`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 2018-01-26, the current version of the package is 0.7.5. `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")`

.

In this vignette, we provide a short guide to the use of `tRophicPosition`

in its current version (0.7.5).

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)`

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)`

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.

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
```

Here FG stands for functional group, and NS refers to an integer representing the north to south ordering of locations. 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, consumer = "Bilagay", consumersColumn = "FG",
b1 = "Pelagic_BL", b2 = "Benthic_BL",
baselineColumn = "FG",
group = "Coquimbo", groupsColumn = "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” and coincide with “Coquimbo” in the column “location” will be extracted as consumer values. 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 the internal database 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 mean 2.9 +- 0.32 se
```

`## Muscle tissue d13C: 18 values with mean 1.3 +- 0.3 se`

```
# Then we use those values within the call to loadIsotopeData()
consumer_with_McCutchan <- loadIsotopeData(BilagayMEC,
consumer = "Bilagay",
b1 = "Pelagic_BL",
b2 = "Benthic_BL",
group = "Coquimbo",
consumersColumn = "FG",
baselineColumn = "FG",
groupsColumn = "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)`

.

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.

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: 16
## Total graph size: 120
##
## 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.

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 3.720 0.1108 0.001751 0.001826
## muDeltaN 3.393 0.1343 0.002123 0.002085
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## TP 3.505 3.647 3.718 3.789 3.946
## muDeltaN 3.124 3.306 3.394 3.481 3.661
```

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
## 3.68 3.44
```

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.

`plot(posterior.samples)`