EcoDiet explored on a realistic example

The introduction employed a simplistic expemple of food web to familiarize the user with the basic commands and options of the EcoDiet package. Here we will use a more realistic example (although still artificial!) to run the different EcoDiet configurations, compare their results and hence higlight the complementarity in the different data used.

The data corresponds to 10 trophic groups with stomach content data, and very distinct isotopic measures.

realistic_stomach_data_path <- system.file("extdata", "realistic_stomach_data.csv",
                                           package = "EcoDiet")
realistic_stomach_data <- read.csv(realistic_stomach_data_path)
knitr::kable(realistic_stomach_data)
X Cod Pout Sardine Shrimps Crabs Bivalves Worms Zooplankton Phytoplankton Detritus
Cod 0 0 0 0 0 0 0 0 0 0
Pout 1 0 0 0 0 0 0 0 0 0
Sardine 9 0 0 0 0 0 0 0 0 0
Shrimps 4 4 29 0 24 0 0 0 0 0
Crabs 1 24 0 0 0 0 0 0 0 0
Bivalves 0 3 0 0 11 0 0 0 0 0
Worms 16 30 0 1 24 0 0 0 0 0
Zooplankton 0 27 6 3 0 0 0 0 0 0
Phytoplankton 0 0 14 10 0 16 0 20 0 0
Detritus 0 0 0 12 19 18 18 0 0 0
full 21 30 29 19 29 27 18 20 0 0 
realistic_biotracer_data_path <- system.file("extdata", "realistic_biotracer_data.csv",
                                           package = "EcoDiet")
realistic_biotracer_data <- read.csv(realistic_biotracer_data_path)
knitr::kable(realistic_biotracer_data[c(1:3, 31:33, 61:63), ])
group d13C d15N
1 Cod -12.94144 19.18913
2 Cod -14.96070 20.23939
3 Cod -13.77822 19.48809
31 Pout -13.47127 18.57353
32 Pout -13.16888 17.58714
33 Pout -14.23085 17.38938
61 Sardine -14.56111 16.95231
62 Sardine -15.04729 17.15197
63 Sardine -14.63688 16.90906 
library(EcoDiet)

plot_data(biotracer_data = realistic_biotracer_data,
          stomach_data = realistic_stomach_data)

#> Warning: Use of `biotracer_data$group` is discouraged.
#> ℹ Use `group` instead.

Yes, we are aware that isotopic data is usually messier, but isn’t it a beautiful plot?

The configuration without literature data

We define the configuration we are in, and preprocess the data:

literature_configuration <- FALSE

data <- preprocess_data(biotracer_data = realistic_biotracer_data,
                        trophic_discrimination_factor = c(0.8, 3.4),
                        literature_configuration = literature_configuration,
                        stomach_data = realistic_stomach_data)
#> The model will investigate the following trophic links:
#>               Bivalves Cod Crabs Detritus Phytoplankton Pout Sardine Shrimps
#> Bivalves             0   0     1        0             0    1       0       0
#> Cod                  0   0     0        0             0    0       0       0
#> Crabs                0   1     0        0             0    1       0       0
#> Detritus             1   0     1        0             0    0       0       1
#> Phytoplankton        1   0     0        0             0    0       1       1
#> Pout                 0   1     0        0             0    0       0       0
#> Sardine              0   1     0        0             0    0       0       0
#> Shrimps              0   1     1        0             0    1       1       0
#> Worms                0   1     1        0             0    1       0       1
#> Zooplankton          0   0     0        0             0    1       1       1
#>               Worms Zooplankton
#> Bivalves          0           0
#> Cod               0           0
#> Crabs             0           0
#> Detritus          1           0
#> Phytoplankton     0           1
#> Pout              0           0
#> Sardine           0           0
#> Shrimps           0           0
#> Worms             0           0
#> Zooplankton       0           0

In this configuration, priors are set for each trophic link identified as plausible by the user but the priors are not informed by literature data, and are thus uninformative:

plot_prior(data, literature_configuration)

The marginal prior distributions have different shape depending on the variables:

  • it is flat or uniform for η, the probabilities that a trophic link exists (all the probabilities of existence are thus equiprobable),

  • the marginal distributions for each diet proportion Π are peaking at zero, although the joint distribution for Πs is a flat Dirichlet prior, because all the diet proportions must sum to one.

plot_prior(data, literature_configuration, pred = "Pout")

We define the model, and test if it compiles well with a few iterations and adaptation steps:

filename <- "mymodel.txt"
write_model(file.name = filename, literature_configuration = literature_configuration, print.model = F)
mcmc_output <- run_model(filename, data, run_param="test")
#> 
#> Processing function input....... 
#> 
#> Done. 
#>  
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 316
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 1104
#> 
#> Initializing model
#> 
#> Adaptive phase, 500 iterations x 3 chains 
#> If no progress bar appears JAGS has decided not to adapt 
#>  
#> 
#>  Burn-in phase, 500 iterations x 3 chains 
#>  
#> 
#> Sampling from joint posterior, 500 iterations x 3 chains 
#>  
#> 
#> Calculating statistics....... 
#> 
#> Done.
#> 
#>   /!\ Convergence warning:
#> Out of the 51 variables, 16 variables have a Gelman-Rubin statistic > 1.1.
#> You may consider modifying the model run settings.
#> The variables with the poorest convergence are: PI[7,2], PI[6,2], PI[10,7], PI[4,8], PI[3,2], PI[5,7], PI[8,2], PI[8,7], PI[9,8], PI[5,1].
#> JAGS output for model 'mymodel.txt', generated by jagsUI.
#> Estimates based on 3 chains of 1000 iterations,
#> adaptation = 500 iterations (sufficient),
#> burn-in = 500 iterations and thin rate = 1,
#> yielding 1500 total samples from the joint posterior. 
#> MCMC ran for 0.196 minutes at time 2024-11-21 06:31:23.00638.
#> 
#>              mean     sd    2.5%     50%   97.5% overlap0 f  Rhat n.eff
#> eta[4,1]    0.664  0.085   0.493   0.666   0.819    FALSE 1 1.001  1364
#> eta[5,1]    0.587  0.091   0.411   0.587   0.758    FALSE 1 1.008   238
#> eta[3,2]    0.086  0.057   0.009   0.074   0.217    FALSE 1 1.003   589
#> eta[6,2]    0.088  0.058   0.011   0.077   0.225    FALSE 1 1.022   155
#> eta[7,2]    0.441  0.100   0.252   0.438   0.635    FALSE 1 1.032    66
#> eta[8,2]    0.227  0.084   0.090   0.216   0.417    FALSE 1 1.017   141
#> eta[9,2]    0.730  0.092   0.530   0.738   0.885    FALSE 1 1.008   231
#> eta[1,3]    0.395  0.088   0.225   0.391   0.576    FALSE 1 1.002   787
#> eta[4,3]    0.650  0.084   0.478   0.652   0.808    FALSE 1 1.004   725
#> eta[8,3]    0.808  0.067   0.666   0.813   0.922    FALSE 1 1.003   726
#> eta[9,3]    0.811  0.068   0.664   0.818   0.927    FALSE 1 1.000  1500
#> eta[1,6]    0.122  0.056   0.037   0.115   0.247    FALSE 1 1.000  1500
#> eta[3,6]    0.784  0.072   0.638   0.789   0.904    FALSE 1 1.002  1126
#> eta[8,6]    0.155  0.061   0.056   0.147   0.294    FALSE 1 1.000  1500
#> eta[9,6]    0.970  0.028   0.896   0.979   0.999    FALSE 1 1.000  1500
#> eta[10,6]   0.877  0.057   0.748   0.884   0.966    FALSE 1 1.000  1500
#> eta[5,7]    0.487  0.090   0.324   0.485   0.669    FALSE 1 1.002   666
#> eta[8,7]    0.966  0.032   0.885   0.975   0.999    FALSE 1 1.006   703
#> eta[10,7]   0.233  0.075   0.106   0.226   0.393    FALSE 1 1.013   153
#> eta[4,8]    0.603  0.106   0.394   0.606   0.801    FALSE 1 1.014   140
#> eta[5,8]    0.520  0.104   0.326   0.519   0.723    FALSE 1 1.015   132
#> eta[9,8]    0.098  0.064   0.012   0.084   0.255    FALSE 1 1.025    90
#> eta[10,8]   0.191  0.082   0.059   0.183   0.368    FALSE 1 1.003   551
#> eta[4,9]    0.951  0.048   0.824   0.965   0.999    FALSE 1 1.001  1500
#> eta[5,10]   0.956  0.042   0.843   0.968   0.999    FALSE 1 1.001  1500
#> PI[4,1]     0.415  0.325   0.000   0.373   1.000    FALSE 1 1.182    18
#> PI[5,1]     0.585  0.325   0.000   0.627   1.000    FALSE 1 1.182    18
#> PI[3,2]     0.056  0.162   0.000   0.000   0.622    FALSE 1 1.556    10
#> PI[6,2]     0.128  0.266   0.000   0.000   0.863    FALSE 1 1.992     5
#> PI[7,2]     0.398  0.372   0.000   0.398   0.995    FALSE 1 2.766     4
#> PI[8,2]     0.261  0.330   0.000   0.070   0.981    FALSE 1 1.383     9
#> PI[9,2]     0.156  0.172   0.000   0.102   0.598    FALSE 1 1.097    26
#> PI[1,3]     0.264  0.246   0.000   0.213   0.920    FALSE 1 1.151    18
#> PI[4,3]     0.205  0.154   0.000   0.188   0.529    FALSE 1 1.064    37
#> PI[8,3]     0.242  0.181   0.000   0.224   0.635    FALSE 1 1.106    23
#> PI[9,3]     0.289  0.218   0.000   0.254   0.756    FALSE 1 1.044    56
#> PI[1,6]     0.024  0.067   0.000   0.000   0.208    FALSE 1 1.160    36
#> PI[3,6]     0.331  0.187   0.005   0.328   0.705    FALSE 1 1.002  1500
#> PI[8,6]     0.044  0.093   0.000   0.001   0.328    FALSE 1 1.025   396
#> PI[9,6]     0.327  0.205   0.021   0.305   0.775    FALSE 1 1.006   374
#> PI[10,6]    0.274  0.187   0.000   0.253   0.667    FALSE 1 1.005   591
#> PI[5,7]     0.225  0.191   0.000   0.218   0.613    FALSE 1 1.463     8
#> PI[8,7]     0.478  0.237   0.062   0.486   0.998    FALSE 1 1.353     9
#> PI[10,7]    0.297  0.312   0.000   0.184   0.911    FALSE 1 1.949     5
#> PI[4,8]     0.143  0.172   0.000   0.077   0.578    FALSE 1 1.594     7
#> PI[5,8]     0.271  0.207   0.000   0.248   0.732    FALSE 1 1.156    19
#> PI[9,8]     0.244  0.247   0.000   0.188   0.909    FALSE 1 1.317    12
#> PI[10,8]    0.341  0.244   0.000   0.317   0.879    FALSE 1 1.119    24
#> PI[4,9]     1.000  0.000   1.000   1.000   1.000    FALSE 1    NA     1
#> PI[5,10]    1.000  0.000   1.000   1.000   1.000    FALSE 1    NA     1
#> deviance  866.573 11.206 846.335 866.144 889.857    FALSE 1 1.014   151
#> 
#> **WARNING** Some Rhat values could not be calculated.
#> **WARNING** Rhat values indicate convergence failure. 
#> Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
#> For each parameter, n.eff is a crude measure of effective sample size. 
#> 
#> overlap0 checks if 0 falls in the parameter's 95% credible interval.
#> f is the proportion of the posterior with the same sign as the mean;
#> i.e., our confidence that the parameter is positive or negative.
#> 
#> DIC info: (pD = var(deviance)/2) 
#> pD = 62 and DIC = 928.601 
#> DIC is an estimate of expected predictive error (lower is better).

You should now try to run the model until it converges (it should take around half an hour to run, so we won’t do it in this vignette):

mcmc_output <- run_model(filename, data, run_param="normal", parallelize = T)

Here are the figures corresponding to the results that have converged:

plot_results(mcmc_output, data)

plot_results(mcmc_output, data, pred = "Pout")

You can also plot the results for specific prey if you want a clearer figure:

plot_results(mcmc_output, data, pred = "Pout", 
             variable = "PI", prey = c("Bivalves", "Worms"))

The configuration with literature data

We now change the configuration to add literature data to the model:

literature_configuration <- TRUE
realistic_literature_diets_path <- system.file("extdata", "realistic_literature_diets.csv",
                                               package = "EcoDiet")
realistic_literature_diets <- read.csv(realistic_literature_diets_path)
knitr::kable(realistic_literature_diets)
X Cod Pout Sardine Shrimps Crabs Bivalves Worms Zooplankton Phytoplankton Detritus
Cod 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0 0.0 0 0
Pout 0.4275065 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0 0.0 0 0
Sardine 0.3603675 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0 0.0 0 0
Shrimps 0.0300737 0.5295859 0.0002143 0.0000000 0.0082107 0.0000000 0.0 0.0 0 0
Crabs 0.1410430 0.3332779 0.0000000 0.0000000 0.0000000 0.0000000 0.0 0.0 0 0
Bivalves 0.0000000 0.0006130 0.0000000 0.0000000 0.3441081 0.0000000 0.0 0.0 0 0
Worms 0.0410093 0.1023676 0.0000000 0.0171336 0.4435377 0.0000000 0.0 0.0 0 0
Zooplankton 0.0000000 0.0341557 0.7381375 0.9121505 0.0000000 0.0000000 0.0 0.0 0 0
Phytoplankton 0.0000000 0.0000000 0.2616482 0.0000610 0.0000000 0.9966847 0.0 1.0 0 0
Detritus 0.0000000 0.0000000 0.0000000 0.0706550 0.2041434 0.0033153 1.0 0.0 0 0
pedigree 0.8000000 0.1000000 0.5000000 0.3000000 0.7000000 0.1000000 0.2 0.2 1 1 
data <- preprocess_data(biotracer_data = realistic_biotracer_data,
                        trophic_discrimination_factor = c(0.8, 3.4),
                        literature_configuration = literature_configuration,
                        stomach_data = realistic_stomach_data,
                        literature_diets = realistic_literature_diets,
                        nb_literature = 12,
                        literature_slope = 0.5)
#> The model will investigate the following trophic links:
#>               Bivalves Cod Crabs Detritus Phytoplankton Pout Sardine Shrimps
#> Bivalves             0   0     1        0             0    1       0       0
#> Cod                  0   0     0        0             0    0       0       0
#> Crabs                0   1     0        0             0    1       0       0
#> Detritus             1   0     1        0             0    0       0       1
#> Phytoplankton        1   0     0        0             0    0       1       1
#> Pout                 0   1     0        0             0    0       0       0
#> Sardine              0   1     0        0             0    0       0       0
#> Shrimps              0   1     1        0             0    1       1       0
#> Worms                0   1     1        0             0    1       0       1
#> Zooplankton          0   0     0        0             0    1       1       1
#>               Worms Zooplankton
#> Bivalves          0           0
#> Cod               0           0
#> Crabs             0           0
#> Detritus          1           0
#> Phytoplankton     0           1
#> Pout              0           0
#> Sardine           0           0
#> Shrimps           0           0
#> Worms             0           0
#> Zooplankton       0           0

Now we see that the prior distributions are informed by the literature data:

  • when the literature diet input is > 0, the trophic link probabilities η are shifted toward one. Here this is the case for all prey but we could imagine that the user identify a species as a plausible prey whereas it has not been observed being consumed by the predator in the literature. In that case, the literature diet of 0 would drive η toward 0.

  • the average prior for the diet proportions Π is directly the literature diet input.

plot_prior(data, literature_configuration)

plot_prior(data, literature_configuration, pred = "Pout")

Again, we verify that the model compiles well:

filename <- "mymodel_literature.txt"
write_model(file.name = filename, literature_configuration = literature_configuration, print.model = F)
mcmc_output <- run_model(filename, data, run_param="test")
#> 
#> Processing function input....... 
#> 
#> Done. 
#>  
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 316
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 1594
#> 
#> Initializing model
#> 
#> Adaptive phase, 500 iterations x 3 chains 
#> If no progress bar appears JAGS has decided not to adapt 
#>  
#> 
#>  Burn-in phase, 500 iterations x 3 chains 
#>  
#> 
#> Sampling from joint posterior, 500 iterations x 3 chains 
#>  
#> 
#> Calculating statistics....... 
#> 
#> Done.
#> 
#>   /!\ Convergence warning:
#> Out of the 51 variables, 19 variables have a Gelman-Rubin statistic > 1.1.
#> You may consider modifying the model run settings.
#> The variables with the poorest convergence are: PI[8,6], PI[9,8], PI[5,1], PI[4,1], PI[9,3], PI[3,6], PI[3,2], PI[1,3], PI[10,8], PI[7,2].
#> JAGS output for model 'mymodel_literature.txt', generated by jagsUI.
#> Estimates based on 3 chains of 1000 iterations,
#> adaptation = 500 iterations (sufficient),
#> burn-in = 500 iterations and thin rate = 1,
#> yielding 1500 total samples from the joint posterior. 
#> MCMC ran for 0.197 minutes at time 2024-11-21 06:31:37.734993.
#> 
#>              mean     sd    2.5%     50%   97.5% overlap0 f  Rhat n.eff
#> eta[4,1]    0.667  0.084   0.502   0.670   0.820    FALSE 1 1.000  1500
#> eta[5,1]    0.607  0.087   0.432   0.612   0.763    FALSE 1 1.007   304
#> eta[3,2]    0.360  0.082   0.210   0.357   0.522    FALSE 1 1.002   929
#> eta[6,2]    0.358  0.082   0.207   0.350   0.528    FALSE 1 1.003   595
#> eta[7,2]    0.589  0.085   0.422   0.593   0.744    FALSE 1 1.009   221
#> eta[8,2]    0.451  0.086   0.287   0.449   0.620    FALSE 1 1.005  1010
#> eta[9,2]    0.811  0.070   0.659   0.817   0.924    FALSE 1 1.009   311
#> eta[1,3]    0.519  0.079   0.370   0.518   0.673    FALSE 1 1.007   262
#> eta[4,3]    0.718  0.071   0.575   0.724   0.847    FALSE 1 1.000  1500
#> eta[8,3]    0.848  0.057   0.721   0.854   0.943    FALSE 1 1.000  1500
#> eta[9,3]    0.849  0.057   0.723   0.856   0.941    FALSE 1 1.003   786
#> eta[1,6]    0.158  0.065   0.056   0.149   0.306    FALSE 1 1.000  1500
#> eta[3,6]    0.789  0.069   0.644   0.795   0.907    FALSE 1 1.003   465
#> eta[8,6]    0.191  0.067   0.078   0.184   0.344    FALSE 1 1.034    67
#> eta[9,6]    0.970  0.028   0.899   0.979   0.999    FALSE 1 1.000  1500
#> eta[10,6]   0.882  0.054   0.764   0.889   0.964    FALSE 1 1.001  1500
#> eta[5,7]    0.563  0.080   0.402   0.562   0.715    FALSE 1 1.000  1500
#> eta[8,7]    0.972  0.027   0.902   0.981   0.999    FALSE 1 0.999  1500
#> eta[10,7]   0.366  0.078   0.220   0.363   0.529    FALSE 1 1.002  1500
#> eta[4,8]    0.673  0.093   0.489   0.676   0.843    FALSE 1 1.000  1500
#> eta[5,8]    0.590  0.097   0.399   0.590   0.777    FALSE 1 1.000  1500
#> eta[9,8]    0.229  0.081   0.092   0.221   0.398    FALSE 1 1.002  1500
#> eta[10,8]   0.313  0.092   0.151   0.309   0.512    FALSE 1 1.002  1500
#> eta[4,9]    0.957  0.042   0.847   0.969   0.999    FALSE 1 1.003  1500
#> eta[5,10]   0.960  0.039   0.856   0.972   0.999    FALSE 1 0.999  1500
#> PI[4,1]     0.139  0.287   0.000   0.000   0.995    FALSE 1 1.436    10
#> PI[5,1]     0.861  0.287   0.005   1.000   1.000    FALSE 1 1.436    10
#> PI[3,2]     0.283  0.323   0.000   0.156   0.983    FALSE 1 1.415     9
#> PI[6,2]     0.344  0.328   0.000   0.304   0.958    FALSE 1 1.173    16
#> PI[7,2]     0.195  0.299   0.000   0.000   0.946    FALSE 1 1.361    10
#> PI[8,2]     0.130  0.200   0.000   0.039   0.763    FALSE 1 1.199    20
#> PI[9,2]     0.047  0.091   0.000   0.003   0.302    FALSE 1 1.056   184
#> PI[1,3]     0.342  0.284   0.000   0.305   0.932    FALSE 1 1.393     9
#> PI[4,3]     0.113  0.122   0.000   0.079   0.403    FALSE 1 1.091    28
#> PI[8,3]     0.011  0.031   0.000   0.000   0.107    FALSE 1 1.112    70
#> PI[9,3]     0.533  0.296   0.000   0.540   0.999    FALSE 1 1.434     8
#> PI[1,6]     0.029  0.085   0.000   0.000   0.338    FALSE 1 1.183    26
#> PI[3,6]     0.345  0.270   0.000   0.322   0.915    FALSE 1 1.431     8
#> PI[8,6]     0.265  0.331   0.000   0.090   0.990    FALSE 1 2.882     4
#> PI[9,6]     0.279  0.244   0.000   0.254   0.788    FALSE 1 1.121    22
#> PI[10,6]    0.082  0.157   0.000   0.005   0.581    FALSE 1 1.207    17
#> PI[5,7]     0.099  0.159   0.000   0.010   0.555    FALSE 1 1.024    97
#> PI[8,7]     0.087  0.189   0.000   0.000   0.714    FALSE 1 1.239    17
#> PI[10,7]    0.813  0.268   0.015   0.934   1.000    FALSE 1 1.137    24
#> PI[4,8]     0.221  0.241   0.000   0.135   0.805    FALSE 1 1.052    82
#> PI[5,8]     0.092  0.168   0.000   0.010   0.592    FALSE 1 1.214    23
#> PI[9,8]     0.119  0.230   0.000   0.001   0.812    FALSE 1 1.555     8
#> PI[10,8]    0.567  0.333   0.000   0.627   0.999    FALSE 1 1.388    10
#> PI[4,9]     1.000  0.000   1.000   1.000   1.000    FALSE 1    NA     1
#> PI[5,10]    1.000  0.000   1.000   1.000   1.000    FALSE 1    NA     1
#> deviance  866.127 11.445 845.890 865.288 890.411    FALSE 1 1.008   221
#> 
#> **WARNING** Some Rhat values could not be calculated.
#> **WARNING** Rhat values indicate convergence failure. 
#> Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
#> For each parameter, n.eff is a crude measure of effective sample size. 
#> 
#> overlap0 checks if 0 falls in the parameter's 95% credible interval.
#> f is the proportion of the posterior with the same sign as the mean;
#> i.e., our confidence that the parameter is positive or negative.
#> 
#> DIC info: (pD = var(deviance)/2) 
#> pD = 65 and DIC = 931.11 
#> DIC is an estimate of expected predictive error (lower is better).

You should now try to run the model until it converges (it should take around half an hour to run, so we won’t do it in this vignette):

mcmc_output <- run_model(filename, data, run_param=list(nb_iter=100000, nb_burnin=50000, nb_thin=50, nb_adapt=50000), parallelize = T)

Here are the figures corresponding to the results that have converged:

plot_results(mcmc_output, data)

plot_results(mcmc_output, data, pred = "Pout")

You can save the figures as PNG using:

plot_results(mcmc_output, data, pred = "Pout", save = TRUE, save_path = ".")

Last, if you want to explore further in detail the a posteriori distribution of your parameters Π and η, you can run the following code line, which will store the values for all iterations into a data frame.

reshape_mcmc(mcmc_output, data)