, iterations = 100)

Below diagonal: FST values | Above diagonal: P values
Pairwise FST: WeirCockerham (with p-values)
                CapeCanaveral  Georgia   SouthCarolina  FloridaKeys  MideastGulf  NortheastGulf  SoutheastGulf 
───────────────────────────────────────────────────────────────────────────────────────────────────────────────
 CapeCanaveral        0.0       0.17           0.66         0.01         0.01           0.08              0.01
       Georgia        0.00081   0.0            0.83         0.01         0.01           0.05              0.02
 SouthCarolina       -0.0003   -0.00076        0.0          0.01         0.01           0.09              0.03
   FloridaKeys        0.00282   0.00202        0.00204      0.0          0.23           0.6               0.65
   MideastGulf        0.00423   0.00354        0.00329      0.00042      0.0            0.64              0.18
 NortheastGulf        0.00264   0.00147        0.00146     -7.0e-5      -0.00023        0.0               0.15
 SoutheastGulf        0.00312   0.00222        0.00191     -3.0e-5       0.00079        0.00118           0.0

by locus

julia> sharks = @gulfsharks ;
julia> pairwisefst(sharks, method = Nei, by = "locus")
Pairwise FST: Nei
pop1           pop2           locus         fst      
String         String         String        Float64  
─────────────────────────────────────────────────────
CapeCanaveral  Georgia        contig_35208  -0.01309
CapeCanaveral  Georgia        contig_23109  -0.0235
CapeCanaveral  Georgia        contig_4493   -0.02533
CapeCanaveral  Georgia        contig_10742   0.01365
CapeCanaveral  Georgia        contig_14898   0.00107
CapeCanaveral  Georgia        contig_8483   -0.00372
      ⋮              ⋮             ⋮           ⋮
NortheastGulf  SoutheastGulf  contig_43517  -0.00146
NortheastGulf  SoutheastGulf  contig_27356   0.02708
NortheastGulf  SoutheastGulf  contig_475     0.0081
NortheastGulf  SoutheastGulf  contig_19384   0.05055
NortheastGulf  SoutheastGulf  contig_22368  -0.0036
NortheastGulf  SoutheastGulf  contig_2784   -0.00066
                                            46377 rows omitted