backward.elimination {QFASA}

Returns diet estimates corresponding to a sample of predators based on a backward elimination algorithm that chooses the prey species to be included in the modelling.

Description

Returns diet estimates corresponding to a sample of predators based on a backward elimination algorithm that chooses the prey species to be included in the modelling.

Usage

backward.elimination(
  pred.mat,
  prey.mat,
  cal.vec,
  FC,
  ext.fa,
  k = 2,
  cutoff = 0.1,
  silence = FALSE
)

Arguments

pred.mat

matrix containing the FA signatures of the predators, where each row corresponds to a predator and each column to a FA.

prey.mat

data frame containing the FA signatures of the prey, where each row corresponds to a single individual prey. The first column must index the prey group, while the remaining columns correspond to FAs.

cal.vec

numeric vector of calibration coefficients corresponding to the FAs contained in the modelling subset ext.fa. A vector of ones in the length of ext.fa may be used for modelling without calibration coefficients.

FC

numeric vector of the average lipid contents for each prey group, in the order of the alphabetized prey groups. vector of ones equal in length to the number of prey groups may be used for modelling without adjustment for fat content.

ext.fa

character vector containing the subset of FAs to be used in modelling.

k

scaling factor to be used in calculating the value of the information criterion (IC). The default value of 2 corresponds to the Akaike Information Criterion. For a sample of size n, k = log(n) corresponds to the Bayesian Information Criterion. As this factor is numeric, values corresponding to other IC may be used freely.

cutoff

numeric proportion to be used as the threshold for the candidacy for removal of a species in backward elimination. If initial diet estimates for any individual predator find a species to be present in proportions greater than this threshold, that species will not be considered for removal from the model. This reduces computation times and safeguards against the removal of species which may be present in the diets of few predators. All species are considered candidates for removal at a value of 1, while lower values are more conservative. The default value is 0.1.

silence

if true, additional information is printed. Default is false.

Details

The function uses a backward elimination algorithm and the simplified MLE method to choose the prey species to be included in the model and then returns the diet estimates corresponding to these species.

Value

A list with components:

Diet_Estimates

A matrix of the diet estimates for each predator where each row corresponds to a predator and each column to a prey species. The estimates are expressed as proportions summing to one.

Selection_Order

A data frame summarizing each step of the algorithm, giving the order of species removal and the corresponding IC values.

Selection_Tables

A list containing a data frame for each step of the selection process, providing the IC values associated with removing any one candidate species at that step.

See Also

forward.selection()

Examples

 ## This example takes some time to run.
 ## Please uncomment code below to run.

#library(dplyr)
#library(compositions)
## Package data: FAs
#data(FAset)
#fa.set = as.vector(unlist(FAset))

## Package data: Prey
#data(preyFAs)
#prey.sub=(preyFAs[,4:(ncol(preyFAs))])[fa.set]
#prey.sub=prey.sub/apply(prey.sub,1,sum)
#group=as.vector(preyFAs$Species)
#prey.sub = cbind(group,prey.sub)
#sort.preytype <- order(prey.sub[, 1])
#prey.matrix <- prey.sub[sort.preytype,]

## Package data: Predators
#data(predatorFAs)
#tombstone.info = predatorFAs[,1:4]
#predator.matrix = predatorFAs[,5:(ncol(predatorFAs))]
#npredators = nrow(predator.matrix)

## Package data: Fat content
#FC = preyFAs[,c(2,3)]
#FC = as.vector(tapply(FC$lipid,FC$Species,mean,na.rm=TRUE))

## Package data: Calibration coefficients
#data(CC)
#cal.vec = CC[,2]
#cal.mat = replicate(npredators, cal.vec)
#rownames(cal.mat) <- CC$FA
#names(cal.vec) <- rownames(cal.mat)

## QFASA (KL)
#sample.qfasa <- p.QFASA(predator.matrix,MEANmeth(prey.matrix),cal.mat,
#dist.meas = 1,gamma=1,FC,
#start.val = rep(1,nrow(MEANmeth(prey.matrix))),fa.set)

## Backward Elimination
#sample.be <- backward.elimination(predator.matrix, prey.matrix, cal.vec,FC,
#fa.set,cutoff = 0.01)

## Output
#be.estimates <- sample.be$`Diet Estimates`