conf.meth {QFASA}

Confidence Intervals for Diet Proportions

Description

Returns simultaneous confidence intervals for the diet of each species in the prey database.

Usage

conf.meth(
  predator.mat,
  prey.mat,
  p.mat,
  cal.mat = rep(1, length(ext.fa)),
  dist.meas,
  FC = rep(1, nrow(prey.mat)),
  alpha = 0.05,
  nprey = 30,
  R.p = 1,
  R.ps = 100,
  R = 100,
  R.bias = 100,
  noise = 0,
  ext.fa
)

Arguments

predator.mat

matrix containing fatty acid signatures of the predators with fatty acids summing to one.

prey.mat

prey database. A data frame with first column a Species label and other columns fatty acid proportions summing to one..

p.mat

matrix of previously computed predator diet estimates needed for confidence interval calculation.

cal.mat

matrix or vector of calibration coefficients of predators. Each COLUMN corresponds to a different predator. Default is a vector of ones. The number of fatty acids should be the same as the number of predator and prey fatty acids.

dist.meas

distance measure to use for estimation: 1=KL, 2=AIT or 3=CS

FC

vector of prey fat content, one for each individual in prey database. Note that this vector is passed to the gen.pseudo.seals which expects fat content values for individual prey samples while pseudo.seal and p.QFASA expect a species average. Default is a vector of ones.

alpha

1-alpha is the family-wise or overall confidence level. Default is 0.05 for an overall confidence level of 0.95.

nprey

number of prey to sample from the prey database when generating pseudo predators for the nuisance parameter estimation using original QFASA simulating code. Default is 30.

R.p

number of times to re-sample data. Due to algorithm being slow, the default parameter is 1.

R.ps

number of pseudo predators to generate when estimating nuisance parameters. Default is 100.

R

number of bootstrap replicates to use when generating p-values for confidence interval estimation. Default is 100.

R.bias

number of replicates for bias computation. Default is 100.

noise

proportion of noise to include in the generation of pseudo predators using original QFASA simulating code.

ext.fa

subset of fatty acids to be used. These should be the same as those in predator.mat, prey.mat and cal.mat.

Details

Intervals are biased corrected as recommended in Stewart, C. (2013). Intervals are slow to obtain, particularly if there are many prey types. See vignette on parallel execution to speed up calculations.

Value

Simultaneous (1-alpha)*100 zero-inflated beta distribution.

References

Stewart, C. (2013) Zero-inflated beta distribution for modeling the proportions in quantitative fatty acid signature analysis. Journal of Applied Statistics, 40(5), 985-992.

Examples

## Reducing prey database to three species so that code below will run more quickly.
## Please uncomment code to run.

#set.seed(1234)
## Fatty Acids
#data(FAset)
#fa.set = as.vector(unlist(FAset))

## Sample of Predators
#data(predatorFAs)
#predator.matrix = predatorFAs[, -c(1:4)]
#predator.matrix.ext = predatorFAs[,fa.set]
#predator.matrix.ext = predator.matrix.ext/rowSums(predator.matrix.ext)

# Prey Database
#prey.red =
#preyFAs[preyFAs$Species=="capelin"|preyFAs$Species=="herring"|preyFAs$Species=="sandlance", ]
#prey.red = prey.red[,-c(1,3)]
#prey.red.ext = prey.red[,c("Species",fa.set)]
#prey.red.ext[,-1] <- prey.red.ext[,-1]/rowSums(prey.red.ext[,-1])
#prey.red.ext.means = MEANmeth(prey.red.ext)

## Calibration Coefficients

#data(CC)
#cal.vec = CC[CC$FA %in% fa.set, 2]

#diet.est <- p.QFASA(predator.mat = predator.matrix.ext,
#                    prey.mat = prey.red.ext.means,
#                    cal.mat = cal.vec,
#                   dist.meas = 2,
#                    start.val = rep(1,nrow(prey.red.ext.means)),
#                    ext.fa = fa.set)[['Diet Estimates']]

## conf.meth needs the full prey matrix unlike in p.QFASA
#ci <- conf.meth(predator.mat = predator.matrix.ext, prey.mat = prey.red.ext, cal.mat = cal.vec,
#          p.mat = diet.est, dist.meas = 2, ext.fa = fa.set)