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EcoTroph Example

1. Installation of the EcoTroph package

The EcoTroph package version 1.6 is available on CRAN and can be installed by calling the install.packages function first and then load the package using the function library.

install.packages("EcoTroph")
library(EcoTroph)

2. Data import and validation

The EcoTroph package requires an input data table containing the following columns: 1) the name of the group representing one or several species gathered together (group_name), 2) the trophic level of the group (TL), 3) the biomass of the group (biomass), 4) the production over biomass ratio or P/B (prod), 5) the catch per fleet of the group (catch.1) and 6) the ratio of the group biomass that would be caught assuming an infinite fishing pressure (accessibility). These parameters generally come from an Ecopath model but can also be independent. Use catch.1, catch.2, catch.x if you have to insert several fisheries. Another column can be added containing the omnivory index of each group (OI). This index is used in the create.smooth function, which we will see in section 3.1.

Your data table should have any of the common formats (e.g. excel, csv, txt) and can be loaded into R using, e.g., the functions read.table or read.csv.
Below you find an example containing the first six rows of a suitable data frame. The example is based on the ecopath model ecopath_guinee (Gascuel et al., 2005; Gascuel et al., 2011) and is included in the package:

data("ecopath_guinee")          # load the example data
kable(head(ecopath_guinee))     # access the first six rows of the data.frame
group_name TL biomass prod catch.1 catch.2 accessibility OI
Whales 4.01 0.03090 0.020 0.000 0.000 0.0 0.059
Dolphins 4.48 0.04330 0.070 0.000 0.000 0.0 0.331
Turtles 2.19 0.02960 0.150 0.000 0.000 0.0 0.338
Sea birds 3.81 0.00128 0.300 0.000 0.000 0.0 0.353
Rays+ 3.97 0.38600 0.363 0.012 0.024 0.9 0.329
Sharks+ 4.31 0.10500 0.410 0.007 0.003 0.8 0.633

\(\color{red}{\text{Note, that the row names have to be specified exactly as above}}\): group_name, TL, biomass, prod, catch.1, accessibility, OI (optional).

You can check the compatibility of your input data table with the EcoTroph package, using the check.table function:

check.table(ecopath_guinee)

If a message appears, read it carefully and correct the dataset in view of the comments. \(\color{red}{\text{No NA is accepted in the inputs}}\), a yield column has to be entered with 0-values if no catches are registered. Yield and the P/B (prod) of detritus groups have to be set to 0.

3. Implementation of the EcoTroph approach

3.1. Creation of the smooth function

The smooth function creates a table enabling the conversion of data referring to specific taxons or functional group’s (e.g. Ecopath trophic groups) into data referring to trophic classes. The major assumption of this function is that the distributions of the trophic groups’ biomass, yield, etc. around their mean trophic level follow a lognormal distribution. The lognormal is defined by a mean (the mean trophic level of the group) and a standard deviation (sigmaLN) which is a measure of the trophic level variability within the group. The create.smooth function contains the following arguments:

\(\color{slategrey}{\text{create.smooth(tab_input,smooth_type=NULL,sigmaLN_cst=NULL,pas=NULL,shift=NULL,smooth_param=NULL)}}\)
  • tab_input is the input data table
  • pas defines the splitting of the trophic classes and has by default a value of 0.1.
  • the argument smooth_type defines the form of the standard deviation (sigmaLN) for the lognormal distribution. Three options are implemented:
    1. If smooth_type=1 (default), sigmaLN is constant. This constant sigmaLN, corresponding to the argument sigmaLN_cst in the function, has by default a value of 0.12, with a shift value (shift) of 1.8 by default.
    2. If smooth_type=2, sigmaLN=smooth_paramln\(\times(TL-0.05)\). The argument smooth_param of this formula defines the slope of the log-linear trophic level variability increase around the mean trophic level of the group. By default, smooth_param=0.07 and shift=0.95 (no need to change the shift value in the function, let shift=NULL; it will be automatically adjusted at 0.95 for smooth_type=2. Same for the argument smooth_param).
    3. If smooth_type=3, sigmaLN for each group is equal to the omnivory index calculated by Ecopath. A warning message will appear if OI’s are equal to 0, they will be automatically changed for a value of 0.01. The argument shift is by default equal to 0 (no need to change the shift value in the function; let shift=NULL, it will be automatically adjusted at 0 for smooth_type=3).

The create.smooth function returns a table of the distribution of each mean trophic level within trophic classes. This enables the construction of trophic spectra.

create.smooth(ecopath_guinee)                      # default choice, sigmaLN
create.smooth(ecopath_guinee, smooth_type = 2)     # sigmaLN=smooth_param*ln(TL-0.5)
create.smooth(ecopath_guinee, smooth_type = 3)     # sigmaLN=ecopath_guinee$OI

We also included the possibility to graphically explore the outputs of the different EcoTroph functions. To plot the output of the create.smooth function, simply call the plot function. For smooth_type 2:

plot(create.smooth(ecopath_guinee, smooth_type=2))

For smooth_type 3

plot(create.smooth(ecopath_guinee, smooth_type=3))

3.2. Data Transposition

The Transpose function uses the output of the create.smooth function to convert the biomass, catches and P/B (prod) values referring to specific taxons or functional groups into data referring to trophic classes. The Transpose function, distributes these variables continuously along the trophic classes. Transpose contains the following arguments:

\(\color{slategrey}{\text{Transpose(tab_smooth, tab_input, column)}}\)
  • tab_smooth is the table returned by the create.smooth function
  • tab_input is the input data table
  • column is the column (e.g. biomass or catch) you want to distribute by trophic class
Transpose(create.smooth(ecopath_guinee), ecopath_guinee, "biomass")     # transpose of the biomass column
Transpose(create.smooth(ecopath_guinee), ecopath_guinee, "catch.1")     # transpose of the catch.1 column

Results are displayed graphically calling the plot function on the table returned by the Transpose function. It returns the principal plots according to the selected column, in particular a plot by group and the associated trophic spectra: biomass trophic spectra (‘biomass’ column), catch trophic spectra (‘catch’ column), P/B trophic spectra (‘prod’ column). Results are displayed graphically calling the plot function on the table returned by the Transpose function.

\(\color{slategrey}{\text{plot(x, scale = NULL, title = NULL, legend.cex = NULL)}}\)
  • x is the table returned by the Transpose function
  • scale specifies whether or not the scale of the y-axis is logarithmic (scale = “log”), by default the scale is linear.
  • title is an argument used to display the title of the plot.
  • legend.cex controls the size of the legend text (default = 0.8).
plot(Transpose(create.smooth(ecopath_guinee), ecopath_guinee, "biomass"), title="biomass", log, legend.cex=0.6) # log scale for the biomasses

plot(Transpose(create.smooth(ecopath_guinee),ecopath_guinee,"catch.1"),title="Small scale fishery", legend.cex=0.6) # insertion of a title

3.3. ET.Main table construction

The create.ETmain function returns a list with 1) a summary table, called ET_Main, containing the principal variables by trophic class; and 2) some intermediate tables: biomass (biomass), accessible biomass (biomass_acc), P/B (prod), accessible P/B (prod_acc), the distribution of each mean trophic level within trophic classes (tab_smooth) and the catch tables (Y). This function can be called directly on the data input table. There is no need of the previous steps (3.1 and 3.2). However, we highly recommend you to follow them for a proper understanding of the EcoTroph model. The create.ETmain function contains the following arguments:

\(\color{slategrey}{\text{create.ETmain(ecopath,smooth_type=NULL,sigmaLN_cst=NULL,pas=NULL,shift=NULL,smooth_param=NULL)}}\)
  • ecopath is the input data table
  • other arguments are arguments of the create.smooth function (3.1.)
create.ETmain(ecopath_guinee)                              # constant sigmaLN
create.ETmain(ecopath_guinee,smooth_type=2)                # sigmaLN=smooth_param*ln(TL-0.05) (cf. 2.1)

Results are displayed graphically calling the plot function on the table returned by the creat.ETmain function. Different plots are created, for instances the biomass trophic spectra, the accessible biomass trophic spectra and the catch trophic spectra. The plot function called on the output of the create.ETmain function, takes the following arguments:

\(\color{slategrey}{\text{plot(x, scale1 = NULL, scale2 = NULL, scale3 = NULL, legend.cex = NULL, ask = interactive)}}\)
  • x is the table returned by the create.ETmain function
  • scale1, scale2 and scale3 specify whether or not the scale of the y-axis in the biomass, accessible biomass or catch plots is logarithmic (scale = “log”) or not (default is linear).
  • legend.cex controls the size of the legend text (default = 0.8).
  • ask is an argument used to control the display of each graph. The default value is interactive.
plot(create.ETmain(ecopath_guinee),legend.cex = 0.6)

4. Simulation of different fishing mortality scenarios

4.1. ET-Diagnosis simulation

ET-Diagnosis is used to simulate the effect of different fishing mortality scenarios on the trophic spectra coming from ET-Transpose and the ET-Main table (create.ETmain). Fishing mortality can be increased or decreased globally, per fleet and/or for selected trophic groups. Thus different combinations of effort multipliers are applied to the initial fishing mortality F\(\tau\). Flow equations enable the calculation of the biomasses B\(\tau\), the productions P\(\tau\) and the catches Y\(\tau\) at equilibrium for each trophic class (\(\tau\)) and combination of fishing effort multipliers. Thereby, we obtain all the trophic spectra representing the situation at equilibrium for each fishing effort multiplier. The model provides an overview of the current fishing impact on the ecosystem (compared to the unexploited state), and the consequences of increasing or decreasing fishing pressures. Effects of fishing mortality at an ecosystem scale include changes in biomass, accessible biomass, production, kinetics (P/B*delta\(\tau\)) and changes of the mean trophic level of the catch and the total biomass. ET.Diagnosis also enables you to investigate effects of different ecosystem functioning hypotheses on the ecosystem and trophic scale properties: 1) the extent of top-down control in the system and 2) the degree of recycling of biomass.

The create.ETdiagnosis function contains the following arguments:

\(\color{slategrey}{\text{create.ETdiagnosis(data, Mul_eff = NULL, Group = NULL, fleet.of.interest = NULL, same.mE = NULL,}}\)
\(\color{slategrey}{\text{B.Input = NULL, Beta = NULL, TopD = NULL, FormD = NULL, TLpred = NULL, Forag.A = NULL,}}\)
\(\color{slategrey}{\text{Kfeed = NULL, Ponto = NULL)}}\)
  • data is the list returned by create.ETmain.
  • Mul_eff is a vector of the different effort multipliers, this vector must contain the value 1 (reference state), by default Mul_eff= 0:5.
  • Group is (are) the trophic group(s) for which fishing pressure is (are) specifically altered, by default all the trophic groups are affected in the same way.
  • fleet.of.interest is a character vector of fleet(s) for which the wants to study specifically the impact of changing associated fishing efforts (default = NULL). This argument is particularly useful if there is more fleet because it limits the mE combination to test and thus reduce the computation time.
  • same.mE is a logical argument (default=F), if TRUE the same effort multipliers are simultaneously applied to all fleets
  • some arguments determining ecosystem functioning:
  • Biomass Input control: B.Input is a logical argument specifying whether or not “Biomass Input Control” has to be implemented in computations (by default B.Input=FALSE), and Beta an argument specifying the magnitude of biomass recycling (trophic level 1, by default Beta=0.2).
  • Top-down control: TopD an argument specifying the magnitude of the control of prey abundances by abundances of theirs predators (by default TopD=0.4), and FormD is a shape parameter (by default FormD=0.5).
  • TLpred the trophic class at which the “predator” trophic classes starts (by default TLpred=3.5).

create.ETdiagnosis returns a list, with one element for each simulated combination of fishing effort multipliers. Each element is a list of two types of results:

  • variables characterizing the state and functioning of the ecosystem, for instance biomass (BIOM_MF), production (Prod_MF), kinetics (P/B*delta\(\tau\), Kin_MF), catches (total and per fleet) and fishing mortality (Fish_Mort) per trophic level.
  • summary statistics (contained in the table ET_Main_diagnose) in absolute and relative values (in comparison with reference state); e.g. total biomass (TOT_B), production (TOT_P), catches (Y), mean trophic level of biomass (TL_TOT_B) and mean trophic level of catches (TL_Y).
res <- create.ETdiagnosis(create.ETmain(ecopath_guinee))

# test impacts on the ecosystem by applying the effort multiplier only on the groups "Barracudas+" and "Carangids"
res2 <- create.ETdiagnosis(create.ETmain(ecopath_guinee), Group = c("Barracudas+","Carangids"))

Calling the plot function on the output of the create.ETdiagnosis function displays the following plots: biomass and catch ratio plots (e.g. R_TOT_B, R_Y_catch.1) as well as biomass and catch trophic spectra for the different effort multipliers and the B/Bref (reference state, effort multiplier = 1) and Y/Yref plots for the principal trophic classes.

In the plot function you can define the following arguments:

\(\color{slategrey}{\text{plot(x, scale = NULL, maxrange = NULL, legend.cex = NULL, ask = interactive)}}\)
  • x is the list object returned by the create.ETdiagnosis function.
  • maxrange is the maximum wanted trophic level for the x-axis (by default maxrange=5.5)
  • for the other arguments refer to section 3.2. and 3.3.
plot(res, scale = "log")       # plots impacts of global changes in fishing effort

4.2. The isopleth plot

Another graphic function, implemented in the EcoTroph package, is the plot_ET.diagnosis_ispoleth. This function enables you to plot the mixed impacts of changing fishing effort of two fleets.

The plot_ET.diagnosis_ispoleth function contains the following arguments:

\(\color{slategrey}{\text{plot_ET.diagnosis_isopleth(x, fleet1, fleet2, var = NULL, n.level = NULL, relative = NULL,}}\)
\(\color{slategrey}{\text{name.fleet1 = NULL, name.fleet2 = NULL, color = NULL, ask = interactive)}}\)
  • x is the list returned by create.ETdiagnosis function.
  • fleet1 is the first group of fleets.
  • fleet2 is the second group of fleets; fishing effort of fleets not assigned in arguments fleet1 and fleet2 remain unchanged. If fleet2=NULL, all fleets, not assigned in fleet1, are assigned in fleet2. If the argument fleet.of.interest has been assigned in the function create.ETdiagnosis, fleet1=fleet.of.interest and thus fleet2 is composed of the remaining fleet(s) (not assigned in fleet.of.interest).
  • var is the argument that defines the variables to be plotted: TOT_B, TOT_B_acc, Y, TL_TOT_B, TL_TOT_B_acc, TL_Y (see 4.1). By default all variables are plotted.
  • n.level is the approximate number of areas (isopleth lines) plotted (by default n.level=7).
  • relative is a logical string (by default relative=FALSE), specifying if the variables have to be plotted in absolute or relative values (in comparison with reference state, Mul_eff=1). Note that if relative=TRUE, mean trophic level of biomass or catches (TL_B, TL_Y) are not plotted.
  • name.fleet1 and name.fleet2 are the names of the fleets, respectively, displayed in x-axis and y-axis titles, by default name.fleet1=‘fleet1’ and name.fleet2=‘fleet2’. If the argument fleet.of.interest has been assigned in the function create.ETdiagnosis, name.fleet1=‘fleet of interest’ and name.fleet2=‘other fleets’.
  • color is the vector of colors of the plot (the length of this vector must be equal to the value of the argument n.level ), by default color=rainbow(n.level).
  • ask is an argument used to control the display of each graph. The default value is interactive.
plot_ETdiagnosis_isopleth(res, fleet1 = "catch.1", fleet2 = "catch.2")

4.3. Maximum sustainable yield (MSY) analysis

The function E_MSY_0.1 tests a range of fishing effort multipliers applied to the global fishing mortality through the create.ETdiagnosis function, and then computes indicators of exploitation state of the different trophic classes: Fmsy & Emsy (fishing mortality or effort multiplier leading to the maximum sustainable yield) and F0.1 & E0.1 (a common precautionary reference point; the fishing mortality or effort multiplier corresponding to 10 % of the slope of the yield-per-recruit curve at it’s origin, Gulland, 1983). E_MSY_0.1 returns a data frame with these four indicators per trophic level. For more information see Gasche et al. (2012). “Global assessment of the fishing impacts on the Southern Benguela ecosystem using an EcoTroph modelling approach”.

E_MSY_0.1 contains the following arguments:

\(\color{slategrey}{\text{E_MSY_0.1(data, Mul_eff = NULL, B.Input = NULL, Beta = NULL, TopD = NULL, FormD = NULL,}}\)
\(\color{slategrey}{\text{TLpred = NULL, maxTL = NULL)}}\)
  • data is the list returned by the create.ETmain function.
  • maxTL is the maximum trophic level for which indicators are computed (by default 5.5).
  • Other arguments are arguments of the create.ETdiagnosis function.

For any trophic level, if E0.1 and/or Emsy value(s) computed by E_MSY_0.1 is (are) equal to the maximum effort multiplier tested, E/F0.1 and or E/Fmsy are replaced by NA.

MSY_0.1<-E_MSY_0.1(create.ETmain(ecopath_guinee))
x11() ; par(mfrow=c(1,2))
plot(row.names(MSY_0.1),MSY_0.1[,"E_0.1"],xlim=c(2,5.5),type="l",lwd=2,col="blue",xlab="Trophic levels",ylab="E 0.1")
plot(row.names(MSY_0.1),MSY_0.1[,"F_0.1"],xlim=c(2,5.5),type="l",lwd=2,col="blue",xlab="Trophic levels",ylab="F 0.1")

5. References

Gasche, L., Gascuel, D., Shannon, L., Shin, Y.J., 2012. Global assessment of the fishing impacts on the Southern Benguela ecosystem using an EcoTroph modelling approach. J. Mar. Syst. 90, 1-12. https://doi.org/10.1016/j.jmarsys.2011.07.012

Gulland, J.A., 1983. Fish Stock Assessment: A Manual of Basic Methods. FAO/Wiley, Chichester, UK, 223 pp.