### R script for three-part partitioning of fractions and error calculation using matricies

# Make sure you are in the correct working directory

# To use this script, prepare a .csv file with the following headings, from left to right: dTotal1, dTotal2, dA, dB, dC1, dC2, Flux1, and Flux2 as described in the accompanying paper, and all the values for each parameter listed in each column. The example .csv file associated with this script is called "Supplementary_Dataset_3.csv"

######## Calculating all possible solutions

library(plyr)

data <- read.csv("Supplementary_Dataset_3.csv")
# Imports file
data
# Displays top of your data, to check it is correct

fractions <- function(dTotal1,dTotal2,dA,dB,dC1,dC2,FluxMean) {
	R <- matrix(c(dTotal1,dTotal2,1),ncol=1)
	D <- matrix(c(dA,dA,1,dB,dB,1,dC1,dC2,1),ncol=3)
	fit <- lm(R ~ 0 + D)
	coeffs<-data.frame(summary(fit)[4])[,1]
    fA <- coeffs[1]
    fB <- coeffs[2]
    fC <- coeffs[3]
	FluxA <- coeffs[1]*FluxMean
	FluxB <- coeffs[2]*FluxMean
	FluxC <- coeffs[3]*FluxMean
    m = c(fA,fB,fC,FluxA,FluxB,FluxC)
    return(m)
#	return(summary(fit))
}

fractionscalculator <- function(x){
	results <- data.frame(fA=as.numeric(""),fB=as.numeric(""),fC=as.numeric(""), FluxA=as.numeric(""), FluxB=as.numeric(""),FluxC=as.numeric(""))
	for (i in 1:dim(x)[1]) {
		results[i,] <- t(fractions(x[i,1],x[i,2],x[i,3],x[i,4],x[i,5],x[i,6],x[i,7]))
	}
	return(results)
}
# Creating the function that will calculate the three fractions, given the d13C values as inputs
# This is done by making a 3x3 matrix with the d13C values dA, dB, dC1 / dA, dB, dC2 / 1,1,1. These are our X values in our linear model
# We make a 3x1 matrix with the d13C values dTotal1 / dTotal2 / 1. These are the Y values in our linear model.
# When we fit the linear model, it returns the three coefficients that best fit the two matrices, which correspond to our fA, fB, and fC values.

alld13C <- expand.grid(data[,1:6])
alld13C <- alld13C[complete.cases(alld13C),]
# Creates a dataframe with all possible values of each variable, excluding any NA values.

FluxTable <- data.frame(dTotal1=as.numeric(""),dTotal2=as.numeric(""),Flux1=as.numeric(""),Flux2=as.numeric(""))
for (i in 1:dim(data)[1]){
	FluxTable[i,1] <- data[i,1]
	FluxTable[i,2] <- data[i,2]
	FluxTable[i,3] <- data[i,7]
	FluxTable[i,4] <- data[i,8]
}
FluxTable<-FluxTable[complete.cases(FluxTable),]
FluxTable
# Creating lookup table with just the Total d13C and Total flux 

alld13CFlux1 <- join(alld13C, data.frame(dTotal1=FluxTable[,1],Flux1=FluxTable[,3]), by = "dTotal1")
alld13CFlux <- join(alld13CFlux1, data.frame(dTotal2=FluxTable[,2],Flux2=FluxTable[,4]), by = "dTotal2")
FluxMean <- (alld13CFlux$Flux1 + alld13CFlux$Flux2)/2
alld13CFlux$FluxMean <- FluxMean
alld13CFlux <- alld13CFlux[,c(1:6,9)]
alld13CFlux[1:20,]
# Adding the flux values to the corresponding d13C values

allfractions<-fractionscalculator(alld13CFlux)
# Creates a table reporting all possible values of each fraction
# This can take a long time if you have a large dataset and a regular computer.

fAma <- mean(allfractions$fA)
fBma <- mean(allfractions$fB)
fCma <- mean(allfractions$fC)
FluxAma <- mean(allfractions$FluxA)
FluxBma <- mean(allfractions$FluxB)
FluxCma <- mean(allfractions$FluxC)
DataSummaryAll<-data.frame(fA=fAma, fB=fBma, fC=fCma, FluxA=FluxAma, FluxB=FluxBma, FluxC=FluxCma)
# Calculates mean fractions of each component, A, B, and C and stores them in a data frame
DataSummaryAll

fAva <- var(allfractions$fA)
fBva <- var(allfractions$fB)
fCva <- var(allfractions$fC)
FluxAva <- var(allfractions$FluxA)
FluxBva <- var(allfractions$FluxB)
FluxCva <- var(allfractions$FluxC)
DataSummaryAll<-rbind(DataSummaryAll,data.frame(fA=fAva, fB=fBva, fC=fCva, FluxA=FluxAva, FluxB=FluxBva, FluxC=FluxCva))
# Calculates the variances for each fraction, fA, fB, and fC and adds them to the summary data frame

DataSummaryAll[3,]<-sqrt(DataSummaryAll[2,])
# Adds standard deviation to our Data Summary Table

n=dim(FluxTable)[1]
# Counts total experimental replicates

DataSummaryAll[4,] <- DataSummaryAll[3,]/sqrt(n)
# Adds standard error to the table

alpha = 0.05
# Sets our alpha value of interest

#DataSummaryAll[5,] <- DataSummaryAll[1,]-1.96*DataSummaryAll[4,]
#DataSummaryAll[6,] <- DataSummaryAll[1,]+1.96*DataSummaryAll[4,]
DataSummaryAll[5,] <- DataSummaryAll[1,]-qt(1-alpha/2,df=n-1)*DataSummaryAll[4,]
DataSummaryAll[6,] <- DataSummaryAll[1,]+qt(1-alpha/2,df=n-1)*DataSummaryAll[4,]
# Adds the lower and upper quantiles to the plot - note the function assumes two tails

row.names(DataSummaryAll)<-c("Mean","Variance","StDev","SE","lQ","hQ")
# Sets the final row names for the table

write.table(DataSummaryAll,"ResultsSummaryMatrix.csv",sep=",",row.names=TRUE,col.names=NA)
# Saves the summary data in a file in your working directory