```
#' OutFLANK: An Fst outlier approach by Mike Whitlock and Katie Lotterhos, University of British Columbia.
#'
#' This function is the original implementation of Outflank by Whitlock and Lotterhos. dartR simply provides a convinient wrapper around their functions and an easier install being an r package (for information please refer to their github repository)
#' This method looks for Fst outliers from a list of Fst's for different loci. It
#'assumes that each locus has been genotyped in all populations with approximately equal coverage.
#'OutFLANK estimates the distribution of Fst based on a trimmed sample of Fst's. It
#'assumes that the majority of loci in the center of the distribution are
#'neutral and infers the shape of the distribution of neutral Fst using a trimmed set of
#'loci. Loci with the highest and lowest Fst's are trimmed from the data set
#'before this inference, and the distribution of Fst df/(mean Fst) is assumed to
#'follow a chi-square distribution. Based on this inferred distribution, each
#'locus is given a q-value based on its quantile in the inferred null
#'distribution.
#'The main procedure is called OutFLANK -- see comments in that
#'function immediately below for input and output formats. The other functions
#'here are necessary and must be uploaded, but are not necessarily needed by the
#'user directly.
#'Steps:
#'@param FstDataFrame A data frame that includes a row for each locus, with columns as follows:
#'\itemize{
#' \item $LocusName: a character string that uniquely names each locus.
#' \item $FST: Fst calculated for this locus. (Kept here to report the unbased Fst of the results)
#' \item $T1: The numerator of the estimator for Fst (necessary, with $T2, to calculate mean Fst)
#' \item $T2: The denominator of the estimator of Fst
#' \item $FSTNoCorr: Fst calculated for this locus without sample
#' size correction. (Used to find outliers)
#' \item $T1NoCorr: The numerator of the estimator for Fst without sample size correction (necessary, with $T2, to
#' calculate mean Fst)
#' \item $T2NoCorr: The denominator of the estimator of Fst
#' without sample size correction
#' \item $He: The heterozygosity of the locus (used to screen out low heterozygosity loci that have a different distribution)
#' }
#'
#' @param LeftTrimFraction The proportion of loci that are trimmed from the lower end of the range of Fst before the likelihood funciton is applied.
#'
#' @param RightTrimFraction The proportion of loci that are trimmed from the upper end of the range of Fst before the likelihood funciton is applied.
#'
#' @param Hmin The minimum heterozygosity required before including calculations from a locus.
#'
#' @param NumberOfSamples The number of spatial locations included in the data set.
#'
#' @param qthreshold The desired false discovery rate threshold for calculating q-values.
#'
#' @return
#'
#' The function returns a list with seven elements:
#' \itemize{
#' \item FSTbar: the mean FST inferred from loci not marked as outliers
#' \item FSTNoCorrbar: the mean FST (not corrected for sample size -gives an upwardly biased estimate of FST)
#' \item dfInferred: the inferred number of degrees of freedom for the chi-square distribution of neutral FST
#' \item numberLowFstOutliers: Number of loci flagged as having a signficantly low FST (not reliable)
#' \item numberHighFstOutliers: Number of loci identified as haivng significantly high FST
#' \item results: a data frame with a row for each locus. This data frame includes all the original columns in the
#' data set, and six new ones:
#' \itemize{
#' \item $indexOrder (the original order of the input data set),
#' \item $GoodH (Boolean variable which is TRUE if the expected heterozygosity is greater than the Hemin set by input),
#' \item $OutlierFlag (TRUE if the method identifies the locus as an outlier, FALSE otherwise), and
#' \item $q (the q-value for the test of neutrality for the locus)
#' \item $pvalues (the p-value for the test of neutrality for the locus)
#' \item $pvaluesRightTail the one-sided (right tail) p-value for a locus
#' }
#' }
#' @export
#' @author Bernd Gruber (bugs? Post to \url{https://groups.google.com/d/forum/dartr}); original implementation of Whitlock & Lotterhos
util.outflank <- function(FstDataFrame, LeftTrimFraction=0.05, RightTrimFraction=0.05, Hmin=0.1, NumberOfSamples, qthreshold=0.05){
#
#
#Setting up necessary columns in dataframe
Fstdata= outputDFStarterNoCorr(FstDataFrame,Hmin)
#making working dataframe with real Fst (no NAs), storing NAs to add back later
workingDataFrame=Fstdata[which(!is.na(Fstdata$FSTNoCorr)),]
storedDataFrameNA=Fstdata[which(is.na(Fstdata$FSTNoCorr)),]
#Finding upper and lower bounds for trimming (eliminating NAs, but not negative FSTs)
sortedDataFrame=workingDataFrame[order(workingDataFrame$FSTNoCorr),]
NLociTotal=length(sortedDataFrame$FSTNoCorr)
SmallestKeeper=ceiling(NLociTotal*LeftTrimFraction)
LargestKeeper=floor(NLociTotal*(1-RightTrimFraction))
LowTrimPoint=sortedDataFrame$FSTNoCorr[[SmallestKeeper]]
HighTrimPoint=sortedDataFrame$FSTNoCorr[[LargestKeeper]]
if(LowTrimPoint<0) {writeLines("ERROR: The smallest FST in the trimmed set must be > 0. Please use a larger LeftTrimFraction."); return()}
if(HighTrimPoint>=1) {writeLines("ERROR: The largest FST in the trimmed set must be < 1. Please use a larger RightTrimFraction."); return()}
#finding dfInferred and Fstbar iteratively
putativeNeutralListTemp=ifelse(workingDataFrame$FSTNoCorr>0,TRUE,FALSE)
oldOutlierFlag=rep(FALSE,NLociTotal)
#Note: All negative FST loci are maked as putative outliers, which will need
#to be tested with the coalescent model later. In the meantime, they are
#removed so as to not confuse the likelihood function.
keepGoing=TRUE
count = 0
#writeLines(paste(mean(workingDataFrame$FSTNoCorr[putativeNeutralListTemp])))
while(keepGoing){
count=count+1
if(count>19) {
keepGoing=FALSE
writeLines("Exceeded iteration maximum.") ###Try with increased maximum value for count two lines above.
}
FstbarNoCorrTemp=fstBarCalculatorNoCorr(workingDataFrame[putativeNeutralListTemp,])
dfInferredTemp=EffectiveNumberSamplesMLE(workingDataFrame$FSTNoCorr[putativeNeutralListTemp],FstbarNoCorrTemp,NumberOfSamples,LowTrimPoint,HighTrimPoint)
workingDataFrame=pOutlierFinderChiSqNoCorr(workingDataFrame,FstbarNoCorrTemp,dfInferredTemp,qthreshold)
#### mark all negative FSTs as outliers if lowest nonneg FST is outlier
#### (because negative Fst estimates can't be evaluated through the
#### chi-square approach on their own)
if(any(workingDataFrame$OutlierFlag[workingDataFrame$FSTNoCorr<LowTrimPoint])) workingDataFrame$OutlierFlag[workingDataFrame$FSTNoCorr<0]=TRUE
####Any loci previously marked as $OutlierFlag=TRUE remain so, even if the new iteration doesn''t flag them as outliers
# workingDataFrame$OutlierFlag=!as.logical((!workingDataFrame$OutlierFlag)*(!oldOutlierFlag))
#Resetting neutral list, and checking whether the outlier list has stabilized
putativeNeutralListTemp=ifelse((!workingDataFrame$OutlierFlag),TRUE,FALSE)
if(sum(putativeNeutralListTemp)==0) {writeLines("No loci in neutral list..."); return("FAIL")}
if(identical(oldOutlierFlag,workingDataFrame$OutlierFlag)) keepGoing=FALSE
######if all in trimmed get IDed as outlier - return to user with warning
if(all(workingDataFrame$OutlierFlag[workingDataFrame$FSTNoCorr<LowTrimPoint])){
writeLines("All loci with Fst below the lower (lefthand) trim point were marked as outliers. Re-run with larger LeftTrimFraction or smaller qthreshold.")
return(0)
}
if(all(workingDataFrame$OutlierFlag[workingDataFrame$FSTNoCorr>HighTrimPoint])){
writeLines("All loci with Fst above the upper (righthand) trim point were marked as outliers. Re-run with smaller RightTrimFraction or smaller qthreshold.")
return(0)
}
oldOutlierFlag=workingDataFrame$OutlierFlag
#writeLines(paste(as.character(count)," ",as.character(sum(putativeNeutralListTemp))))
}
if(count>19) writeLines("Loop iteration limit exceeded.")
numberLowFstOutliers=sum(workingDataFrame$OutlierFlag[(workingDataFrame$FSTNoCorr<LowTrimPoint)])
numberHighFstOutliers=sum(workingDataFrame$OutlierFlag[(workingDataFrame$FSTNoCorr>HighTrimPoint)])
FSTbar=fstBarCalculator(workingDataFrame[putativeNeutralListTemp,])
#merge NA list back to working list, and sort by original order
resultsDataFrame=rbind(workingDataFrame,storedDataFrameNA)
resultsDataFrame=resultsDataFrame[order(resultsDataFrame$indexOrder),]
#return new dataframe
list(FSTbar=FSTbar,FSTNoCorrbar=FstbarNoCorrTemp,dfInferred=dfInferredTemp,numberLowFstOutliers=numberLowFstOutliers,numberHighFstOutliers=numberHighFstOutliers,results=resultsDataFrame)
}
outputDFStarterNoCorr=function(FstDataFrame,Hmin=0.1) {
#This will take a given dataframe with $LocusName, $FST,$He, $T1, $T2, etc. and
# initialize $indexOrder,$GoodH,$OutlierFlag (to 0), and $q (to 1).
#Hmin is the smallest allowable He for which a locus should be included in
#the initial calculations. By default this requires that a locus have
#heterozygosity equal to 10% or more.
len=length(FstDataFrame$FSTNoCorr)
indexOrder=seq(1,len)
GoodH=ifelse(FstDataFrame$He<Hmin,"lowH","goodH")
OutlierFlag=ifelse(is.na(FstDataFrame$FSTNoCorr),NA,FALSE)
qvalues=rep(NA,len)
pvalues=rep(NA,len)
pvaluesRightTail=rep(NA,len)
cbind(FstDataFrame, indexOrder, GoodH, qvalues,pvalues,pvaluesRightTail,OutlierFlag )
}
pOutlierFinderChiSqNoCorr=function(DataList, Fstbar, dfInferred, qthreshold=0.05){
#Finds outliers based on chi-squared distribution
#Takes given values of dfInferred and Fstbar, and returns a list of p-values and q-values for all loci based on chi-square.
#Assumes that the DataList input has a column called $FSTNoCorr and that empty columns exist for $qvalues and $OutlierFlag
#
#
#Divide DataList into 3 lists: DataListGood has $FST>0; DataListNeg has cases where $FST <=0; and
# DataListNA has cases where $FST is NA.
#DataListNeg is necessary to keep separate here because these cases do not have meaningful results with the chi-square aprach;
# however, they do carry information.
DataListGood=DataList[which(DataList$FSTNoCorr>0),]
DataListNonPosFst=DataList[which(DataList$FSTNoCorr<=0),]
DataListNA=DataList[which(is.na(DataList$FSTNoCorr)),]
pList=pTwoSidedFromChiSq(DataListGood$FSTNoCorr*(dfInferred)/Fstbar,dfInferred)
pListRightTail=1-pchisq(DataListGood$FSTNoCorr*(dfInferred)/Fstbar,dfInferred)
#Note: Change made 13 June 2014; q-values now only calcualted on right-tail one-sided p-values
qtemp=qvalue(pListRightTail,fdr.level=qthreshold,pi0.method="bootstrap")
#Note: Using the bootstrap method here seems OK, but if this causes problems remove the pi0.method="bootstrap" in the previous line to revert to the default.
DataListGood$pvalues=pList
DataListGood$pvaluesRightTail=pListRightTail
DataListGood$qvalues=qtemp$qvalues
DataListGood$OutlierFlag=qtemp$significant
rbind(DataListGood,DataListNonPosFst,DataListNA)
}
pTwoSidedFromChiSq=function(x,df){
#Takes a value x, finds the two-sided p-value for comparison to a chi-square distribution with df degrees of freedom.
pOneSided=pchisq(x,df)
ifelse(pOneSided>.5,(1-pOneSided)*2,pOneSided*2)
}
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.