Integration and simulation with fisheries

Early development of management strategy evaluation (MSE) models originated in fisheries (Polacheck et al. 1999; Smith, Sainsbury, and Stevens 1999; Sainsbury, Punt, and Smith 2000). Consequently, fisheries-focused software for MSE has been extensively developed, including R libraries that focus on the management of species of exceptional interest, such as the Atlantic Bluefin Tuna (Thunnus thynnus) (ABFTMSE; Carruthers and Butterworth 2018a; Carruthers and Butterworth 2018b), and Indian Ocean Bigeye (T. obesus) and Yellowfin (T. albacares) Tuna (MSE-IO-BET-YFT; Kolody and Jumppanen 2016). The largest of all such libraries is the Fisheries Library in R (FLR), which includes an extensive collection of tools targeted for fisheries science. The FLR library has been used in over a hundred publications (recent publications include Jardim et al. 2018; Mackinson et al. 2018; Utizi et al. 2018), and includes an MSE framework for evaluating different harvest control rules.

As part of the ConFooBio project, a central focus of GMSE is on simulating the management of animal populations of conservation interest, with a particular emphasis on understanding conservation conflict; further development of GMSE is expected to continue with this as a priority, further building upon the decision-making algorithms of managers and users to better understand how conflict arises and can be managed and mitigated. Hence, GMSE is not intended as a substitute for packages such as FLR, but the integration of these packages with GMSE could make use of GSME’s current and future simulation capabilities, and particularly the genetic algorithm. Such integration might be possible using the gmse_apply function, which allows for custom defined sub-models to be used within the GMSE framework, and with default GMSE sub-models. Hence, GMSE might be especially useful for modelling the management of fisheries under conditions of increasing competing stakeholder demands and conflicts. We do not attempt such an ambitious project here, but instead show how such a project could be developed through integration of FLR and gmse_apply.

Here we follow a Modelling Stock-Recruitment with FLSR example, then integrate this example with gmse_apply to explore the behaviour of a number of simulated fishers who are goal-driven to maximise their own harvest and a manager that aims to keep the fish stocks at a predefined target level. The core concept in GMSE is that manager can only incentivise fishers to harvest less or more by varying the cost of fishing (through e.g. taxes) given a set manager budget; please note that the manager cannot force the fisher to follow any policy. Based on the cost of fishing, the fisher can then given their own budget decide whether to invest in fishing or keep the budget. This concepts represents a nartural resource managmeent and conservation conflict, where one party aims to maximise their livelihood (fisher) and the other aims to keep a population at a sustainable level and prevent it from going extinct. Importantly, the manager does not have full control over fishers but can set policies to incentivise sustainable behaviour. We emphasise that this example is provided only as demonstration of how GMSE can potentially be integrated with already developed fisheries models, and is not intended to make recommendations for management in any population.

Integrating with the Fisheries Library in R (FLR)

The FLR toolset includes a series of packages, with several tutorials for using them. For simplicity, we focus on a model of stock recruitment to be used as the population model in gmse_apply. This population model will use sample data and one of the many available stock-recruitment models available in FLR, and a custom function will be written to return a single value for stock recruitment. Currently, gmse_apply requires that sub-models return subfunction results either as scalar values or data frames that are structured in the same way as GMSE sub-models. But interpretation of scalar values is left up to the user (e.g., population model results could be interpreted as abundance or biomass; manager policy could be interpreted as cost of harvesting or as total allowable catch). For simplicity, the observation (i.e., estimation) model will be the stock reported from the population model with error. The manager and user models, however, will employ the full power of the default GMSE functions to simulate management and user actions. We first show how a custom function can be made that applies the FLR toolset to a population model.

Modelling stock-recruitment for the population model

Here we closely follow a tutorial from the FLR project. To build the stock-recruitment model, the FLCore package is needed (Kell et al. 2007).

install.packages("FLCore", repos="http://flr-project.org/R");

To start, we need to read in the FLCore and GMSE libraries.

library(FLCore);
## Loading required package: lattice
## FLCore (Version 2.6.7, packaged: 2018-04-17 09:12:42 UTC)
library(GMSE);

For a simplified example in GMSE, we will simulate the process of stock recruitment over multiple time steps using an example stock-recruitment model. The stock-recruitment model describes the relationship between stock-recruitment and spawning stock biomass. The sample that we will work from is a recreation of the North Sea Herring (nsher) dataset available in the FLCore package (Kell et al. 2007). This data set includes recruitment and spawning stock biomass data between 1960 and 2004. First, we initialise an empty FLSR object and read in the recreated herring data files from GMSE, which contains recruitment (rec.n) and spawning stock biomass (ssb.n)

newFL   <- FLSR(); # Initialises the empty FLSR object
data(nsher_data);  # Called from GMSE library (not from FLCore)

The recruitment (rec.n) and spawning stock biomass (ssb.n) data need to be in the form of a vector, array, matrix to use them with FLQuant. We will convert rec.n and ssb.n into matrices.

rec.m        <- as.matrix(rec.n);
ssb.m        <- as.matrix(ssb.n);

We can then construct two FLQuant objects, specifying the relevant years and units.

Frec.m       <- FLQuant(rec.m, dimnames=list(age=1, year = 1960:2004));
Fssb.m       <- FLQuant(ssb.m, dimnames=list(age=1, year = 1960:2004));
Frec.m@units <- "10^3";
Fssb.m@units <- "t*10^3";

We then place the recruitment and spawning stock biomass data into the FLSR object that we created.

rec(newFL)    <- Frec.m;
ssb(newFL)    <- Fssb.m;
range(newFL)  <- c(0, 1960, 0, 2004);

The FLCore package offers several stock-recruitment models. Here we use a Ricker model of stock recruitment (Ricker 1954), and insert this model into the FLSR object below.

model(newFL) <- ricker();

Parameters for the Ricker stock-recruitment model can be estimated with maximum likelihood.

newFL <- fmle(newFL);

Diagnostic plots, identical to those of the modelling stock-recruitment tutorial for the nsher_ri example, are shown below.

plot(newFL);
Output of the FLR plot function for an example Ricker model of stock recruitment on North Sea Herring data.

Output of the FLR plot function for an example Ricker model of stock recruitment on North Sea Herring data.

We now have a working example of a stock-recruitment model, but for our integration with gmse_apply, we will want a function that automates the above to simulate the process of updating the stock-recruitment model. We do this using the custom function created below.

update_SR_model <- function(rec_m, ssb_m, years){
    Frec_m       <- FLQuant(rec_m, dimnames=list(age = 1, year = years));
    Fssb_m       <- FLQuant(ssb_m, dimnames=list(age = 1, year = years));
    Frec_m@units <- "10^3";
    Fssb_m@units <- "t*10^3";
    rec(newFL)   <- Frec.m;
    ssb(newFL)   <- Fssb.m;
    range(newFL) <- c(0, years[1], 0, years[length(years)]);
    model(newFL) <- ricker();
    newFL        <- fmle(newFL);
    return(newFL);
}

The above function will be used within another custom function to predict the next time step of recruitment.

predict_recruitment <- function(rec_m, ssb_m, years, new_ssb){
    newFL <- update_SR_model(rec_m, ssb_m, years);
    a     <- params(newFL)[[1]] # Extract 'a' parameter of the Ricker model
    b     <- params(newFL)[[2]] # Extract 'b' parameter of the Ricker model
    rec   <- a * new_ssb * exp(-b * new_ssb); # Predict the new recruitment
    return(rec)
}

In gmse_apply, we will use the predict_recruitment function above as the resource (i.e., operational) model. The new_ssb reads in the new spawning stock biomass, which will be calculated from the built-in GMSE user model.

Integrating predict_recruitment with gmse_apply

The FLR project includes libraries that can be used to perform a management strategy evaluation (MSE) under fisheries-focused observation, manager, and user models. We will not recreate this approach, or integrate any other sub-models into GMSE as was done for the population model above, although such integration of sub-models should be possible using similar techniques. Our goal here is to instead show how the predict_recruitment model created above can be integrated with gmse_apply, which can then make use of the genetic algorithm to predict the fishers’ behaviour.

We will use a custom observation model, which will simply estimate recruitment with some fixed error.

obs_ssb <- function(resource_vector){
    obs_err <- rnorm(n = 1, mean = 0, sd = 100);
    the_obs <- resource_vector + obs_err;
    return(the_obs);
}

Hence, we can now feed the data from rec.m and ssb.m through predict_recruitment, which will return a value for new recruitment, and this new value can in turn be fed into obs_ssb to predict recruitment with some error. We also need a new spawning stock biomass new_ssb, which we can just initialise with the biomass from the last year in ssb.m

ssb_ini <- ssb.m[length(ssb.m)];
new_rec <- predict_recruitment(rec_m = rec.m, ssb_m = ssb.m, years = 1960:2004,
                               new_ssb = ssb_ini);
obs_rec <- obs_ssb(new_rec);

An initial run of these models gives values of 3835.21 for new_rec and 4005.25 for obs_rec. We are now ready to use the built-in manager and user sub-models in gmse_apply. We will assume that managers attempt to keep a recruitment of 5000, and that there are 10 independent fishers who attempt to maximise their catch. We assign a user budget of manager_budget = 10000, and all other values are set to GMSE defaults. In the built-in GMSE functions, the manager will use the estimate of recruitment based on obs_rec and use it to set the cost of harvesting (culling in GMSE).

yrspan       <- 1960:2004;
rec.m        <- as.matrix(rec.n);
ssb.m        <- as.matrix(ssb.n);

sim <- gmse_apply(res_mod = predict_recruitment, obs_mod = obs_ssb,
                  rec_m = rec.m, ssb_m = ssb.m, years = yrspan, 
                  new_ssb = ssb_ini, manage_target = 5000, stakeholders = 10,
                  manager_budget = 10000);
print(sim);
## $resource_results
## [1] 3835
## 
## $observation_results
## [1] 3786.006
## 
## $manager_results
##          resource_type scaring culling castration feeding help_offspring
## policy_1             1      NA     451         NA      NA             NA
## 
## $user_results
##         resource_type scaring culling castration feeding help_offspring
## Manager             1      NA       0         NA      NA             NA
## user_1              1      NA       2         NA      NA             NA
## user_2              1      NA       2         NA      NA             NA
## user_3              1      NA       2         NA      NA             NA
## user_4              1      NA       2         NA      NA             NA
## user_5              1      NA       2         NA      NA             NA
## user_6              1      NA       2         NA      NA             NA
## user_7              1      NA       2         NA      NA             NA
## user_8              1      NA       2         NA      NA             NA
## user_9              1      NA       2         NA      NA             NA
## user_10             1      NA       2         NA      NA             NA
##         tend_crops kill_crops
## Manager         NA         NA
## user_1          NA         NA
## user_2          NA         NA
## user_3          NA         NA
## user_4          NA         NA
## user_5          NA         NA
## user_6          NA         NA
## user_7          NA         NA
## user_8          NA         NA
## user_9          NA         NA
## user_10         NA         NA

The resource and observation results above are interpreted in terms of recruitment, while the manager results are interpreted in terms of the cost of harvesting a unit of spawning stock biomass and the user results are interpreted in terms of how much biomass was harvested. Note in the run of gmse_apply that the arguments for our custom resource and observation models (predict_recruitment and obs_ssb, respectively) are read directly in as arguments of gmse_apply itself. The gmse_apply function will figure out which subfunctions custom arguments should go to, then update these arguments as needed over the course of a single run of gmse_apply.

Simulation with gmse_apply over multiple time steps

We are now ready to loop the gmse_apply function over multiple time steps. To do this, we will update the rec.m and ssb.m matrices after each time step, simulating 20 years into the future. The population model predict_recruitment will use these data to dynamically update parameters of the Ricker model, as might occur in an empirical fishery that is being monitored. We will use the results from the observation model to update recruitment for the new year in rec.m. For simplicity, spawning stock biomass prior to harvest will be randomly sampled from a value in the last 10 years (i.e., from ssb.m between 1994 and 2004), but more realistic models could relate this spawning stock biomass to recruitment and environmental variables from a previous year; spawning stock biomass will be decreased after harvest based on user actions. The GMSE initialisation and simulation is below.

# This code initialises the simulation -----------------------------------------
yrspan       <- 1960:2004;
rec.m        <- as.matrix(rec.n);
ssb.m        <- as.matrix(ssb.n);
ssb_ini      <- ssb.m[length(ssb.m)];
sim_old      <- gmse_apply(res_mod = predict_recruitment, obs_mod = obs_ssb,
                           rec_m = rec.m, ssb_m = ssb.m, years = yrspan, 
                           new_ssb = ssb_ini, manage_target = 3500, 
                           stakeholders = 10, manager_budget = 10000, 
                           get_res = "Full");
# The code below simulates 20 time steps ---------------------------------------
sim_sum  <- matrix(data = NA, nrow = 20, ncol = 6); # Hold results here
for(time_step in 1:20){
    # Update the relevant parameter values as necessary -----------------------
    rand_ssb        <- sample(x = ssb.m[35:45], size = 1);
    harvest         <- sum(sim_old$basic_output$user_results[,3]);
    new_rec_m       <- c(sim_old$rec_m, sim_old$observation_vector);
    new_ssb_m       <- c(sim_old$ssb_m, rand_ssb - harvest);
    sim_old$rec_m   <- matrix(data = new_rec_m, nrow = 1);
    sim_old$ssb_m   <- matrix(data = new_ssb_m, nrow = 1);
    sim_old$years   <- c(sim_old$years, time_step + 2004);
    sim_old$new_ssb <- sim_old$ssb_m[length(sim_old$ssb_m)];
    # Run a new simulation in the loop: custom functions are always specified -
    sim_new  <- gmse_apply(get_res = "Full", old_list = sim_old,
                           res_mod = predict_recruitment, obs_mod = obs_ssb);
    # Record the results in sim_sum -------------------------------------------
    sim_sum[time_step, 1] <- time_step + 2004;
    sim_sum[time_step, 2] <- sim_new$basic_output$resource_results[1];
    sim_sum[time_step, 3] <- sim_new$basic_output$observation_results[1];
    sim_sum[time_step, 4] <- sim_new$basic_output$manager_results[3];
    sim_sum[time_step, 5] <- harvest;
    sim_sum[time_step, 6] <- sim_new$new_ssb;
    # Redefine the old list --------------------------------------------------
    sim_old               <- sim_new;
}
colnames(sim_sum) <- c("Year", "Recruitment", "Recruit_estim", "Harvest_cost", 
                         "Harvested", "SSB");
print(sim_sum);
##       Year Recruitment Recruit_estim Harvest_cost Harvested      SSB
##  [1,] 2005        3747     3836.2917          219        20  50.6639
##  [2,] 2006        3339     3284.8034          695        40  41.3340
##  [3,] 2007        4208     4074.7835          223        10 160.1926
##  [4,] 2008        2739     2721.5187          681        40  30.6639
##  [5,] 2009        4339     4238.2185          239        10  71.3340
##  [6,] 2010        1427     1323.0842          707        40  13.5966
##  [7,] 2011        2994     3049.7367          890        10  34.8673
##  [8,] 2012        4387     4398.9411          222        10 145.9025
##  [9,] 2013        1146     1127.9553          677        40  10.6133
## [10,] 2014        4387     4290.0107          248        10 145.9025
## [11,] 2015        4547     4572.7221          233        40  85.2627
## [12,] 2016         633      718.4861          699        40   5.5913
## [13,] 2017        3988     4017.3335          247        10 175.5799
## [14,] 2018        1146      999.7101          696        40  10.6133
## [15,] 2019        4339     4324.8141          225        10  71.3340
## [16,] 2020         633      748.0605          713        40   5.5913
## [17,] 2021        3447     3475.5788          886        10  43.5966
## [18,] 2022        4339     4387.0962          241        10  71.3340
## [19,] 2023        3310     3554.8077          219        40  40.7603
## [20,] 2024        2739     2752.7507          698        40  30.6639

The above output from sim_sum reports the recruitment (resource or operational model), recruitment estimate (observation error model), management set harvest cost (harvest control model), user harvested numbers (implementation model) and spawning stock biomass (SSB) simulation results. This example simulation demonstrates the ability of GMSE to integrate with fisheries libraries such as FLR through gmse_apply. In addition to being a useful wrapping function for MSE sub-models, gmse_apply can therefore be used to take advantage of the genetic algorithm in the GMSE default manager and user models. This flexibility will be retained in future versions of gmse_apply, allowing custom resource and observation models that are built for specific systems to be integrated with an increasingly complex genetic algorithm simulating various aspects of human decision-making.

Conclusions

GMSE is a general, flexible, tool for simulating the management of resources under situations of uncertainty and conflict. Management Strategy Evaluation (Bunnefeld, Hoshino, and Milner-Gulland 2011; Punt et al. 2016), the framework upon which GMSE is based, had its origin in fisheries management (Polacheck et al. 1999; Smith, Sainsbury, and Stevens 1999; Sainsbury, Punt, and Smith 2000), and here we showed one example of how GMSE could be integrated with the core package of the Fisheries Library in R.

Future versions of GMSE will continue to be open-source and developed to avoid unecessary dependencies (GMSE v.0.4.0.3 requires only base R). Key goals including (1) providing highly general and useful default resource, observation, manager, and user sub-models for a variety of MSE modelling tasks, (2) keeping these sub-models highly modular so that they can be developed in isolation given standardised data structures, and (3) allowing these modular sub-models to be integrated with custom defined sub-models as flexibly as possible using gmse_apply. Contributions in line with these goals, and suggestions for new features, can be made on GitHub.

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