Estimate correction factors from stable isotope data with known dietary proportions

This function runs a slightly different version of the main simmr_mcmc function with the key difference that it estimates the correction factors (sometimes called trophic enrichment or trophic discrimination factors; TEFs/TDFs) for a given set of dietary proportions.

simmr_mcmc_tdf(
  simmr_in,
  p = matrix(rep(1/simmr_in$n_sources, simmr_in$n_sources), ncol = simmr_in$n_sources,
    nrow = simmr_in$n_obs, byrow = TRUE),
  prior_control = list(c_mean_est = rep(2, simmr_in$n_tracers), c_sd_est = rep(2,
    simmr_in$n_tracers)),
  mcmc_control = list(iter = 10000, burn = 1000, thin = 10, n.chain = 4)
)

Arguments

simmr_in

An object created via the function simmr_load

p

The known dietary proportions for the feeding study. Dietary proportions should be given per individual (even if they are all identical)

prior_control

A list of values including arguments named means and sd which represent the prior means and standard deviations of the correction factors. These can usually be left at their default values unless you wish to include to include prior information on them.

mcmc_control

A list of values including arguments named iter (number of iterations), burn (size of burn-in), thin (amount of thinning), and n.chain (number of MCMC chains).

Value

An object of class simmr_tdf with two named top-level components:

input

The simmr_input object given to the simmr_mcmc function

output

A set of MCMC chains of class mcmc.list from the coda package. These can be analysed using summary.simmr_output_tdf

.

Details

The idea is that this code can be used for feeding studies where an organism is fed a known proportional diet with a view to estimating the correction factors to be used in a later stable isotope mixing model when the organisms are observed in the field.

The main argument of the function is an object created from simmr_load which contains mixture data on a number of tracers and food source means and standard deviations. Any correction factors included in this object will be ignored. The known dietary proportions should be provided for each individual (i.e. should be a matrix with the same number of rows as mix). It is advisable to have multiple different dietary proportion values as part of the feeding experimental design

The output of the function is a posterior distribution on the correction factors for each food source. Just like the output from simmr_mcmc, this should be checked for convergence. Examples are included below to help assist with this check and further plots

If, after running simmr_mcmc_tdf the convergence diagnostics in summary.simmr_output_tdf are not satisfactory, the values of iter, burn and thin in mcmc_control should be increased by e.g. a factor of 10.

References

Andrew C. Parnell, Donald L. Phillips, Stuart Bearhop, Brice X. Semmens, Eric J. Ward, Jonathan W. Moore, Andrew L. Jackson, Jonathan Grey, David J. Kelly, and Richard Inger. Bayesian stable isotope mixing models. Environmetrics, 24(6):387–399, 2013.

Andrew C Parnell, Richard Inger, Stuart Bearhop, and Andrew L Jackson. Source partitioning using stable isotopes: coping with too much variation. PLoS ONE, 5(3):5, 2010.

See also

simmr_load for creating objects suitable for this function, simmr_mcmc for estimating dietary proportions, plot.simmr_input for creating isospace plots, summary.simmr_output_tdf for summarising output

Author

Andrew Parnell <andrew.parnell@mu.ie>

Examples

if (FALSE) {
## Example of estimating TDFs for a simple system with known dietary proportions

# Data set 1: 10 obs on 2 isos, 4 sources, with tefs and concdep
# Assume p = c(0.25, 0.25, 0.25, 0.25)

# The data
data(simmr_data_1)
# Load into simmr
simmr_tdf <- with(
  simmr_data_1,
  simmr_load(
    mixtures = mixtures,
    source_names = source_names,
    source_means = source_means,
    source_sds = source_sds,
    correction_means = correction_means,
    correction_sds = correction_sds,
    concentration_means = concentration_means
  )
)

# Plot
plot(simmr_tdf)

# MCMC run
simmr_tdf_out <- simmr_mcmc_tdf(simmr_tdf,
  p = matrix(
    rep(
      1 / simmr_tdf$n_sources,
      simmr_tdf$n_sources
    ),
    ncol = simmr_tdf$n_sources,
    nrow = simmr_tdf$n_obs,
    byrow = TRUE
  )
)

# Summary
summary(simmr_tdf_out, type = "diagnostics")
summary(simmr_tdf_out, type = "quantiles")

# Now put these corrections back into the model and check the
# iso-space plots and dietary output
simmr_tdf_2 <- with(
  simmr_data_1,
  simmr_load(
    mixtures = mixtures,
    source_names = source_names,
    source_means = source_means,
    source_sds = source_sds,
    correction_means = simmr_tdf_out$c_mean_est,
    correction_sds = simmr_tdf_out$c_sd_est,
    concentration_means = concentration_means
  )
)

# Plot with corrections now
plot(simmr_tdf_2)

simmr_tdf_2_out <- simmr_mcmc(simmr_tdf_2)
summary(simmr_tdf_2_out, type = "diagnostics")
plot(simmr_tdf_2_out, type = "boxplot")
}