Estimating genotype probabilities in a mapping population
In this example, we’ll import some data from an F1 mapping population of Miscanthus sinensis that were output by the UNEAK pipeline. These data are from a study by Liu et al. (2015; doi:10.1111/gcbb.12275; data available at http://hdl.handle.net/2142/79522), and can be found in the “extdata” folder of the polyRAD installation. Miscanthus is an ancient tetraploid that has undergone diploidization. Given the ability of the UNEAK pipeline to filter paralogs, we expect most loci to behave in a diploid fashion, but some may behave in an allotetraploid fashion.
We’ll start by loading polyRAD and importing the data into a RADdata object. The possiblePloidies argument indicates the expected inheritance modes: diploid (2) and allotetraploid (2 2).
library(polyRAD)
maphmcfile <- system.file("extdata", "ClareMap_HapMap.hmc.txt",
package = "polyRAD")
mydata <- readHMC(maphmcfile,
possiblePloidies = list(2, c(2, 2)))
mydata## ## RADdata object ##
## 299 taxa and 50 loci
## 766014 total reads
## Assumed sample cross-contamination rate of 0.001
##
## Possible ploidies:
## Autodiploid (2)
## Allotetraploid (2 2)We can view the imported taxa names (subsetted here for space).
## [1] "IGR-2011-001" "Kaskade-Justin" "Map1-001"
## [4] "Map1-002" "Map1-003" "Map1-005"
## [7] "Map1-008" "Map1-011" "Map1-016"
## [10] "Map1-018" "Map1-488" "Map1-489"
## [13] "Map1-490" "Map1-491" "Zebrinus-Justin"
## [16] "p196-150A-c" "p877-348-b"All names starting with “Map” are progeny. “Kaskade-Justin” and “Zebrinus-Justin” are the parents. “IGR-2011-001”, “p196-150A-c”“, and”p877-348-b" aren’t part of the population, but were doubled haploid lines that were used to screen for paralogous markers. We can tell polyRAD which taxa are the parents; since this is an F1 population it doesn’t matter which is “donor” and which is “recurrent”.
mydata <- SetDonorParent(mydata, "Kaskade-Justin")
mydata <- SetRecurrentParent(mydata, "Zebrinus-Justin")The next thing we’ll want to do is add our genomic alignment data. For this dataset, we have alignment data stored in a CSV file, also in the “extdata” directory of the polyRAD installation. We’ll add it to the locTable slot of our RADdata object. Be sure to name the new columns “Chr” and “Pos”.
alignfile <- system.file("extdata", "ClareMap_alignments.csv",
package = "polyRAD")
aligndata <- read.csv(alignfile, row.names = 1)
head(aligndata)## Sorghum.LG Position.on.Sorghum.LG..bp.
## TP5489 1 4560204
## TP13305 1 4584260
## TP18261 1 2911329
## TP18674 1 387849
## TP19030 1 7576879
## TP26698 1 6972841mydata$locTable$Chr <- aligndata[GetLoci(mydata), 1]
mydata$locTable$Pos <- aligndata[GetLoci(mydata), 2]
head(mydata$locTable)## Chr Pos
## TP5489 1 4560204
## TP13305 1 4584260
## TP18261 1 2911329
## TP18674 1 387849
## TP19030 1 7576879
## TP26698 1 6972841If you don’t have alignment data in your own dataset, you can still use the pipeline described here. Just set useLinkage = FALSE in the code below. The advantage of including alignment data is that gentoypes at linked markers are used for imputing missing or correcting erroneous genotypes.
Now we can run the pipeline. We’ll specify that we don’t want to include the parents or doubled haploid lines in the estimation of allele frequencies or evaluation of genotype frequenecies (excludeTaxa argument). The allowedDeviation argument indicates how different the apparent allele frequency (based on read depth ratios) can be from an expected allele frequency (determined based on ploidy and mapping population type) and still be classified as that allele frequency. The default settings assume an F1 population, but the population type can be adjusted using the n.gen.backcrossing, n.gen.intermating, and n.gen.selfing arguments.
mydata <- PipelineMapping2Parents(mydata,
freqExcludeTaxa = c("Kaskade-Justin",
"Zebrinus-Justin",
"IGR-2011-001",
"p196-150A-c",
"p877-348-b"),
freqAllowedDeviation = 0.06,
useLinkage = TRUE)## Making initial parameter estimates...## Updating priors using linkage...## Done.We can examine the allele frequencies. Allele frequencies that fall outside of the expected ranges will be recorded as they were estimated from read depth.
##
## 0.125 0.185006617653235 0.25 0.375
## 1 1 41 1
## 0.5 0.625 0.75 0.814993382346765
## 12 1 41 1
## 0.875
## 1Genotype likelihood is also stored in the object for each possible genotype at each locus, taxon, and ploidy. This is the probability of seeing the observed distribution of reads.
## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 1 7 0 51 0 32 15
## TP28986_1 TP31810_0 TP31810_1
## 21 10 13## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0
## 0 5.968571e-03 4.881592e-25 9.748162e-01 4.440892e-169 9.920309e-01
## 1 3.115636e-02 3.115636e-02 4.440892e-16 4.440892e-16 2.365849e-10
## 2 4.881592e-25 5.968571e-03 4.440892e-169 9.748162e-01 1.004524e-100
## TP28602_1 TP28986_0 TP28986_1 TP31810_0 TP31810_1
## 0 1.004524e-100 5.158357e-45 1.309455e-56 1.087526e-30 2.697672e-35
## 1 2.365849e-10 8.126672e-02 8.126672e-02 1.365876e-01 1.365876e-01
## 2 9.920309e-01 1.309455e-56 5.158357e-45 2.697672e-35 1.087526e-30## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0
## 0 5.968571e-03 4.881592e-25 9.748162e-01 4.440892e-169 9.920309e-01
## 1 2.662559e-01 3.662109e-04 4.175805e-07 2.075288e-31 1.004524e-04
## 2 3.115636e-02 3.115636e-02 4.440892e-16 4.440892e-16 2.365849e-10
## 3 3.662109e-04 2.662559e-01 2.075288e-31 4.175805e-07 5.778929e-20
## 4 4.881592e-25 5.968571e-03 4.440892e-169 9.748162e-01 1.004524e-100
## TP28602_1 TP28986_0 TP28986_1 TP31810_0 TP31810_1
## 0 1.004524e-100 5.158357e-45 1.309455e-56 1.087526e-30 2.697672e-35
## 1 5.778929e-20 1.233327e-02 1.746741e-05 2.592075e-02 9.787414e-04
## 2 2.365849e-10 8.126672e-02 8.126672e-02 1.365876e-01 1.365876e-01
## 3 1.004524e-04 1.746741e-05 1.233327e-02 9.787414e-04 2.592075e-02
## 4 9.920309e-01 1.309455e-56 5.158357e-45 2.697672e-35 1.087526e-30Above, for one individal (Map1-001), we see its read depth at the first ten alleles (first five loci), followed by the genotype likelihoods under diploid and tetraploid models. For example, at locus TP26698, heterozygosity is the most likely state, although there is a chance that this individual is homozygous for allele 1 and the one read of allele 0 was due to contamination. If this locus is allotetraploid, it is most likely that there is one copy of allele 0 and three copies of allele 1. Other loci have higher depth and as a result there is less uncertainty in the genotype, particularly for the diploid model.
The prior genotype probabilities (expected genotype distributions) are also stored in the object for each possible ploidy. These distributions are estimated based on the most likely parent genotypes. Low confidence parent genotypes can be ignored by increasing the minLikelihoodRatio argument to PipelineMapping2Parents.
## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 0 0.0 0.5 0.25 0.25 0.5 0.0 0.5
## 1 0.5 0.5 0.50 0.50 0.5 0.5 0.5
## 2 0.5 0.0 0.25 0.25 0.0 0.5 0.0
## TP28986_1 TP31810_0 TP31810_1
## 0 0.0 0.5 0.0
## 1 0.5 0.5 0.5
## 2 0.5 0.0 0.5## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 0 0.0 0.0 0 0 0 0 NA
## 1 0.0 0.5 0 0 1 0 NA
## 2 0.5 0.5 1 1 0 0 NA
## 3 0.5 0.0 0 0 0 1 NA
## 4 0.0 0.0 0 0 0 0 NA
## TP28986_1 TP31810_0 TP31810_1
## 0 NA 0 0
## 1 NA 1 0
## 2 NA 0 0
## 3 NA 0 1
## 4 NA 0 0Here we see some pretty big differences under the diploid and allotetraploid models. For example, if TP28405 is behaving in a diploid fashion we expect F2-like segregation since both parents were heterozygous. However, if TP28405 is behaving in an allotetraploid fashion, we expect that both parents are homozygous at differing paralogous loci, resulting in no segregation.
Now we want to determine which ploidy is the best fit for each locus. This is done by comparing genotype prior probabilities to genotype likelihoods and estimating a \(\chi^2\) statistic. Lower values indicate a better fit.
## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1
## [1,] 6.156873 6.156873 7.390125 7.390125 17.60031 17.60031
## [2,] 130.424838 130.424838 178.066213 178.066213 230.45413 230.45413
## TP28986_0 TP28986_1 TP31810_0 TP31810_1
## [1,] 2.107682 2.107682 0.1076233 0.1076233
## [2,] NA NA 238.0402426 238.0402426We can make a plot to get an overall sense of how well the markers fit the diploid versus tetraploid model.
plot(mydata$ploidyChiSq[1,], mydata$ploidyChiSq[2,],
xlab = "Chi-squared for diploid model",
ylab = "Chi-squared for tetraploid model")
abline(a = 0, b = 1, col = "red")
Alleles above the red line fit the diploid model better, and alleles below the red line fit the tetraploid model better. In this case it looks like everything is diploid with fairly high confidence.
Now we’ll examine the posterior genotype probabilities. These are still estimated separately for each ploidy.
## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0
## 0 0.00000e+00 4.95033e-28 1.000000e+00 2.131711e-174 1.000000e+00
## 1 1.00000e+00 1.00000e+00 2.142491e-17 2.142491e-17 2.384855e-10
## 2 4.95033e-28 0.00000e+00 2.131711e-174 1.000000e+00 0.000000e+00
## TP28602_1 TP28986_0 TP28986_1 TP31810_0 TP31810_1
## 0 0.000000e+00 1.287625e-40 0.000000e+00 7.96211e-30 0.00000e+00
## 1 2.384855e-10 1.000000e+00 1.000000e+00 1.00000e+00 1.00000e+00
## 2 1.000000e+00 0.000000e+00 1.287625e-40 0.00000e+00 7.96211e-30## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 0 0.00000000 0.00000000 0 0 0 0 NaN
## 1 0.00000000 0.01442306 0 0 1 0 NaN
## 2 0.98557694 0.98557694 1 1 0 0 NaN
## 3 0.01442306 0.00000000 0 0 0 1 NaN
## 4 0.00000000 0.00000000 0 0 0 0 NaN
## TP28986_1 TP31810_0 TP31810_1
## 0 NaN 0 0
## 1 NaN 1 0
## 2 NaN 0 0
## 3 NaN 0 1
## 4 NaN 0 0We can export the results for use in downstream analysis. The function below weights possible ploidies for each allele based on the results in mydata$ploidyChiSq, and for each taxon outputs a continuous, numerical genotype that is the mean of all possible genotypes weighted by genotype posterior probabilities. By default, one allele per locus is discarded in order to avoid mathematical singularities in downstream analysis. The continuous genotypes also range from zero to one by default, which can be changed with the minval and maxval arguments.
## TP26698_1 TP28405_1 TP28602_0 TP28986_0
## Zebrinus-Justin 5.110893e-01 0.50000014 2.485904e-18 3.232376e-39
## Kaskade-Justin 1.521187e-06 0.49989345 5.002103e-01 5.000000e-01
## Map1-001 4.998375e-01 0.98007584 1.773836e-02 5.000000e-01
## Map1-002 1.126958e-02 0.47687372 4.822616e-01 1.740322e-24
## Map1-003 1.126960e-02 0.03777935 1.773836e-02 5.000000e-01
## Map1-005 1.126958e-02 0.50000000 4.746178e-01 1.578666e-42
## TP31810_0
## Zebrinus-Justin 5.000000e-01
## Kaskade-Justin 1.583328e-20
## Map1-001 4.998870e-01
## Map1-002 1.129795e-04
## Map1-003 1.129795e-04
## Map1-005 4.998870e-01Note that the parent weighted mean genotypes were estimated using gentoype likelihood only, ignoring the priors set for the progeny. In some places they may not match the progeny genotypes, indicating a likely error in parental genotype calling. We can see the parental genotypes that were used for estimating progeny priors using $likelyGeno_donor and $likelyGeno_recurrent.
## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 2 2 0 1 1 1 1 1
## 4 4 0 2 2 2 2 NA
## TP28986_1 TP31810_0 TP31810_1
## 2 1 0 2
## 4 NA 0 4## TP26698_0 TP26698_1 TP28405_0 TP28405_1 TP28602_0 TP28602_1 TP28986_0
## 2 1 1 1 1 0 2 0
## 4 1 3 2 2 0 4 0
## TP28986_1 TP31810_0 TP31810_1
## 2 2 1 1
## 4 4 2 2
