# tRophicPosition

tRophicPosition, is an R package incorporating a Bayesian model for the calculation of consumer trophic position using stable isotopes with one or two baselines. As of 2017-10-05, the current version of the package is 0.7.2. tRophicPosition uses the powerful approach of Markov Chain Monte Carlo simulations provided by JAGS and the statistical language R. Vignettes can be browsed with browseVignettes("tRophicPosition").

# Introduction

In this vignette, we provide a short guide to the use of tRophicPosition in its current version (0.7.2).

### Stable version - CRAN

First of all, you need to install JAGS for your platform, and then install the stable version of tRophicPosition from CRAN:

install.packages("tRophicPosition")

After that, you have to load the package with:

library(tRophicPosition)

### Development version - GitHub

If you want to install the development version of tRophicPosition, you must install it from GitHub. For this, we use the function install_github() from the package devtools (installation instructions here), which needs to be installed previously (either from CRAN or GitHub):

install.packages("devtools")
library(devtools)

If you are working in Windows, devtools also requires Rtools, or if you are working on a Mac, Xcode (from Apple Store). In Linux you will need to install a compiler and various development libraries.

Besides installing devtools, you must also install JAGS (Just Another Gibbs Sampler), which is at the core of the Bayesian model analysis supporting tRophicPosition.

install_github("clquezada/tRophicPosition", build_vignettes = TRUE)

After installing tRophicPosition, it should be loaded into memory, which automatically reports the version of the software (we need at least 0.6.8-8 to use the routines described in this vignette).

library(tRophicPosition)

## Future releases and how to get support

You are encouraged to use tRophicPosition with your own data, test the package and see if there are any issues or problems. You can send your questions or commentaries to the google group tRophicPosition-support or directly to the email trophicposition-support@googlegroups.com. You can send your questions to http://stackexchange.com/ http://stackoverflow.com/ or even Facebook (stable isotope ecology group).

We are constantly working on future releases of tRophicPosition, so feedback is very much appreciated.

# Working with tRophicPosition

To use tRophicPosition, you need to load data into R. You can use any function you prefer (e.g. read.csv, read.table, etc.) to accomplish this. For convenience, we have included a csv file within the package and we will load it with read.csv. The dataset Bilagay-MEC.csv includes $$\delta^{13}$$C and $$\delta^{15}$$N stable isotope data for one locality for the bilagay Cheilodactylus variegatus (http://www.fishbase.se/summary/Cheilodactylus-variegatus.html), a fish common to the coastal kelp forests of N Chile. It also includes $$\delta^{13}$$C and $$\delta^{15}$$N for two groups of primary consumers -one that provides a long-term integrated indicator of the pelagic baseline (filter feeding bivalves) and another for the benthic baseline (grazing gastropods)-, following Post (2002).

BilagayMEC <- read.csv(system.file("extdata", "Bilagay-MEC.csv",
package = "tRophicPosition"))

In this case we have indicated a system.file function to locate the file within the package. After loading the file, we need to extract the stable isotope data and convert it to a format recognized by the package. If you want to use the package with your own data, you will need to use a data frame that has a similar structure:

head(BilagayMEC)
##   Study Location                       Spp         FG  d13C d15N NS
## 1   MEC Coquimbo Echinolittorina peruviana Benthic_BL -11.1 14.9  1
## 2   MEC Coquimbo Echinolittorina peruviana Benthic_BL -11.9 15.2  1
## 3   MEC Coquimbo Echinolittorina peruviana Benthic_BL -11.7 15.0  1
## 4   MEC Coquimbo Echinolittorina peruviana Benthic_BL -11.5 15.2  1
## 5   MEC Coquimbo         Prisogaster niger Benthic_BL -14.6 16.3  1
## 6   MEC Coquimbo         Prisogaster niger Benthic_BL -13.8 15.7  1

To extract the stable isotope data from the data frame above we will use a function we have provided in the package called loadIsotopeData(). By default, this function extracts $$\delta^{13}$$C and $$\delta^{15}$$N stable isotope values from the columns d13C and d15N, grouping observations by a consumer, one or two baselines and a group identifier (here community, but can be location, time etc):

consumer <- loadIsotopeData(BilagayMEC, species = "Bilagay", speciesColumn = "FG",
b1 = "Pelagic_BL", b2 = "Benthic_BL",
baselineColumn = "FG",
community = "Coquimbo", communityColumn = "Location")

In the case above we have indicated that all observations that coincide with “Pelagic_BL” in the column “FG” will be extracted as baseline1, and all observations that coincide with “Benthic_BL” in the same column will be extracted as baseline2. And also, all observations that coincide with “Bilagay” in the column “FG” will be extracted as consumer values, while also belong to the community “Coquimbo”, coded in the column “Location”. Other options are available, and they can be found with help(loadIsotopeData).

An essential component of the model to estimate trophic position is the trophic discrimination factor (TDF). By default the function loadIsotopeData() returns $$\Delta$$N (3.4 $$\pm$$ 0.98 sd) and $$\Delta$$C (0.39 $$\pm$$ 1.3 sd) based on Post’s (2002) assumptions. But you can change this assumption to use any values, simply adding them as arguments within the call to this function. For example, to get McCutchan’s et al (2003) values on TDF, instead of Post’s (2002) assumptions we could write the following:

# First we get TDF values from bibliography using McCutchan's et al (2003) paper
TDF_values <- TDF(author = "McCutchan", element = "both", type = "muscle")
## You selected McCutchan's et al (2003)
##                   Muscle tissue d15N: 15 values with 2.9 mean +- 0.32 se
## Muscle tissue d13C: 18 values with 1.3 mean +- 0.3 se
# Then we use those values within the call to loadIsotopeData()
species = "Bilagay",
b1 = "Pelagic_BL",
b2 = "Benthic_BL",
community = "Coquimbo",
speciesColumn = "FG",
baselineColumn = "FG",
communityColumn = "Location",
deltaN = TDF_values$deltaN, deltaC = TDF_values$deltaC)

Instead of using mean values $$\pm$$ sd, one possibility of including the uncertainty of TDF is using the raw data. So you can use a list of values given your knowledge of your consumer or a colleague’s information, e.g. deltaN = c(2, 2.1, 1.9, 2.01, 2.2) and/or deltaC = c(0.3, 0.31, 0.4, 0.32).

## Plot the data

At this point we have a consumer object (stable isotope values of bilagay), pelagic and benthic baselines (in this case, $$\delta^{13}$$C and $$\delta^{15}$$N values of filter feeding [pelagic indicator] and grazing [benthic indicator] primary consumer molluscs) plus TDF assumptions based on Post (2002). We have to plot the data to check that everything is fine:

# Here we explicitly include a label for both baseline 1 and baseline 2.
# We could change the label for the consumer (consumer = "new_label"), or even
# change the position of the legend (legend = c(1.15, 1.15) is the default).
plot(consumer, b1 = "Pelagic baseline", b2 = "Benthic baseline")

Here we see that the data for our fish bilagay lay between both $$\delta^{13}$$C baselines, and are $$^{15}$$N-enriched relative to the baselines (which also apparently differ in $$\delta^{15}$$N values).

We have several options for estimating bilagay trophic position. We can calculate a single baseline Bayesian trophic position model which only includes a TDF for nitrogen, or we can include both baselines (which seeing they have different $$\delta^{15}$$N values, seems reasonable), and we can include fractionation for both nitrogen and carbon. This is what we will do – first estimate TP using a single baseline, and then we will calculate the full model, including both baselines and a TDF for both nitrogen and carbon.

## The Bayesian Model

We have coded three Bayesian models into tRophicPosition: one baseline (jagsOneBaseline()), two baselines, without TDF for carbon (jagsTwoBaselines()) and two baseline full model, that includes a TDF for carbon (jagsTwoBaselinesFull()). The model can be defined using either of the functions mentioned, or using the new function jagsBayesianModel(), first introduced in the release 0.6.8 of tRophicPosition.

To make full use of the Bayesian approach coded in tRophicPosition, the user can change the priors for any of the parameters of the different models, or the constants (e.g. lambda). Here we will define an one baseline model:

model.string <- jagsBayesianModel(model = "oneBaseline", TP = "dnorm(4, 0.1)")

The function jagsBayesianModel() receives as arguments the model variable (with three options: “oneBaseline”, “twoBaselines” or “twoBaselinesFull”), and optionally receives any distribution for the parameters. If no argument is received, then by default this function returns the two baselines full model. In the example above we have defined also a normal distribution with a mean of 4 and SD of 0.1 as priors for the parameter TP, which is trophic position. Here we are pretty confident (given the stomach contents) that our fish has a TP = 4. All of the functions that define a Bayesian model, by default return lambda = 2 to indicate the trophic level of the baseline, which in this case is the bivalve Perumytilus purpuratus (pelagic baseline). If you want to change it, simply add this argument within the call to jagsBayesianModel() or any of the other functions.

The next step is to initialize the model, using the function TPmodel(). The only two arguments needed are data and model.string, where the first is the stable isotope data and the second is the Bayesian model we just defined above. The other arguments are optional.

model <- TPmodel(data = consumer, model.string = model.string,
n.adapt = 20000, n.chains = 2)
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 81
##    Unobserved stochastic nodes: 6
##    Total graph size: 110
##
## Initializing model

The initializating phase is needed because samplers adapt their parameters to maximize their efficiency. After the initialization it takes place the actual Markov Chain Monte Carlo sampling, which is done with the function posteriorTP().

posterior.samples <- posteriorTP(model = model, n.iter = 20000,
variable.names = c("TP", "muDeltaN"))

In the example above we set 20,000 MCMC iterations to sample the posterior using the model defined with TPmodel(). Also we defined to monitor the variables "TP" and "muDeltaN" (which is the default). TP is trophic position, our main parameter of interest, but also we included muDeltaN which is the mean for $$\Delta$$N.

## Analyzing and plotting the posterior estimation of trophic position

If everything went well, then we have calculated trophic position with Bayesian inference. The function posteriorTP() returns an object of the class “mcmc.list”, so we can use the generic method summary from the coda package:

summary(posterior.samples)
##
## Iterations = 20010:40000
## Thinning interval = 10
## Number of chains = 2
## Sample size per chain = 2000
##
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
##
##           Mean     SD Naive SE Time-series SE
## TP       3.721 0.1110 0.001755       0.001755
## muDeltaN 3.392 0.1329 0.002102       0.002102
##
## 2. Quantiles for each variable:
##
##           2.5%   25%   50%   75% 97.5%
## TP       3.511 3.647 3.718 3.792 3.949
## muDeltaN 3.120 3.305 3.392 3.482 3.650

The coda package provided useful summary statistics, but some researchers feel that best practice when describing central tendency of posterior distributions is to use the mode. We will use the function getPosteriorMode() to estimate this:

# First we combine both chains (if we sample them)
posterior.combined <- coda::mcmc(do.call(rbind, posterior.samples))

# Then we calculate the mode with this code
getPosteriorMode(posterior.combined)
##       TP muDeltaN
##    3.716    3.343

In order to graphically depict our results we can use the generic plot function from coda package (plot(posterior.samples)), or even use other R packages to process/display the information in the posterior samples, such as MCMCtrace() and MCMCplot() functions from the package MCMCvis:

# First we install the package MCMCvis if we haven't done it before
# install.packages("MCMCvis")

# MCMCvis plots trace and density from posterior samples
MCMCvis::MCMCtrace(posterior.samples)

The plot above (MCMCtrace()) visualizes the trace and density of MCMC chains for our parameters of interest, in this case TP (trophic position) and muDeltaN (mean of TDF for nitrogen). It gives us a quick way to visualize if posterior sampling has converged: there should be no tendency of increase or decrease over time (both chains in trace plot are well mixed) and the density for both parameters should be smooth and unimodal (given the assumptions of the one baseline Bayesian model in this particular case).

The plot below (MCMCplot()) visualizes the posterior distributions of both TP and muDeltaN. It gives a graphic summary of the median and 95 percent credible intervals for each posterior distribution (see ?MCMCplot for details).

# MCMCplot visualize posterior distributions using caterpillar plots
MCMCvis::MCMCplot(posterior.samples, ylim = c(0,5), horiz = FALSE)

When we are dealing with more than one species, or more than one Bayesian model (for one species) we will use the function credibilityIntervals(). This is covered in the rest of vignettes.

# Further use of tRophicPosition

Our aim in building this package was to make it as useful as possible. As such, we have coded a number of more complex (but informative) functions for users who want to take full advantage of tRophicPosition. These functions includes multiple models that compare different means of calculating TP (multiModelTP()), automatic comparisons between multiple species e.g. for community based comparisons, or comparisons for single species across multiple locations (multiSpeciesTP()), pairwise comparison between two (compareTwoDistributions()) or multiple posterior estimations (pairwiseComparisons()), non-Bayesian version of trophic position (parametricTP()), parsing multiple species or communities from a data frame (loadIsotopeData() and extractIsotopeData()), or screening food webs for more than one species (screenFoodWeb()). These functions are described in a number of other vignettes included within the package. To access them with, simply use the following code:

browseVignettes("tRophicPosition")