Round Robin Allele Frequencies

This function utilizes rrmlg to calculate multilocus genotypes and then subsets each locus by the resulting MLGs to calculate the round-robin allele frequencies used for pgen and psex.

Usage

rraf(gid, pop = NULL, res = "list", by_pop = FALSE, correction = TRUE, ...)

Arguments

gid

a genind or genclone object

pop

either a formula to set the population factor from the strata slot or a vector specifying the population factor for each sample. Defaults to NULL.

res

either "list" (default), "vector", or "data.frame".

by_pop

When this is TRUE, the calculation will be done by population. Defaults to FALSE

correction

a logical indicating whether or not zero-valued allele frequencies should be corrected using the methods outlined in correcting rare alleles. (Default: TRUE)

...

options from correcting rare alleles. The default is to correct allele frequencies to 1/n

Value

a vector or list of allele frequencies

Details

Calculating allele frequencies for clonal populations is a difficult task. Frequencies calculated on non-clone-corrected data suffer from bias due to non-independent samples. On the other hand, frequencies calculated on clone-corrected data artificially increases the significance of rare alleles. The method of round-robin allele frequencies as presented in Parks and Werth (1993) provides a method of calculating allele frequencies in a way that minimizes both of these effects.

Rare Alleles

Allele frequencies at a given locus are calculated based on samples that are clone corrected without that locus. When this happens, rare alleles have a high likelihood of dropping out, giving them a frequency of "0". For some analyses, this is a perfectly fine outcome, but for analyses such as pgen and psex, this could result in undefined values. Setting correction = TRUE will allow you to control how these zero-valued allele frequencies are corrected. For details, please see the documentation on correcting rare alleles and examples.

Note

When by_pop = TRUE, the output will be a matrix of allele frequencies. Additionally, when the argument pop is not NULL, by_pop is automatically TRUE.

References

Arnaud-Haond, S., Duarte, C. M., Alberto, F., & Serrão, E. A. 2007. Standardizing methods to address clonality in population studies. Molecular Ecology, 16(24), 5115-5139.

Parks, J. C., & Werth, C. R. 1993. A study of spatial features of clones in a population of bracken fern, Pteridium aquilinum (Dennstaedtiaceae). American Journal of Botany, 537-544.

See also

rrmlg, pgen, psex, rare_allele_correction

Author

Zhian N. Kamvar, Jonah Brooks, Stacy A. Krueger-Hadfield, Erik Sotka

Examples

data(Pram)

# Round robin allele frequencies, correcting zero-valued frequencies to 1/nInd(Pram)
rraf(Pram)
#> $PrMS6A1
#> PrMS6A1.165 PrMS6A1.168 
#>   0.5360825   0.4639175 
#> 
#> $Pr9C3A1
#> Pr9C3A1.216 Pr9C3A1.226 
#>   0.5357143   0.4642857 
#> 
#> $PrMS39A1
#> PrMS39A1.130 PrMS39A1.213 PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250 
#>  0.500000000  0.001371742  0.007575758  0.001371742  0.121212121  0.363636364 
#> PrMS39A1.254 
#>  0.007575758 
#> 
#> $PrMS45A1
#> PrMS45A1.154 PrMS45A1.166 PrMS45A1.186 
#>  0.001371742  0.505747126  0.494252874 
#> 
#> $PrMS43A1
#> PrMS43A1.213 PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 PrMS43A1.349 PrMS43A1.357 
#>  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742 
#> PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 PrMS43A1.376 PrMS43A1.380 
#>  0.001371742  0.001371742  0.076923077  0.115384615  0.153846154  0.038461538 
#> PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469 PrMS43A1.473 PrMS43A1.477 
#>  0.115384615  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742 
#> PrMS43A1.481 PrMS43A1.485 PrMS43A1.489 PrMS43A1.493 PrMS43A1.497 PrMS43A1.505 
#>  0.076923077  0.384615385  0.038461538  0.001371742  0.001371742  0.001371742 
#> 


# \dontrun{

## Round robin allele frequencies will be different than observed

# Compare to without round robin:
PrLoc <- seploc(Pram, res = "mat") # get locus by matrix
lapply(PrLoc, colMeans, na.rm = TRUE)
#> $PrMS6A1
#> PrMS6A1.165 PrMS6A1.168 
#>   1.0397805   0.9602195 
#> 
#> $Pr9C3A1
#> Pr9C3A1.216 Pr9C3A1.226 
#>   1.0411523   0.9588477 
#> 
#> $PrMS39A1
#> PrMS39A1.130 PrMS39A1.213 PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250 
#>  1.000000000  0.001371742  0.001371742  0.001371742  0.322359396  0.648834019 
#> PrMS39A1.254 
#>  0.024691358 
#> 
#> $PrMS45A1
#> PrMS45A1.154 PrMS45A1.166 PrMS45A1.186 
#>  0.001371742  1.008230453  0.990397805 
#> 
#> $PrMS43A1
#> PrMS43A1.213 PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 PrMS43A1.349 PrMS43A1.357 
#>  0.001371742  0.027434842  0.001371742  0.002743484  0.004115226  0.001371742 
#> PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 PrMS43A1.376 PrMS43A1.380 
#>  0.002743484  0.035665295  0.189300412  0.209876543  0.407407407  0.058984911 
#> PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469 PrMS43A1.473 PrMS43A1.477 
#>  0.082304527  0.015089163  0.001371742  0.001371742  0.001371742  0.038408779 
#> PrMS43A1.481 PrMS43A1.485 PrMS43A1.489 PrMS43A1.493 PrMS43A1.497 PrMS43A1.505 
#>  0.117969822  0.556927298  0.138545953  0.100137174  0.001371742  0.002743484 
#> 

# Without round robin, clone corrected:
Pcc    <- clonecorrect(Pram, strata = NA) # indiscriminantly clone correct
PccLoc <- seploc(Pcc, res = "mat")
lapply(PccLoc, colMeans, na.rm = TRUE)
#> $PrMS6A1
#> PrMS6A1.165 PrMS6A1.168 
#>   1.0612245   0.9387755 
#> 
#> $Pr9C3A1
#> Pr9C3A1.216 Pr9C3A1.226 
#>   1.0714286   0.9285714 
#> 
#> $PrMS39A1
#> PrMS39A1.130 PrMS39A1.213 PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250 
#>   1.00000000   0.01020408   0.01020408   0.01020408   0.30612245   0.58163265 
#> PrMS39A1.254 
#>   0.08163265 
#> 
#> $PrMS45A1
#> PrMS45A1.154 PrMS45A1.166 PrMS45A1.186 
#>   0.01020408   1.03061224   0.95918367 
#> 
#> $PrMS43A1
#> PrMS43A1.213 PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 PrMS43A1.349 PrMS43A1.357 
#>   0.01020408   0.04081633   0.01020408   0.02040816   0.02040816   0.01020408 
#> PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 PrMS43A1.376 PrMS43A1.380 
#>   0.01020408   0.07142857   0.15306122   0.21428571   0.24489796   0.16326531 
#> PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469 PrMS43A1.473 PrMS43A1.477 
#>   0.08163265   0.05102041   0.01020408   0.01020408   0.01020408   0.07142857 
#> PrMS43A1.481 PrMS43A1.485 PrMS43A1.489 PrMS43A1.493 PrMS43A1.497 PrMS43A1.505 
#>   0.18367347   0.37755102   0.14285714   0.06122449   0.01020408   0.02040816 
#> 

## Different methods of obtaining round robin allele frequencies

# Get vector output.
rraf(Pram, res = "vector")
#>  PrMS6A1.165  PrMS6A1.168  Pr9C3A1.216  Pr9C3A1.226 PrMS39A1.130 PrMS39A1.213 
#>  0.536082474  0.463917526  0.535714286  0.464285714  0.500000000  0.001371742 
#> PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250 PrMS39A1.254 PrMS45A1.154 
#>  0.007575758  0.001371742  0.121212121  0.363636364  0.007575758  0.001371742 
#> PrMS45A1.166 PrMS45A1.186 PrMS43A1.213 PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 
#>  0.505747126  0.494252874  0.001371742  0.001371742  0.001371742  0.001371742 
#> PrMS43A1.349 PrMS43A1.357 PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 
#>  0.001371742  0.001371742  0.001371742  0.001371742  0.076923077  0.115384615 
#> PrMS43A1.376 PrMS43A1.380 PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469 
#>  0.153846154  0.038461538  0.115384615  0.001371742  0.001371742  0.001371742 
#> PrMS43A1.473 PrMS43A1.477 PrMS43A1.481 PrMS43A1.485 PrMS43A1.489 PrMS43A1.493 
#>  0.001371742  0.001371742  0.076923077  0.384615385  0.038461538  0.001371742 
#> PrMS43A1.497 PrMS43A1.505 
#>  0.001371742  0.001371742 

# Getting the output as a data frame allows us to use ggplot2 to visualize
(Prdf <- rraf(Pram, res = "data.frame"))
#>                frequency    locus       allele
#> PrMS6A1.165  0.536082474  PrMS6A1  PrMS6A1.165
#> PrMS6A1.168  0.463917526  PrMS6A1  PrMS6A1.168
#> Pr9C3A1.216  0.535714286  Pr9C3A1  Pr9C3A1.216
#> Pr9C3A1.226  0.464285714  Pr9C3A1  Pr9C3A1.226
#> PrMS39A1.130 0.500000000 PrMS39A1 PrMS39A1.130
#> PrMS39A1.213 0.001371742 PrMS39A1 PrMS39A1.213
#> PrMS39A1.214 0.007575758 PrMS39A1 PrMS39A1.214
#> PrMS39A1.242 0.001371742 PrMS39A1 PrMS39A1.242
#> PrMS39A1.246 0.121212121 PrMS39A1 PrMS39A1.246
#> PrMS39A1.250 0.363636364 PrMS39A1 PrMS39A1.250
#> PrMS39A1.254 0.007575758 PrMS39A1 PrMS39A1.254
#> PrMS45A1.154 0.001371742 PrMS45A1 PrMS45A1.154
#> PrMS45A1.166 0.505747126 PrMS45A1 PrMS45A1.166
#> PrMS45A1.186 0.494252874 PrMS45A1 PrMS45A1.186
#> PrMS43A1.213 0.001371742 PrMS43A1 PrMS43A1.213
#> PrMS43A1.281 0.001371742 PrMS43A1 PrMS43A1.281
#> PrMS43A1.285 0.001371742 PrMS43A1 PrMS43A1.285
#> PrMS43A1.345 0.001371742 PrMS43A1 PrMS43A1.345
#> PrMS43A1.349 0.001371742 PrMS43A1 PrMS43A1.349
#> PrMS43A1.357 0.001371742 PrMS43A1 PrMS43A1.357
#> PrMS43A1.360 0.001371742 PrMS43A1 PrMS43A1.360
#> PrMS43A1.364 0.001371742 PrMS43A1 PrMS43A1.364
#> PrMS43A1.368 0.076923077 PrMS43A1 PrMS43A1.368
#> PrMS43A1.372 0.115384615 PrMS43A1 PrMS43A1.372
#> PrMS43A1.376 0.153846154 PrMS43A1 PrMS43A1.376
#> PrMS43A1.380 0.038461538 PrMS43A1 PrMS43A1.380
#> PrMS43A1.384 0.115384615 PrMS43A1 PrMS43A1.384
#> PrMS43A1.388 0.001371742 PrMS43A1 PrMS43A1.388
#> PrMS43A1.465 0.001371742 PrMS43A1 PrMS43A1.465
#> PrMS43A1.469 0.001371742 PrMS43A1 PrMS43A1.469
#> PrMS43A1.473 0.001371742 PrMS43A1 PrMS43A1.473
#> PrMS43A1.477 0.001371742 PrMS43A1 PrMS43A1.477
#> PrMS43A1.481 0.076923077 PrMS43A1 PrMS43A1.481
#> PrMS43A1.485 0.384615385 PrMS43A1 PrMS43A1.485
#> PrMS43A1.489 0.038461538 PrMS43A1 PrMS43A1.489
#> PrMS43A1.493 0.001371742 PrMS43A1 PrMS43A1.493
#> PrMS43A1.497 0.001371742 PrMS43A1 PrMS43A1.497
#> PrMS43A1.505 0.001371742 PrMS43A1 PrMS43A1.505
library("ggplot2")
ggplot(Prdf, aes(y = allele, x = frequency)) +
  geom_point() +
  facet_grid(locus ~ ., scale = "free_y", space = "free")


## Round Robin allele frequencies by population (matrix only)

# By default, allele frequencies will be corrected by 1/n per population
(Prbp <- rraf(Pram, by_pop = TRUE))
#>               PrMS6A1.165 PrMS6A1.168 Pr9C3A1.216 Pr9C3A1.226 PrMS39A1.130
#> Nursery_CA      0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Nursery_OR      0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> JHallCr_OR      0.6166667   0.3833333   0.6166667   0.3833333          0.5
#> NFChetHigh_OR   0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Coast_OR        0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> HunterCr_OR     0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Winchuck_OR     0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> ChetcoMain_OR   0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> PistolRSF_OR    0.5000000   0.5000000   0.5000000   0.5000000          0.5
#>               PrMS39A1.213 PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250
#> Nursery_CA     0.006896552  0.006896552  0.006896552   0.35000000   0.15000000
#> Nursery_OR     0.014084507  0.014084507  0.035714286   0.07142857   0.35714286
#> JHallCr_OR     0.004098361  0.004098361  0.004098361   0.01923077   0.48076923
#> NFChetHigh_OR  0.008771930  0.020000000  0.008771930   0.04000000   0.42000000
#> Coast_OR       0.029411765  0.029411765  0.029411765   0.40909091   0.09090909
#> HunterCr_OR    0.015151515  0.015151515  0.015151515   0.33333333   0.16666667
#> Winchuck_OR    0.028571429  0.028571429  0.028571429   0.02857143   0.50000000
#> ChetcoMain_OR  0.062500000  0.062500000  0.062500000   0.20000000   0.20000000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000   0.25000000   0.50000000
#>               PrMS39A1.254 PrMS45A1.154 PrMS45A1.166 PrMS45A1.186 PrMS43A1.213
#> Nursery_CA     0.006896552  0.006896552     0.500000     0.500000  0.006896552
#> Nursery_OR     0.035714286  0.014084507     0.500000     0.500000  0.014084507
#> JHallCr_OR     0.004098361  0.004098361     0.537037     0.462963  0.004098361
#> NFChetHigh_OR  0.020000000  0.008771930     0.500000     0.500000  0.008771930
#> Coast_OR       0.029411765  0.029411765     0.500000     0.500000  0.029411765
#> HunterCr_OR    0.015151515  0.015151515     0.500000     0.500000  0.015151515
#> Winchuck_OR    0.028571429  0.028571429     0.500000     0.500000  0.028571429
#> ChetcoMain_OR  0.100000000  0.062500000     0.500000     0.500000  0.062500000
#> PistolRSF_OR   0.250000000  0.250000000     0.500000     0.500000  0.250000000
#>               PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 PrMS43A1.349 PrMS43A1.357
#> Nursery_CA     0.006896552  0.006896552  0.006896552  0.006896552  0.006896552
#> Nursery_OR     0.014084507  0.014084507  0.014084507  0.014084507  0.014084507
#> JHallCr_OR     0.004098361  0.004098361  0.004098361  0.004098361  0.004098361
#> NFChetHigh_OR  0.008771930  0.008771930  0.008771930  0.008771930  0.008771930
#> Coast_OR       0.029411765  0.029411765  0.029411765  0.029411765  0.029411765
#> HunterCr_OR    0.015151515  0.015151515  0.015151515  0.015151515  0.015151515
#> Winchuck_OR    0.028571429  0.028571429  0.028571429  0.028571429  0.028571429
#> ChetcoMain_OR  0.062500000  0.062500000  0.062500000  0.062500000  0.062500000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000  0.250000000  0.250000000
#>               PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 PrMS43A1.376
#> Nursery_CA     0.006896552  0.006896552  0.166666667  0.333333333  0.006896552
#> Nursery_OR     0.014084507  0.125000000  0.125000000  0.250000000  0.014084507
#> JHallCr_OR     0.004098361  0.004098361  0.004098361  0.004098361  0.428571429
#> NFChetHigh_OR  0.008771930  0.008771930  0.111111111  0.055555556  0.055555556
#> Coast_OR       0.029411765  0.029411765  0.250000000  0.029411765  0.029411765
#> HunterCr_OR    0.015151515  0.015151515  0.500000000  0.015151515  0.015151515
#> Winchuck_OR    0.028571429  0.028571429  0.028571429  0.028571429  0.333333333
#> ChetcoMain_OR  0.062500000  0.062500000  0.062500000  0.062500000  0.500000000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000  0.250000000  0.500000000
#>               PrMS43A1.380 PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469
#> Nursery_CA     0.006896552  0.006896552  0.006896552  0.006896552  0.006896552
#> Nursery_OR     0.014084507  0.014084507  0.014084507  0.014084507  0.014084507
#> JHallCr_OR     0.004098361  0.071428571  0.004098361  0.004098361  0.004098361
#> NFChetHigh_OR  0.111111111  0.166666667  0.008771930  0.008771930  0.008771930
#> Coast_OR       0.029411765  0.250000000  0.029411765  0.029411765  0.029411765
#> HunterCr_OR    0.015151515  0.015151515  0.015151515  0.015151515  0.015151515
#> Winchuck_OR    0.166666667  0.028571429  0.028571429  0.028571429  0.028571429
#> ChetcoMain_OR  0.062500000  0.062500000  0.062500000  0.062500000  0.062500000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000  0.250000000  0.250000000
#>               PrMS43A1.473 PrMS43A1.477 PrMS43A1.481 PrMS43A1.485 PrMS43A1.489
#> Nursery_CA     0.006896552  0.006896552  0.006896552   0.33333333   0.16666667
#> Nursery_OR     0.014084507  0.014084507  0.014084507   0.37500000   0.12500000
#> JHallCr_OR     0.004098361  0.004098361  0.004098361   0.42857143   0.07142857
#> NFChetHigh_OR  0.008771930  0.008771930  0.166666667   0.27777778   0.05555556
#> Coast_OR       0.029411765  0.029411765  0.029411765   0.25000000   0.25000000
#> HunterCr_OR    0.015151515  0.015151515  0.015151515   0.01515152   0.01515152
#> Winchuck_OR    0.028571429  0.028571429  0.500000000   0.02857143   0.02857143
#> ChetcoMain_OR  0.062500000  0.166666667  0.166666667   0.16666667   0.06250000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000   0.50000000   0.25000000
#>               PrMS43A1.493 PrMS43A1.497 PrMS43A1.505
#> Nursery_CA     0.006896552  0.006896552  0.006896552
#> Nursery_OR     0.014084507  0.014084507  0.014084507
#> JHallCr_OR     0.004098361  0.004098361  0.004098361
#> NFChetHigh_OR  0.008771930  0.008771930  0.008771930
#> Coast_OR       0.029411765  0.029411765  0.029411765
#> HunterCr_OR    0.500000000  0.015151515  0.015151515
#> Winchuck_OR    0.028571429  0.028571429  0.028571429
#> ChetcoMain_OR  0.062500000  0.062500000  0.062500000
#> PistolRSF_OR   0.250000000  0.250000000  0.250000000

# This might be problematic because populations like PistolRSF_OR has a 
# population size of four.

# By using the 'e' argument to rare_allele_correction, this can be set to a
# more reasonable value.
(Prbp <- rraf(Pram, by_pop = TRUE, e = 1/nInd(Pram)))
#>               PrMS6A1.165 PrMS6A1.168 Pr9C3A1.216 Pr9C3A1.226 PrMS39A1.130
#> Nursery_CA      0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Nursery_OR      0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> JHallCr_OR      0.6166667   0.3833333   0.6166667   0.3833333          0.5
#> NFChetHigh_OR   0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Coast_OR        0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> HunterCr_OR     0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> Winchuck_OR     0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> ChetcoMain_OR   0.5000000   0.5000000   0.5000000   0.5000000          0.5
#> PistolRSF_OR    0.5000000   0.5000000   0.5000000   0.5000000          0.5
#>               PrMS39A1.213 PrMS39A1.214 PrMS39A1.242 PrMS39A1.246 PrMS39A1.250
#> Nursery_CA     0.001371742  0.001371742  0.001371742  0.350000000   0.15000000
#> Nursery_OR     0.001371742  0.001371742  0.035714286  0.071428571   0.35714286
#> JHallCr_OR     0.001371742  0.001371742  0.001371742  0.019230769   0.48076923
#> NFChetHigh_OR  0.001371742  0.020000000  0.001371742  0.040000000   0.42000000
#> Coast_OR       0.001371742  0.001371742  0.001371742  0.409090909   0.09090909
#> HunterCr_OR    0.001371742  0.001371742  0.001371742  0.333333333   0.16666667
#> Winchuck_OR    0.001371742  0.001371742  0.001371742  0.001371742   0.50000000
#> ChetcoMain_OR  0.001371742  0.001371742  0.001371742  0.200000000   0.20000000
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742  0.001371742   0.50000000
#>               PrMS39A1.254 PrMS45A1.154 PrMS45A1.166 PrMS45A1.186 PrMS43A1.213
#> Nursery_CA     0.001371742  0.001371742     0.500000     0.500000  0.001371742
#> Nursery_OR     0.035714286  0.001371742     0.500000     0.500000  0.001371742
#> JHallCr_OR     0.001371742  0.001371742     0.537037     0.462963  0.001371742
#> NFChetHigh_OR  0.020000000  0.001371742     0.500000     0.500000  0.001371742
#> Coast_OR       0.001371742  0.001371742     0.500000     0.500000  0.001371742
#> HunterCr_OR    0.001371742  0.001371742     0.500000     0.500000  0.001371742
#> Winchuck_OR    0.001371742  0.001371742     0.500000     0.500000  0.001371742
#> ChetcoMain_OR  0.100000000  0.001371742     0.500000     0.500000  0.001371742
#> PistolRSF_OR   0.001371742  0.001371742     0.500000     0.500000  0.001371742
#>               PrMS43A1.281 PrMS43A1.285 PrMS43A1.345 PrMS43A1.349 PrMS43A1.357
#> Nursery_CA     0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Nursery_OR     0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> JHallCr_OR     0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> NFChetHigh_OR  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Coast_OR       0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> HunterCr_OR    0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Winchuck_OR    0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> ChetcoMain_OR  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#>               PrMS43A1.360 PrMS43A1.364 PrMS43A1.368 PrMS43A1.372 PrMS43A1.376
#> Nursery_CA     0.001371742  0.001371742  0.166666667  0.333333333  0.001371742
#> Nursery_OR     0.001371742  0.125000000  0.125000000  0.250000000  0.001371742
#> JHallCr_OR     0.001371742  0.001371742  0.001371742  0.001371742  0.428571429
#> NFChetHigh_OR  0.001371742  0.001371742  0.111111111  0.055555556  0.055555556
#> Coast_OR       0.001371742  0.001371742  0.250000000  0.001371742  0.001371742
#> HunterCr_OR    0.001371742  0.001371742  0.500000000  0.001371742  0.001371742
#> Winchuck_OR    0.001371742  0.001371742  0.001371742  0.001371742  0.333333333
#> ChetcoMain_OR  0.001371742  0.001371742  0.001371742  0.001371742  0.500000000
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742  0.001371742  0.500000000
#>               PrMS43A1.380 PrMS43A1.384 PrMS43A1.388 PrMS43A1.465 PrMS43A1.469
#> Nursery_CA     0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Nursery_OR     0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> JHallCr_OR     0.001371742  0.071428571  0.001371742  0.001371742  0.001371742
#> NFChetHigh_OR  0.111111111  0.166666667  0.001371742  0.001371742  0.001371742
#> Coast_OR       0.001371742  0.250000000  0.001371742  0.001371742  0.001371742
#> HunterCr_OR    0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Winchuck_OR    0.166666667  0.001371742  0.001371742  0.001371742  0.001371742
#> ChetcoMain_OR  0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#>               PrMS43A1.473 PrMS43A1.477 PrMS43A1.481 PrMS43A1.485 PrMS43A1.489
#> Nursery_CA     0.001371742  0.001371742  0.001371742  0.333333333  0.166666667
#> Nursery_OR     0.001371742  0.001371742  0.001371742  0.375000000  0.125000000
#> JHallCr_OR     0.001371742  0.001371742  0.001371742  0.428571429  0.071428571
#> NFChetHigh_OR  0.001371742  0.001371742  0.166666667  0.277777778  0.055555556
#> Coast_OR       0.001371742  0.001371742  0.001371742  0.250000000  0.250000000
#> HunterCr_OR    0.001371742  0.001371742  0.001371742  0.001371742  0.001371742
#> Winchuck_OR    0.001371742  0.001371742  0.500000000  0.001371742  0.001371742
#> ChetcoMain_OR  0.001371742  0.166666667  0.166666667  0.166666667  0.001371742
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742  0.500000000  0.001371742
#>               PrMS43A1.493 PrMS43A1.497 PrMS43A1.505
#> Nursery_CA     0.001371742  0.001371742  0.001371742
#> Nursery_OR     0.001371742  0.001371742  0.001371742
#> JHallCr_OR     0.001371742  0.001371742  0.001371742
#> NFChetHigh_OR  0.001371742  0.001371742  0.001371742
#> Coast_OR       0.001371742  0.001371742  0.001371742
#> HunterCr_OR    0.500000000  0.001371742  0.001371742
#> Winchuck_OR    0.001371742  0.001371742  0.001371742
#> ChetcoMain_OR  0.001371742  0.001371742  0.001371742
#> PistolRSF_OR   0.001371742  0.001371742  0.001371742



# }