Structure of the input files
The general structure for running simmr is as follows:
- Call
simmr_loadon the data to get it into the right format - Plot the data in isotope space (‘iso-space’) using
plot - Run the mixing model with
simmr_mcmc - Explore the results with
plotandsummary - If you have multiple groups and want to compare output between them, use the `compare_groups’ function
For the next part of this document, we concentrate on simple examples without grouping structure.
Step 1: Getting the data into simmr
simmr requires at minimum 3 input objects; the consumers or mixtures, the source means, and the source standard deviations. Optionally, you can also add correction data (also called trophic enrichment factors, TEFs) represented again as means and standard deviations, and concentration dependence values. The easiest way to get these objects into simmr is to create an Excel or similar file creating data and then copying it across as in the following example:
mix = matrix(c(-10.13, -10.72, -11.39, -11.18, -10.81, -10.7, -10.54,
-10.48, -9.93, -9.37, 11.59, 11.01, 10.59, 10.97, 11.52, 11.89,
11.73, 10.89, 11.05, 12.3), ncol=2, nrow=10)
colnames(mix) = c('d13C','d15N')
s_names = c("Zostera", "Grass", "U.lactuca", "Enteromorpha")
s_means = matrix(c(-14, -15.1, -11.03, -14.44, 3.06, 7.05, 13.72, 5.96), ncol=2, nrow=4)
s_sds = matrix(c(0.48, 0.38, 0.48, 0.43, 0.46, 0.39, 0.42, 0.48), ncol=2, nrow=4)
c_means = matrix(c(2.63, 1.59, 3.41, 3.04, 3.28, 2.34, 2.14, 2.36), ncol=2, nrow=4)
c_sds = matrix(c(0.41, 0.44, 0.34, 0.46, 0.46, 0.48, 0.46, 0.66), ncol=2, nrow=4)
conc = matrix(c(0.02, 0.1, 0.12, 0.04, 0.02, 0.1, 0.09, 0.05), ncol=2, nrow=4)The mix object above contains the stable isotopic data for the consumers. The data should be listed as the consumer values for the first isotope, followed by the consumer values for the second isotope and so on. The matrix function turns this into a matrix (a rectangle of numbers) with 2 columns. The first column contains the data for isotope 1, and the second the data for isotope 2. Any number of isotopes and observations can be used. It is recommended but not necessary to give the mixtures column names representing the isotopes to which each column corresponds.
The source names are provided in the s_names object, and the source means and standard deviations in s_means and s_sds. These latter objects must also be matrices, where the number of rows is the number of sources, and the number of columns the number of isotopes. In each case, the data are included by listing the values for the first isotope, then the second isotope, and so on.
The correction data is stored in c_means and c_sds. Again this should be a matrix of the same dimension as s_means and s_sds. Finally the concentration dependencies (i.e. the elemental concentration values) are included as conc.
To load the data into simmr, use:
simmr_in = simmr_load(mixtures=mix,
source_names=s_names,
source_means=s_means,
source_sds=s_sds,
correction_means=c_means,
correction_sds=c_sds,
concentration_means = conc)Remember that the correction_means, correction_sds, and concentration_means are optional.
Step 2: Plotting the data in iso-space
We can now plot the raw isotopic data with:
plot(simmr_in)
This will produce a biplot with the isotope that is in the first column on the x-axis, and the isotope in the second column on the y-axis. You can make the plot slightly nicer with some extra arguments:
plot(simmr_in,xlab=expression(paste(delta^13, "C (\u2030)",sep="")),
ylab=expression(paste(delta^15, "N (\u2030)",sep="")),
title='Isospace plot of example data')
See the help file help(plot.simmr_input) for more options on the plotting commands, including the ability to plot different tracers/isotopes when there are more than 2 isotopes.
If all the mixtures lie inside the mixing polygon defined by the sources, then the data are acceptable for running simmr. See Philips et al 2015, Canadian Journal of Zoology for more details on when data are suitable for running through a mixing model.
Step 3: running simmr
The next step is to actually run the model. This is achieved with the command:
simmr_out = simmr_mcmc(simmr_in)This command takes the object simmr_in we created earlier and uses it as input for the model. It tells simmr to store the output from the model run in an object called simmr_out.
The model should take less than a minute to run, though this will depend on the speed of the computer you are using. Other data sets might take slightly longer or shorter depending on the number of sources, isotopes, and observations. The progress of the model is displayed on the command line window, which shows the percentage complete.
Markov chain Monte Carlo (MCMC) works by repeatedly guessing the values of the dietary proportions and find those values which fit the data best. The initial guesses are usually poor and are discarded as part of an initial phase known as the burn-in. Subsequent iterations are then stored and used for the posterior distribution; the best estimates of the dietary proportions given the data and the model. Because it can take many thousands of iterations to move away from the initial guesses, convergence diagnostics can be created to check the model has run properly. In simmr this is done with:
summary(simmr_out,type='diagnostics')## Gelman diagnostics - these values should all be close to 1.
## If not, try a longer run of simmr_mcmc.
## Point est. Upper C.I.
## Zostera 1 1.00
## Grass 1 1.01
## U.lactuca 1 1.01
## Enteromorpha 1 1.00
## sd_d13C 1 1.00
## sd_d15N 1 1.00If the model run has converged properly the values should be close to 1. If they are above 1.1, we recommend a longer run. See help(simmr_mcmc) for how to do this. The values in this example seem to have converged well. You can alternatively plot the diagnostics with:
#plot(simmr_out,type='convergence')Step 4: exploring the results
simmr produces both textual and graphical summaries of the model run. Starting with the textual summaries, we can get tables of the means, standard deviations and credible intervals (the Bayesian equivalent of a confidence interval) with:
summary(simmr_out,type='statistics')## mean sd
## Zostera 0.220 0.132
## Grass 0.288 0.078
## U.lactuca 0.276 0.032
## Enteromorpha 0.216 0.119
## sd_d13C 0.545 0.235
## sd_d15N 0.422 0.226summary(simmr_out,type='quantiles')## 2.5% 25% 50% 75% 97.5%
## Zostera 0.028 0.111 0.202 0.313 0.502
## Grass 0.148 0.233 0.281 0.339 0.453
## U.lactuca 0.216 0.254 0.275 0.297 0.344
## Enteromorpha 0.032 0.119 0.203 0.299 0.468
## sd_d13C 0.175 0.389 0.515 0.664 1.115
## sd_d15N 0.044 0.271 0.404 0.551 0.922These suggest that the dietary proportions for this model are quite uncertain. However we can see that the credible interval for U.lactuca is the narrowest, running from approximately 20% to 35% of the diet. The reason this one is the narrowest can be seen from the isospace plot - this source is the most clearly separated from the others.
simmr can also produce histograms, boxplots, density plots, and matrix plots of the output. Starting with the density plot:
plot(simmr_out,type='density')
We can see that Zostera and Enteromorpha are poorly constrained in comparison to Grass and especially U.lactuca. Again this is unsurprising since the isospace plot indicated that these were the two most clearly separated sources.
The most useful output plot is the matrix plot:
plot(simmr_out,type='matrix')
This shows the source histograms on the diagonal, contour plots of the relationship between the sources on the upper diagonal, and the correlation between the sources on the lower diagonal. Large negative correlations indicate that the model cannot discern between the two sources; they may lie close together in iso-space. Large positive correlations are also possible when mixture data lie in a polygon consisting of multiple competing sources. Here the largest negative correlation is between Zostera and Enteromorpha. This is because they lie closest together in isospace. In general, high correlations (negative or positive) are indicative of the model being unable to determine which food sources are being consumed, and are an unavoidable part of stable isotope mixing models.
If you want to compare the dietary proportions between two different sources, you can use the compare_sources function. This takes two or more sources and compares the dietary proportions with an optional plot. For example:
compare_sources(simmr_out,source_names=c('Zostera','U.lactuca'))## Prob ( proportion of Zostera > proportion of U.lactuca ) = 0.342
This produces a direct probability that the dietary proportion for the first source is bigger than that of the second. If you want to compare more than two sources, specify them with:
compare_sources(simmr_out,source_names=c('Zostera','U.lactuca','Enteromorpha'))## Most popular orderings are as follows:
## Probability
## Zostera > U.lactuca > Enteromorpha 0.3090
## Enteromorpha > U.lactuca > Zostera 0.2645
## U.lactuca > Enteromorpha > Zostera 0.2245
## U.lactuca > Zostera > Enteromorpha 0.1685
## Enteromorpha > Zostera > U.lactuca 0.0175
## Zostera > Enteromorpha > U.lactuca 0.0160
For further information and options on comparing sources, see help(compare_sources).
