AMOVA with poppr - pegas implementation - interpretation results + compute % variance

Question

I tried running poppr:amova with dist= NULL (Euclidean distance calculated by the function itself) and either the pegas implementation (see code below). My dataset contains 3000 SNPs and my hierarchical structure consists of 2 clusters, and populations within each clusters. So I have 3 levels: variance among clusters, variance among populations within clusters and variance among individuals (within populations or in general across the whole sample??).

Running poppr::amova with pegas implementation

Eucl_popprAMOVAres = poppr::poppr.amova(
 myGenlight,
    hier = ~clusters/pop,
    clonecorrect = FALSE,
    within = FALSE,
    **dist = NULL**,
    **squared = FALSE**, # false, otherwise it gets sqrooted! is this correct if using Euclidean dist?
    freq = TRUE,
    correction = NULL,
    sep = "_",
    filter = FALSE,
    threshold = 0,
    algorithm = "farthest_neighbor", 
    threads = 1L, 
    missing = "loci", 
    cutoff = 0.05,  
    quiet = FALSE, 
    method = c("pegas"), 
    nperm = 100000) 

Results: Warning message: In poppr::poppr.amova(myGenlgiht, : Missing data are not filtered from genlight data

Analysis of Molecular Variance

Call: pegas::amova(formula = hier, data = hierdf, nperm = nperm, is.squared = FALSE)

            SSD       MSD  df

clusters 1500.402 1500.4016 1

pop 3329.225 832.3063 4

Error 142431.371 847.8058 168

Total 147260.997 851.2196 173

Variance components:

        sigma2 P.value

clusters 8.63952 0.0000

pop -0.53478 0.8762

Error 847.80578

Phi-statistics:

clusters.in.GLOBAL (Phi_CT) pop.in.GLOBAL (Phi_ST) pop.in.clusters (Phi_SC)

           0.0100939536                0.0094691422               -0.0006311825

Variance coefficients:

   a            b                c

28.98276 29.03448 77.33333

I would like to know the following:

• is it correct to set "is.squared = FALSE" if I am letting the function calculate the genetic distance with dist() - which computes the Euclidean distance?

• why does the function tell me "warning: missing data are not filtered" even if I set the argument "missing = "loci" ", so that it should remove all loci for which there are missing information (only in each pairwise distances i think?)

• is it correct that the sigma^2 for clusters = variation among clusters & sigma^2 for pop = variation among populations BUT within clusters?

• what does the **Error **correspond to in my case? would that be the remaining variation - so variation among individuals BUT within populations or within the all sample (across all populations)?

• If I use ade4 implementation in poppr::amova, I also obtain the % variance explained by each hierarchical level. How do I obtain that ifrom the pegas results? Is it correct that to obtain the % variance for each hierarchical level --> i sum all sigma^2 values (cluster+pop+error) and then divide each by the sum? i.e. % variance explained by clusters = sigma^2 for clusters/sum sigmas100 and % variance due to variation among individuals = sigma^2 for error/sum sigmas100 ??

• What do the coefficients a, b, c mean? I understand that they represent the slope/effect of each treatment (in this case group/population/individuals) on the genotype...but how would you interpret them along with the variances?

• Finally, I get opposite results (variation among populations more significant then among clusters) if I use ade4 (with same n permutation in randtest) --> any reason why? and which result to trust?

I would really appreciate some feedback and help interpreting these results!

Thanks!

Gabriella

I tried running popprr:amova with either the pegas and the ade4 implementation and 3 hierarchical levels (clusters, populations, individuals). I set within individuals = false when using pegas because I understand that there is a bug in the within individual computation of variation for this package.

Running poppr::amova with ade4 implementation

my ade4 code and results are below for comparison:

Eucl_popprAMOVAres_ade4 = poppr::poppr.amova(
 myGenlight,
    hier = ~clusters/pop,
    clonecorrect = FALSE,
    within = FALSE,
    dist = NULL,
    squared = FALSE, # false, otherwise it gets sqrooted!
    freq = TRUE,
    correction = NULL,
    sep = "_",
    filter = FALSE,
    threshold = 0,
    algorithm = "farthest_neighbor", 
    threads = 1L, 
    missing = "loci", 
    cutoff = 0.05,  
    quiet = FALSE, 
    method = c("ade4"), 
    nperm = 100000) 

Warning message:

In poppr::poppr.amova(myGenlight, :

Missing data are not filtered from genlight data

$call

ade4::amova(samples = xtab, distances = xdist, structures = xstruct)

$results

                                                         Df      Sum Sq  Mean Sq

Between clusters 1 984.7106 984.7106

Between samples Within clusters 4 3844.9162 961.2291

Within samples 168 142431.3705 847.8058

Total 173 147260.9974 851.2196

$componentsofcovariance

                                                                                     Sigma               %

Variations Between clusters 0.2675142 0.03139829

Variations Between samples(*pops) Within clusters 3.9289742 0.46114598

Variations Within samples (*pops) 847.8057771 99.50745573

Total variations 852.0022654 100.00000000

$statphi

                          Phi

Phi-samples-total 0.0049254427

Phi-samples-clusters 0.0046129082

Phi-clusters-total 0.0003139829

random test

Eucl_popprAMOVAres_ade4_amova.test = randtest( Eucl_popprAMOVAres_ade4, nrepet = 100000)

Eucl_popprAMOVAres_ade4_amova.test

class: krandtest lightkrandtest Monte-Carlo tests Call: randtest.amova(xtest = Scallop_Rep98_Loc95_Eucl_popprAMOVAres_ade4, nrepet = 1e+05)

Number of tests: 3

Adjustment method for multiple comparisons: none Permutation number: 100000 Test Obs Std.Obs Alter Pvalue 1 Variations within samples 847.8057771 -9.8469609 less 9.99990e-06 2 Variations between samples 3.9289742 8.3893135 greater 9.99990e-06 3 Variations between clusters 0.2675142 0.1030489 greater 4.00706e-01

In ade4, the p-value of cluster is much larger than for pop, and pop is very significant. While in pegas: cluster is significant populations within clusters is not.