knobi

library(knobi)

In this vignette we illustrate the use of the knobi package through a real case example. For this purpose, the formulation of the Known Biomass Production Models (KBPMs) is explained and then each of the functions of the package is described and applied to a real case study.

Please note that this vignette does not cover all possibilities for each function in this package (i.e., not all arguments or combinations of arguments are used). Instead, it focuses on describing the basic usage of the functions, with some alternatives included for certain functions. For more detailed information, please refer to the help documentation for each function in the package.

1. KBPM formulation

For a correct understanding of KBPM models, we start reviewing the surplus production models (SPMs) framework and then based on this background the KBPM formulation is described.

 

Traditional SPMs are one of the most widely used data-limited (or data moderated) assessment models. Their general structure relates directly to Russell’s formulation of the stock dynamics:

\[B_{t+1}=B_t + f(B_t)-C_t\] Eq. (1)

where Bt is the stock biomass at the beginning of year t, Ct is the biomass caught during year t and f(Bt) is the biomass production function.

There are many formulations of the biomass production function f(Bt), among which the general Pella-Tomlinson (1969) is widely used:

\[f(B_t) = \frac{r}{p}{B_{t}} \left(1-\left( \frac{B_{t}}{K}\right) ^{p}\right)\] Eq. (2)

where r is the intrinsic population growth rate, K is the carrying capacity and p is the asymmetry parameter, which allows non-symmetrical production curves and, consequently, maximum production different from K/2. Schaefer (1954) model corresponds to p=1 (symmetric production curve and \(SP_{max}=K/2\)).

SPMs link the population dynamics, i.e. Eq. (1) with the observations through the relation between the catch and the stock biomass across the catchability coefficient (q).

\[\hat{I}_t=C_t/E_t=qB_t\] where It is the value of the relative biomass index for year t, notation ˆ denotes an estimated value and q is the catchability coefficient, which scales the modeled stock biomass to match the trends in catch rates.

An alternative line of research based on surplus production models named known-biomass production models (KBPM) was developed (MacCall, 2002). The basis of the KBPM model is the idea that the annual surplus production in an unfished stock is equal to Bt+1-Bt, and that, for a fished stock, the calculation of surplus production depends on catch.

\[SP_t=\overline{B}_{t+1}-\overline{B}_t+C_t\] Eq. (3)

where SPt is the surplus production during year t, Bt is the average biomass or SSB, Bt=(Bt+Bt+1)/2, and Ct represents the catch during year t.

In contrast to the traditional SPMs, KBPMs use as input data a biomass time series, estimated using another stock assessment model, instead of a biomass index.

Once the surplus production is calculated using the known average biomass (of two consecutive years) and the observed catch, the KBPMs are fitted as:

\[SP_{t}= \frac{r}{p}\overline{B}_{t}\left(1-\left( \frac{\overline{B}_{t}}{K}\right) ^{p}\right)\] Eq. (4)

2. knobi package

In this section the knobi package functions are described. More precisely, in each one of the next subsections the following package functions are explained:

  1. knobi_fit: fits the KBPM model (main function).

  2. knobi_env: analyzes the production changes in response to environmental fluctuations.

  3. knobi_retro: carries out the retrospective analysis.

  4. knobi_proj: projects the population and fishery dynamics.

2.1. knobi_fit

This section illustrates the use of the knobi_fit function, which allows us to fit the KBPM model.

For that, the case study of European hake (\(Merluccius\) \(merluccius\)) is used. European hake is a resource of great commercial importance in Atlantic Iberian Waters. This species is assessed by the International Council for the Exploration of the Sea (ICES) in two units: the northern and the southern stocks. For the current illustration we focus on the northern hake unit which covers the subareas 4, 6, and 7, and divisions 3.a, 8.a–b, and 8.d (Greater North Sea, Celtic Seas, and the northern Bay of Biscay).

Creating data argument

The first step is to create the data input object.

The data was downloaded using the icesSAG package and saved in the knobi_dataset under the hake_n object.

data( knobi_dataset)
hake_n <- knobi_dataset$hake_n

Then the data list for knobi_fit is created. Mandatory data are the catch time series and the biomass or SSB time series. However, in this example we also include some additional available information.

As you can see, in the code below, the data input argument is created. Firstly we introduce both, the biomass and spawning stock biomass (SSB) series, then below in the control argument we indicate which of the two series is used in the fit. After that, in the next line of code, we introduce the second data source which are the catches. After introducing the two main sources of information, we can add more details that are used mainly for comparing KBPM results with those derived from the assessment model that produced the SSB estimates (a data-rich model). In this particular case, we add the recruitment series, the value of the reference point \(F_{msy}\) and the years associated to the observed catch time series (if omitted, an increasing sequence from 1 onward will be used).

Details about the optional entries of this argument can be found on the help page.

data <- list(
  SSB = hake_n$SSB, 
  Catch = hake_n$catches,
  F_input = hake_n$F, 
  Recruitment = hake_n$recruitment,
  RP = list( F_MSY = 0.26),           # Provided by ICES        
  years = hake_n$Year )

Creating control object

control list contains a set of settings for the KBPM fit. In this example. it includes the argument pella, which is an optional logical argument where “TRUE” means that Pella-Tomlinson model is fitted instead of the Schaefer one.

 

control <- list( pella = "TRUE")

There is the possibility of defining other control settings such as start_r, start_K or start_p, optional start values of the model parameters \(r\) (intrinsic growth rate), \(K\) (maximum population size) and \(p\) (shape parameter in Pella-Tomlinson model), respectively.

KBPM model fit

After preparing both lists, data and control, we can apply the knobi_fit function over them for fitting the KBPM model.

In addition to the arguments mentioned above, the plot_out=TRUE argument allows the creation of an external folder with the corresponding plots files also displayed in the plot window. We can set the folder name and its directory through the plot_filename and the plot_dir arguments, respectively.

hake_n_results <- knobi_fit( data = data, 
                             control = control,
                             plot_out = FALSE)

Note that if the length of the input catch time series does not match with the SSB length, a warning is returned indicating that the series of catch is reduced so that the fit can be done.

#> Warning in knobi_fit(data, control, plot_out = FALSE): The length of the catch
#> time series is reduced according to biomass or SSB time series length.

As you can see, the following input quantities are plotted: fishing mortality time series, SSB, surplus production and catch time series. Note that in this example we are using control$method=SSB, which means that we are going to operate with the SSB and not with the stock biomass. Plots of catch over fishing mortality, fishing mortality over SSB, and catch over SSB time series with a smooth line from a “loess” regression are also displayed. Plot of input-output time series of fishing mortality is also provided with horizontal lines at fishing mortalities at MSY (two lines representing both input and output). The fishing mortality relative to \(F_{msy}\) is also plotted including a reference horizontal line at 1. The analogous SSB plots are also reported. It is important to mention that, in these cases, inputs are represented in blue and outputs in red, highlighting the case of the SSB, where the absolute value is an input of the model, while the relative SSB (SSB/SSBmsy) depends on the estimation of the reference point, so it is represented in red as well. On the other hand, the fitted surplus production curve is plotted twice with the observed Sp over SSB (first plot) and with the catch over SSB observations (second plot). Finally, a plot with the KBPM fit residuals is shown.

Quantitative results

The formula and the parameter estimates of the fit are printed running the name of the output object.

hake_n_results
#> 
#>  Formula:
#>  SP_t = (r/p)*B_t*(1-(B_t/K)^p) 
#>  
#> Parameter estimates:
#> r  0.6303395 
#> K  529631.1 
#> p  0.25 
#>

The hake_n_results object is a list containing the following slots: (1) params, that is the estimated parameters in the fit; (2) BRPs, that are the biological reference points estimates; (3) the residuals of the fit; (4) an error_table with the error measures (5) the input list which is an updated version of its input including the annual average biomass, the surplus production and the F estimated time series; (6) the control output which is the input one updated with the information of the plot settings; and (7) the optimx slot with the results provided by the optimizing function. See the help page for a more completed description.

hake_n_results$BRPs
#>            K        B_MSY        F_MSY          MSY     MSYoverK 
#> 5.296311e+05 2.169369e+05 5.042716e-01 1.093951e+05 2.065496e-01

2.3. knobi_env

After carrying out the KBPM fit using knobi_fit, knobi_env function allows us to analyze and model the relationships between the surplus production and the environmental covariable(s) in order to test whether productivity changes in response to environmental fluctuations. The knobi_env procedure can be summarized in three steps:

  1. The correlation analysis between the environmental variable(s) and the KBPM residuals through the Pearson’s correlation or autoregressive models;
  2. The selection of which lagged environmental variable(s) is included in the environmental KBPM models fit;
  3. The KBPM environmental fit.

In step (3) environmental covariables can be included as additive and multiplicative effects in the KBPM base formulation, i.e. in Eq. (4).

  • Additive model:

\[SP_{t}= \frac{r}{p}\overline{B}_{t}\left(1-\left( \frac{\overline{B}_{t}}{K}\right) ^{p}\right) + cX_{t-lag}\overline{B}_{t}\] Eq. (5)

being c the parameter that represent the effect of the lagged environmental variable Xt-lag (t index represents years and \(lag\) represent the response variable \(lag\), as explained below).

  • Multiplicative model:

\[SP_{t}= \frac{r}{p}\overline{B}_{t}\left(1-\left( \frac{\overline{B}_{t}}{K}\right) ^{p}\right)exp^{cX_{t-lag}}\] Eq. (6)

knobi_env inputs are the object returned by knobi_fit and a data object containing, at least, the mandatory environmental information required for the fit: the env argument, which is a data frame containing the values of each one of the environmental variable(s) in one column; and the years argument, which contains the years in which the environmental variable(s) are reported.

In the following example, we create a data frame in which we introduce the years in which the environmental variables are available, which is from 1973 to 2020. Then, we create four columns containing the values of the Sea Surface Temperature (SST), the Sea Bottom Temperature (SBT) and the Atlantic Multidecadal Oscillation (AMO) and the North Atlantic Oscillation (NAO) indices. Finally, we cut the data frame for starting in the first year of the KBPM fit data minus the value of the nlag or lag argument (below, a detailed explanation of this argument is provided).

Env <- knobi_dataset$Env
nlag <- 5
years <- hake_n_results$df$Year

ind <- which(Env[,1]==years[1])
ind1 <- which(Env[,1]==years[length(years)])

Env <- Env[(ind-nlag):ind1,]

Now, we create the data list

data <- list(
  env = data.frame( AMO=Env$AMO, NAO=Env$NAO, SST = Env$SST, SBT = Env$SBT),
  years = Env$years)

In the optional control input list we provide the settings for the environmental fit. In this example, we set nlag=5. This argument specifies the maximum lag of the environmental variable to test in the correlation analysis, meaning that lags less than or equal to nlag (a natural number) are evaluated. This means that correlation between KBPM residuals at time t and Xt-lag, where X the environmental variable and lag takes values from 0 to nlag, is computed. The lagged environmental variable corresponding to the highest correlation with the KBPM residuals is included in the environmental model.

control <- list( nlag = nlag)

Based on the arguments defined above, we apply the function as you can see below. Note that it reports a plot of the correlation analysis between the environmental variable(s) and the base KBPM residuals. Besides, a plot of the fitted values of the base model (no environmental information) and the environmental ones is also displayed. At last, a plot with the Pearson’s residuals for each KBPM model is also reported.

hake_n_environmental <- knobi_env(knobi_results = hake_n_results, 
                                  data = data,    
                                  control = control,
                                  plot_out = FALSE)

Quantitative results

Running the name of the output object the formula and the parameters estimates for both environmental models fit are printed.

hake_n_environmental
#> 
#>  Multiplicative model:
#>  SP_t = (r/p)*B_t*(1-(B_t/K)^p)*exp(c*X_t) 
#>  
#> Parameter estimates:
#> r   0.6736933 
#> K   452443.7 
#> p   0.25 
#> c   0.1972694 
#> 
#> 
#>  Additive model:
#>  SP_t = (r/p)*B_t*(1-(B_t/K)^p)+c*X_t*B_t 
#>  
#> Parameter estimates:
#> r   0.736126 
#> K   378965.4 
#> p   0.25 
#> c   0.1818502

A detailed description of each slot of the output function’s object is available in the help page. The output object contains the parameter estimates for both models and its reference points estimates, the accuracy measures for each model and the correlation analysis between the environmental variable(s) and the KBPM base residuals, among other results.

From Eq. (5) and Eq. (6) we can derive the formulas that provide the reference points (BRPs). It is important to take into account that in these models the BRPs depend on the value of the environmental covariate (details provided below for each model).

In the case of these environmental models, the estimated BRPs correspond to a value of the scaled environmental variable equal to the mean of the time series, i.e. \(X_t=0\), which cancels out the effect of the parameter \(c\). The estimates of the remain parameters included in the Eq. (2), and therefore for the BRPs as well, will be different from the base model ones because the fact of having included the environmental effect in the equations had an impact on the estimation of the curve.

The mathematical formulation of the BRPs estimates for each KBPM model depending on the centered environmental variable are:

  • In the case of the multiplicative model

\[B_{msy}(X)=K\left(\frac{1}{p+1}\right)^{1/p}\] \[F_{msy}(X)=\frac{r}{p}\left(1-\frac{1}{p+1}\right) cX\] \[MSY(X)=B_{msy}(X)*F_{msy}(X)\] \[K(X)=K\]

where r, p, K and c are the model parameter estimates of the additive and multiplicative environmental models, i.e. Eq. (5) and Eq. (6) respectively; and X the centered environmental variable.

  • In the case of the additive model

\[B_{msy}(X)=K\left(\frac{p c X+r}{r(p+1)}\right)^{1/p}\] \[F_{msy}(X)=\frac{r}{p}\left(1-\frac{1}{p+1}\right)-\frac{cX}{p+1}+cX\] \[MSY(X)=B_{msy}(X)*F_{msy}(X)\] \[K(X)=K+cX\]

where r, p, K and c are the model parameter estimates of the Eq. (5) and Eq. (6) and X the centered environmental variable.

For simplicity, the output slot $BRPs provides the BRPs estimates for a value of the centered environmental variable equal to the mean of the time series, i.e. , which cancels out the environmental effect in the equations defining both models, i.e. the effect of the parameter .

hake_n_environmental$BRPs
#>             K    B_MSY     F_MSY       MSY  MSYoverK
#> Base 529631.1 216936.9 0.5042716 109395.13 0.2065496
#> Add  378965.4 155224.2 0.5889008  91411.67 0.2412138
#> Mult 452443.7 185320.9 0.5389546  99879.58 0.2207558

More options

There is the possibility of obtaining 3D plots reporting the surplus production curve conditioned to a grid of environmental values using the argument control$plot3d=TRUE. In this case, a list named plots3D is added to the output list of knobi_env with the 3D plots objects.

control$plot3d = TRUE
knobi_env( hake_n_results, data, control)

There is also the possibility of fixing which lag is used in the relation among the surplus production and the environmental variable, for that the lag argument is used instead of nlag inside control as you can see below

Furthermore, it is also possible to fit the environmental models considering several variables at the same time using control$multicovar = TRUE. This means that cXt is replaced by \(\sum_{i=1}^{N} c_i X_{t,i}\) in Eq. (5) and Eq. (6), where index N represents the number of environmental variables.

Below you can see how we introduce the same data set as in previous examples but in the control we set multicovar=TRUE so that two of the variables, e.g. “AMO” and “NAO”, are considered in the environmental fit. Note that “AMO” is 2 years lagged whereas “NAO” is 3 years lagged respect the SP.

data2 <- data
data2$env <- data2$env[,c('AMO','NAO')]
control <- list( lag=c(2,3), multicovar=TRUE)
hake_n_multi <- knobi_env( hake_n_results, data2, control)

Finally, there is also the possibility of testing the correlation between the KBPM residuals and the environmental variable(s) through the fit of autoregressive models (AR models). In this case, firstly an AR model is fitted for the residuals in order to determine how the residuals can explain themselves:

\[ r_t=\sum_{i=1}^{\rho}\beta_{i}r_{t-i}+\epsilon_{t}\]

being rt the KBPM base residual for year t and \(\rho\) the AR model order, estimated as the maximum time lag at which the absolute value of the residuals partial autocorrelation is large than qnorm(0.975)Nr being Nr the length of the residuals series.

Then, AR models are fitted considering each one of the lagged environmental variable(s),

\[r_{t,lag}=\sum_{i=1}^{\rho}\beta_{i}r_{t-i}+X_{t-lag}+\epsilon_{t}\]

for lag=0,1,…,nlag, being Xt-lag the lagged environmental variable at year t-lag. Then, we have an autoregressive model for each of the lagged environmental variables. The AIC values of the above models are compared, and the lagged environmental variable whose model reports the lowest AIC is used in the KBPM fit, except if the argument ‘lag’ is used.

This test procedure is carried out using the argument ar_cor = TRUE in control list as you can see below.

control_ar <- list( nlag=3, ar_cor=TRUE)
hake_env_ar <- knobi_env( hake_n_results, data = data, control = control_ar)

A plot with the AIC values for each model is also represented. In the output object env_aic represents the AIC values for each AR model and selected_lag represent the lag corresponding to the model with the lowest AIC.

hake_env_ar$env_aic
#>         base    lag_0    lag_1    lag_2    lag_3
#> AMO 44.34811 45.17682 34.60678 40.01703 44.16061
#> NAO 44.34811 45.17682 41.32029 38.53077 40.20173
#> SST 44.34811 45.17682 41.84362 44.22788 46.34508
#> SBT 44.34811 45.17682 44.45828 38.59642 46.22022
hake_env_ar$selected_lag
#>     lag      aic
#> AMO   1 34.60678
#> NAO   2 38.53077
#> SST   1 41.84362
#> SBT   2 38.59642

2.3. knobi_retro

Once the KBPM fit is carried out using knobi_fit function, its robustness to the deletion of data is tested using the knobi_retro function.

knobi_retro input is the object returned by knobi_fit and the selected retrospective models. In this example, these models are specified by the nR argument, with a value of 5 (that is also the default value). This means that the first retrospective model considers the data deleting the last year and fits the surplus production curve, the next model deletes the two last years of the original data set and fits the SP curve, and then the process continues in this way until the last model is reached in which the last 5 years in the original data are deleted to then fit the curve.

hake_n_retros <- knobi_retro( knobi_results = hake_n_results,         
                              nR = 5,            
                              plot_out = FALSE)

The estimated surplus production curves from the retrospective analysis are plotted. The plot is displayed in the plot window and also saved if plot_out=T in the provided directory and file.

Quantitative results

The knobi_retro output is a list containing the retrospective analysis, that includes the parameter estimates and the reference points for each one of the models.

hake_n_retros
#> $BRPs
#>                    K    B_MSY     F_MSY      MSY  MSYoverK
#> 1978 - 2019 529631.1 216936.9 0.5042716 109395.1 0.2065496
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048597 113174.1 0.2067905
#> 1978 - 2016 585744.5 239921.0 0.4944368 118625.8 0.2025213
#> 1978 - 2015 625579.8 256237.5 0.4807142 123177.0 0.1969005
#> 1978 - 2014 606781.3 248537.6 0.4869952 121036.6 0.1994733
#> 
#> $params
#>                     r        K    p
#> 1978 - 2019 0.6303395 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310746 547288.4 0.25
#> 1978 - 2016 0.6180460 585744.5 0.25
#> 1978 - 2015 0.6008928 625579.8 0.25
#> 1978 - 2014 0.6087441 606781.3 0.25

There is also another possibility for choosing the years to consider in each one of retrospective models. The yR argument specifies the final years of the catch time series for each of the retrospective models, providing greater flexibility in choosing the years from which to delete information. The number of retrospective fits will correspond to the length of the yR vector. Additionally, different starting years can be set using the yR0 argument.

Below, there are two examples of the use of these arguments. In the first example, the retrospective models are fitted from the first year available in the time series (which is the year 1978) up to the years defined by yR(2005, 2010 and 2015), while in the second example the models fit from the years contained in yR0 up to the years included in yR, i. e. , 1990 to 2005, from 1995 to 2010 and from 1995 to 2015.

knobi_retro( hake_n_results, 
             yR = c(2005,2010,2015))

#> $BRPs
#>                     K     B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019  529631.1 216936.92 0.5042716 109395.13 0.2065496
#> 1978 - 2005  154479.7  63274.88 0.9052966  57282.54 0.3708095
#> 1978 - 2010 1059244.7 433866.63 0.4182645 181471.02 0.1713211
#> 1978 - 2015  625579.8 256237.47 0.4807142 123177.00 0.1969005
#> 
#> $params
#>                     r         K    p
#> 1978 - 2019 0.6303395  529631.1 0.25
#> 1978 - 2005 1.1316207  154479.7 0.25
#> 1978 - 2010 0.5228307 1059244.7 0.25
#> 1978 - 2015 0.6008928  625579.8 0.25
knobi_retro( hake_n_results,
             yR = c(2005,2010,2015),
             yR0 = c(1990,1995,1995))

#> $BRPs
#>                    K     B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019 529631.1 216936.92 0.5042716 109395.13 0.2065496
#> 1990 - 2005 164645.5  67438.81 0.8632071  58213.66 0.3535696
#> 1995 - 2010 391203.7 210004.26 0.8258184 173425.39 0.4433122
#> 1995 - 2015 422793.8 195255.57 0.6960105 135899.92 0.3214331
#> 
#> $params
#>                     r        K         p
#> 1978 - 2019 0.6303395 529631.1 0.2500000
#> 1990 - 2005 1.0790089 164645.5 0.2500000
#> 1995 - 2010 2.0000000 391203.7 1.4218399
#> 1995 - 2015 1.1425157 422793.8 0.6415208

The environmental fit information can be considered too in the retrospective analysis through the env_results argument, where the result of the knobi_environmental function has to be provided. For environmental models, both the estimated BRPs and the plotted production curve correspond to a value of the scaled environmental variable equal to the mean of the time series, i.e. \(X_t=0\), which cancels out the environmental effect in the equations defining both models as it has been explained in the knobi_env function help’s details. In this case a panel of plots is provided, where each graph corresponds with a different model.

knobi_retro(hake_n_results, hake_n_environmental, nR = 3); hake_n_retros

#> $base
#> $base$BRPs
#>                    K    B_MSY     F_MSY      MSY  MSYoverK
#> 1978 - 2019 529631.1 216936.9 0.5042716 109395.1 0.2065496
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048597 113174.1 0.2067905
#> 1978 - 2016 585744.5 239921.0 0.4944368 118625.8 0.2025213
#> 
#> $base$params
#>                     r        K    p
#> 1978 - 2019 0.6303395 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310746 547288.4 0.25
#> 1978 - 2016 0.6180460 585744.5 0.25
#> 
#> 
#> $add
#> $add$BRPs
#>                    K    B_MSY     F_MSY      MSY  MSYoverK
#> 1978 - 2019 378965.4 155224.2 0.5889008 91411.67 0.2412138
#> 1978 - 2018 381131.0 156111.3 0.5911377 92283.27 0.2421300
#> 1978 - 2017 388755.9 159234.4 0.5884641 93703.74 0.2410349
#> 1978 - 2016 407308.8 166833.7 0.5766696 96207.91 0.2362039
#> 
#> $add$params
#>                     r        K    p         c
#> 1978 - 2019 0.7361260 378965.4 0.25 0.1818502
#> 1978 - 2018 0.7389222 381131.0 0.25 0.1850930
#> 1978 - 2017 0.7355801 388755.9 0.25 0.1792517
#> 1978 - 2016 0.7208370 407308.8 0.25 0.1655657
#> 
#> 
#> $mult
#> $mult$BRPs
#>                    K    B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019 452443.7 185320.9 0.5389546  99879.58 0.2207558
#> 1978 - 2018 456042.4 186794.9 0.5404260 100948.85 0.2213585
#> 1978 - 2017 463274.6 189757.3 0.5422213 102890.45 0.2220939
#> 1978 - 2016 482842.0 197772.1 0.5363887 106082.71 0.2197048
#> 
#> $mult$params
#>                     r        K    p         c
#> 1978 - 2019 0.6736933 452443.7 0.25 0.1972694
#> 1978 - 2018 0.6755326 456042.4 0.25 0.1988995
#> 1978 - 2017 0.6777767 463274.6 0.25 0.1922609
#> 1978 - 2016 0.6704859 482842.0 0.25 0.1788851
#> $BRPs
#>                    K    B_MSY     F_MSY      MSY  MSYoverK
#> 1978 - 2019 529631.1 216936.9 0.5042716 109395.1 0.2065496
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048597 113174.1 0.2067905
#> 1978 - 2016 585744.5 239921.0 0.4944368 118625.8 0.2025213
#> 1978 - 2015 625579.8 256237.5 0.4807142 123177.0 0.1969005
#> 1978 - 2014 606781.3 248537.6 0.4869952 121036.6 0.1994733
#> 
#> $params
#>                     r        K    p
#> 1978 - 2019 0.6303395 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310746 547288.4 0.25
#> 1978 - 2016 0.6180460 585744.5 0.25
#> 1978 - 2015 0.6008928 625579.8 0.25
#> 1978 - 2014 0.6087441 606781.3 0.25
knobi_retro( hake_n_results, hake_n_multi,
             yR = c(2005,2010,2015),
             yR0 = c(1990,1995,1995))

#> $base
#> $base$BRPs
#>                    K     B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019 529631.1 216936.92 0.5042716 109395.13 0.2065496
#> 1990 - 2005 164645.5  67438.81 0.8632071  58213.66 0.3535696
#> 1995 - 2010 391203.7 210004.26 0.8258184 173425.39 0.4433122
#> 1995 - 2015 422793.8 195255.57 0.6960105 135899.92 0.3214331
#> 
#> $base$params
#>                     r        K         p
#> 1978 - 2019 0.6303395 529631.1 0.2500000
#> 1990 - 2005 1.0790089 164645.5 0.2500000
#> 1995 - 2010 2.0000000 391203.7 1.4218399
#> 1995 - 2015 1.1425157 422793.8 0.6415208
#> 
#> 
#> $add
#> $add$BRPs
#>                    K     B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019 516488.5 211553.67 0.5067793 107211.03 0.2075768
#> 1990 - 2005 111641.9  55622.62 1.0092396  56136.55 0.5028268
#> 1995 - 2010 405142.5 215900.38 0.8428851 181979.21 0.4491734
#> 1995 - 2015 456945.2 214180.97 0.7175821 153692.44 0.3363476
#> 
#> $add$params
#>                     r        K         p          c1           c2
#> 1978 - 2019 0.6334741 516488.5 0.2500000  0.01699060 -0.004395063
#> 1990 - 2005 2.0000000 111641.9 0.9816899 -0.12416790  0.002753767
#> 1995 - 2010 2.0000000 405142.5 1.3728028 -0.07141606  0.019703123
#> 1995 - 2015 1.2207720 456945.2 0.7012297 -0.07482624  0.049011604
#> 
#> 
#> $mult
#> $mult$BRPs
#>                    K     B_MSY     F_MSY       MSY  MSYoverK
#> 1978 - 2019 498824.3 204318.44 0.5217788 106609.03 0.2137206
#> 1990 - 2005 114441.3  57362.27 0.9936139  56995.95 0.4980364
#> 1995 - 2010 396365.5 211096.05 0.8442971 178227.79 0.4496551
#> 1995 - 2015 422155.9 201122.10 0.7438395 149602.56 0.3543776
#> 
#> $mult$params
#>                     r        K         p          c1           c2
#> 1978 - 2019 0.6522235 498824.3 0.2500000  0.05169038 -0.006546162
#> 1990 - 2005 2.0000000 114441.3 1.0128543 -0.09494490  0.001506168
#> 1995 - 2010 2.0000000 396365.5 1.3688343 -0.05364247  0.025982666
#> 1995 - 2015 1.3168214 422155.9 0.7703032 -0.06813650  0.090082469

2.4. knobi_proj

knobi_proj function projects the time series of biomass (or spawning biomass) and then the surplus production for a set of future catch or fishing mortality values.

One of the knobi_proj arguments is a data frame containing the selected catch for the projected years. In this case three catch scenarios are considered: (i) constant catch value equal to the last historical catch, (ii) last historical catch with a 20% increase; and (iii) last historical catch with a 20% decrease.

catch <- rep(hake_n_results$input$Catch[length(hake_n_results$input$Catch)],8)
C <- data.frame(catch=catch, catch08=0.8*catch, catch12=1.2*catch)

The resulting plots are displayed in the plot window. In this example, four plots are presented in a panel reporting the SSB, surplus production, catch and fishing mortality projections for each catch catch scenario. Note that, in this case, plot_out = FALSE (by default), then plots are not saved like in the previous examples.

Then, on the basis of the above catch scenarios and the hake_n_results object, the projections are carried out.

projections <- knobi_proj( knobi_results=hake_n_results, c=C)

Quantitative results

Running the name of the output object the data frame with the projections for each scenario are printed. Details of the additional output information are provided in the help page.

projections
#> 
#>  Projections: 
#>  
#>       SSB        SP Year        C         F      Sc Model
#>  235508.2 108904.40 2020  87238.0 0.3704245   catch  base
#>  256339.7 107234.53 2021  87238.0 0.3403219   catch  base
#>  275106.4 104775.01 2022  87238.0 0.3171064   catch  base
#>  291242.7 101973.58 2023  87238.0 0.2995371   catch  base
#>  304589.9  99196.75 2024  87238.0 0.2864113   catch  base
#>  315290.3  96680.05 2025  87238.0 0.2766910   catch  base
#>  323660.3  94535.93 2026  87238.0 0.2695357   catch  base
#>  330084.2  92787.89 2027  87238.0 0.2642901   catch  base
#>  243962.5 108365.38 2020  69790.4 0.2860702 catch08  base
#>  280323.4 103937.24 2021  69790.4 0.2489639 catch08  base
#>  311323.0  97642.81 2022  69790.4 0.2241736 catch08  base
#>  335916.5  91124.99 2023  69790.4 0.2077611 catch08  base
#>  354385.5  85393.72 2024  69790.4 0.1969336 catch08  base
#>  367707.9  80832.02 2025  69790.4 0.1897985 catch08  base
#>  377046.9  77426.73 2026  69790.4 0.1850974 catch08  base
#>  383464.6  74989.40 2027  69790.4 0.1819996 catch08  base
#>  226957.6 109250.89 2020 104685.6 0.4612561 catch12  base
#>  231444.6 109094.31 2021 104685.6 0.4523138 catch12  base
#>  235752.0 108891.57 2022 104685.6 0.4440497 catch12  base
#>  239838.4 108652.39 2023 104685.6 0.4364840 catch12  base
#>  243672.5 108387.04 2024 104685.6 0.4296160 catch12  base
#>  247233.2 108105.55 2025 104685.6 0.4234286 catch12  base
#>  250508.9 107817.08 2026 104685.6 0.4178917 catch12  base
#>  253496.6 107529.56 2027 104685.6 0.4129665 catch12  base
#> 
#>

With environmental information

There is the possibility of considering the environmental information in the projections. For this purpose, the knobi_env output and the new environmental values for the future years env argument must be provided.

In the current example, three scenarios are considered: (i) Constant SBT equal to last year’s SBT; (ii) constant SBT equal to last year’s SBT with a 5% increment; and (iii) constant SBT equal to last year’s SBT with a 5% decrease.

last_SBT <- Env$SBT[length(Env$SBT)]
env <- data.frame( SBTi=rep(last_SBT,5),
                   SBTii=rep(last_SBT*1.05,5),
                   SBTiii=rep(last_SBT*0.95,5))

C <- C[(1:5),]

Note that, as shown below, in this case, in addition to the plot with the results from the base KBPM model, additional plots are provided: (1) panels for each catch or fishing mortality scenario, depending on the model and environmental scenario; and (2) the same information, but now presented by each environmental scenario, depending on the model and catch or fishing mortality.

env_projections <- knobi_proj(hake_n_results, hake_n_environmental, c=C, env=env)

env_projections
#> 
#>  Projections: 
#>  
#>       SSB        SP Year        C         F      Sc Model  EnvSc
#>  235508.2 108904.40 2020  87238.0 0.3704245   catch  base   <NA>
#>  256339.7 107234.53 2021  87238.0 0.3403219   catch  base   <NA>
#>  275106.4 104775.01 2022  87238.0 0.3171064   catch  base   <NA>
#>  291242.7 101973.58 2023  87238.0 0.2995371   catch  base   <NA>
#>  304589.9  99196.75 2024  87238.0 0.2864113   catch  base   <NA>
#>  243962.5 108365.38 2020  69790.4 0.2860702 catch08  base   <NA>
#>  280323.4 103937.24 2021  69790.4 0.2489639 catch08  base   <NA>
#>  311323.0  97642.81 2022  69790.4 0.2241736 catch08  base   <NA>
#>  335916.5  91124.99 2023  69790.4 0.2077611 catch08  base   <NA>
#>  354385.5  85393.72 2024  69790.4 0.1969336 catch08  base   <NA>
#>  226957.6 109250.89 2020 104685.6 0.4612561 catch12  base   <NA>
#>  231444.6 109094.31 2021 104685.6 0.4523138 catch12  base   <NA>
#>  235752.0 108891.57 2022 104685.6 0.4440497 catch12  base   <NA>
#>  239838.4 108652.39 2023 104685.6 0.4364840 catch12  base   <NA>
#>  243672.5 108387.04 2024 104685.6 0.4296160 catch12  base   <NA>
#>  239759.5 117407.06 2020  87238.0 0.3638562   catch   add   SBTi
#>  267381.1 112312.17 2021  87238.0 0.3262683   catch   add   SBTi
#>  289601.1 106603.66 2022  87238.0 0.3012351   catch   add   SBTi
#>  306366.1 101402.38 2023  87238.0 0.2847508   catch   add   SBTi
#>  318431.1  97203.57 2024  87238.0 0.2739620   catch   add   SBTi
#>  238962.7 115813.35 2020  87238.0 0.3650696   catch  mult   SBTi
#>  264242.5 109222.30 2021  87238.0 0.3301437   catch  mult   SBTi
#>  283063.5 102895.70 2022  87238.0 0.3081923   catch  mult   SBTi
#>  296177.5  97808.30 2023  87238.0 0.2945463   catch  mult   SBTi
#>  304905.6  94123.95 2024  87238.0 0.2861148   catch  mult   SBTi
#>  261310.6 160509.12 2020  87238.0 0.3338480   catch   add  SBTii
#>  331527.0 154399.69 2021  87238.0 0.2631400   catch   add  SBTii
#>  391656.1 140334.49 2022  87238.0 0.2227414   catch   add  SBTii
#>  437060.4 124950.16 2023  87238.0 0.1996017   catch   add  SBTii
#>  468371.2 112147.43 2024  87238.0 0.1862583   catch   add  SBTii
#>  253021.4 143930.87 2020  87238.0 0.3447850   catch  mult  SBTii
#>  299482.3 123466.83 2021  87238.0 0.2912960   catch  mult  SBTii
#>  327454.0 106952.67 2022  87238.0 0.2664130   catch  mult  SBTii
#>  342219.6  97054.51 2023  87238.0 0.2549182   catch  mult  SBTii
#>  349464.3  91910.81 2024  87238.0 0.2496335   catch  mult  SBTii
#>  217504.6  72897.18 2020  87238.0 0.4010858   catch   add SBTiii
#>  204964.0  76497.74 2021  87238.0 0.4256259   catch   add SBTiii
#>  195390.4  78830.92 2022  87238.0 0.4464805   catch   add SBTiii
#>  187777.7  80419.75 2023  87238.0 0.4645812   catch   add SBTiii
#>  181521.3  81543.35 2024  87238.0 0.4805939   catch   add SBTiii
#>  227179.0  92246.00 2020  87238.0 0.3840056   catch  mult SBTiii
#>  231857.3  91586.54 2021  87238.0 0.3762573   catch  mult SBTiii
#>  235895.4  90965.77 2022  87238.0 0.3698164   catch  mult SBTiii
#>  239339.8  90399.02 2023  87238.0 0.3644943   catch  mult SBTiii
#>  242248.4  89894.03 2024  87238.0 0.3601180   catch  mult SBTiii
#>  247181.9 114804.13 2020  69790.4 0.2823443 catch08   add   SBTi
#>  287643.9 105700.81 2021  69790.4 0.2426277 catch08   add   SBTi
#>  318553.1  95698.39 2022  69790.4 0.2190856 catch08   add   SBTi
#>  340226.4  87229.02 2023  69790.4 0.2051293 catch08   add   SBTi
#>  354553.0  81004.93 2024  69790.4 0.1968405 catch08   add   SBTi
#>  246787.4 114015.16 2020  69790.4 0.2827957 catch08  mult   SBTi
#>  285079.2 102149.34 2021  69790.4 0.2448105 catch08  mult   SBTi
#>  311871.7  91016.38 2022  69790.4 0.2237792 catch08  mult   SBTi
#>  328976.2  82773.37 2023  69790.4 0.2121443 catch08  mult   SBTi
#>  339273.5  77402.07 2024  69790.4 0.2057054 catch08  mult   SBTi
#>  268517.4 157475.26 2020  69790.4 0.2599101 catch08   add  SBTii
#>  351287.3 147645.22 2021  69790.4 0.1986705 catch08   add  SBTii
#>  419511.6 128384.28 2022  69790.4 0.1663611 catch08   add  SBTii
#>  468478.2 109129.60 2023  69790.4 0.1489726 catch08   add  SBTii
#>  500416.7  94328.24 2024  69790.4 0.1394646 catch08   add  SBTii
#>  260423.8 141287.93 2020  69790.4 0.2679878 catch08  mult  SBTii
#>  317778.6 113002.48 2021  69790.4 0.2196196 catch08  mult  SBTii
#>  350184.2  91389.53 2022  69790.4 0.1992963 catch08  mult  SBTii
#>  365877.2  79577.40 2023  69790.4 0.1907481 catch08  mult  SBTii
#>  372889.0  74026.85 2024  69790.4 0.1871613 catch08  mult  SBTii
#>  225180.2  70800.86 2020  69790.4 0.3099313 catch08   add SBTiii
#>  226043.4  70506.33 2021  69790.4 0.3087478 catch08   add SBTiii
#>  226654.3  70296.25 2022  69790.4 0.3079156 catch08   add SBTiii
#>  227085.6  70147.11 2023  69790.4 0.3073308 catch08   add SBTiii
#>  227389.5  70041.59 2024  69790.4 0.3069200 catch08   add SBTiii
#>  235309.2  91058.83 2020  69790.4 0.2965902 catch08  mult SBTiii
#>  254772.5  87448.49 2021  69790.4 0.2739323 catch08  mult SBTiii
#>  270582.5  83752.31 2022  69790.4 0.2579265 catch08  mult SBTiii
#>  282880.7  80425.01 2023  69790.4 0.2467132 catch08  mult SBTiii
#>  292137.1  77668.48 2024  69790.4 0.2388961 catch08  mult SBTiii
#>  232255.6 119846.87 2020 104685.6 0.4507344 catch12   add   SBTi
#>  246419.0 117850.97 2021 104685.6 0.4248277 catch12   add   SBTi
#>  258490.0 115662.25 2022 104685.6 0.4049890 catch12   add   SBTi
#>  268405.7 113540.46 2023 104685.6 0.3900275 catch12   add   SBTi
#>  276312.9 111645.02 2024 104685.6 0.3788662 catch12   add   SBTi
#>  231035.4 117406.38 2020 104685.6 0.4531150 catch12  mult   SBTi
#>  242560.1 115014.16 2021 104685.6 0.4315863 catch12  mult   SBTi
#>  251760.6 112758.13 2022 104685.6 0.4158141 catch12  mult   SBTi
#>  258860.5 110812.91 2023 104685.6 0.4044093 catch12  mult   SBTi
#>  264199.1 109235.51 2024 104685.6 0.3962375 catch12  mult   SBTi
#>  254033.8 163403.27 2020 104685.6 0.4120931 catch12   add  SBTii
#>  311225.5 160351.35 2021 104685.6 0.3363657 catch12   add  SBTii
#>  362276.1 151120.98 2022 104685.6 0.2889663 catch12   add  SBTii
#>  403056.4 139810.73 2023 104685.6 0.2597294 catch12   add  SBTii
#>  433002.5 129452.64 2024 104685.6 0.2417668 catch12   add  SBTii
#>  245512.4 146360.34 2020 104685.6 0.4263964 catch12  mult  SBTii
#>  280473.7 132933.46 2021 104685.6 0.3732457 catch12  mult  SBTii
#>  303025.7 121541.85 2022 104685.6 0.3454677 catch12  mult  SBTii
#>  316114.7 114007.35 2023 104685.6 0.3311633 catch12  mult  SBTii
#>  323246.2 109626.78 2024 104685.6 0.3238572 catch12  mult  SBTii
#>  209731.7  74798.93 2020 104685.6 0.4991407 catch12   add SBTiii
#>  182899.9  80908.67 2021 104685.6 0.5723657 catch12   add SBTiii
#>  160495.5  83653.86 2022 104685.6 0.6522649 catch12   add SBTiii
#>  139675.3  84076.95 2023 104685.6 0.7494924 catch12   add SBTiii
#>  118078.8  82101.17 2024 104685.6 0.8865741 catch12   add SBTiii
#>  218955.7  93246.91 2020 104685.6 0.4781133 catch12  mult SBTiii
#>  208021.9  94256.70 2021 104685.6 0.5032433 catch12  mult SBTiii
#>  197891.5  94853.79 2022 104685.6 0.5290050 catch12  mult SBTiii
#>  188187.1  95108.66 2023 104685.6 0.5562846 catch12  mult SBTiii
#>  178577.5  95043.38 2024 104685.6 0.5862193 catch12  mult SBTiii
#> 
#>

The output list also contains the projections for each of the scenarios catches and environmental scenarios. Details of the output are available in the help page.

Forecast via fishing mortality

Alternatively, projections can be based on fishing mortality. The scenarios presented below have been created from the estimated Fmsy in the knobi_fit analysis.

fmsy <- hake_n_results$BRPs['F_MSY']
ff <- rep(fmsy,5)
f <- data.frame( f=ff, f12=ff*1.2, f08=ff*0.8)

f_projections <- knobi_proj( hake_n_results, f=f, env_results=hake_n_environmental, env=env)

f_projections
#> 
#>  Projections: 
#>  
#>       SSB        SP Year         C         F  Sc Model  EnvSc
#>  223095.0 109340.42 2020 112500.46 0.5042716   f  base   <NA>
#>  220585.4 109375.87 2021 111234.96 0.5042716   f  base   <NA>
#>  219105.6 109388.31 2022 110488.75 0.5042716   f  base   <NA>
#>  218228.5 109392.71 2023 110046.46 0.5042716   f  base   <NA>
#>  217707.1 109394.27 2024 109783.49 0.5042716   f  base   <NA>
#>  214475.7 109386.30 2020 129784.83 0.6051259 f12  base   <NA>
#>  198627.8 108897.43 2021 120194.82 0.6051259 f12  base   <NA>
#>  189718.8 108283.09 2022 114803.74 0.6051259 f12  base   <NA>
#>  184530.5 107808.37 2023 111664.20 0.6051259 f12  base   <NA>
#>  181446.0 107484.41 2024 109797.66 0.6051259 f12  base   <NA>
#>  232338.5 109056.44 2020  93729.38 0.4034173 f08  base   <NA>
#>  244779.5 108303.13 2021  98748.27 0.4034173 f08  base   <NA>
#>  252451.6 107632.76 2022 101843.35 0.4034173 f08  base   <NA>
#>  257070.6 107155.32 2023 103706.73 0.4034173 f08  base   <NA>
#>  259811.7 106846.14 2024 104812.54 0.4034173 f08  base   <NA>
#>  227828.3 121194.07 2020 114887.37 0.5042716   f   add   SBTi
#>  232728.3 120851.51 2021 117358.28 0.5042716   f   add   SBTi
#>  235429.5 120629.66 2022 118720.43 0.5042716   f   add   SBTi
#>  236902.1 120498.93 2023 119463.01 0.5042716   f   add   SBTi
#>  237700.0 120425.24 2024 119865.37 0.5042716   f   add   SBTi
#>  226628.8 118190.18 2020 114282.49 0.5042716   f  mult   SBTi
#>  229545.8 117679.56 2021 115753.41 0.5042716   f  mult   SBTi
#>  230979.1 117416.85 2022 116476.23 0.5042716   f  mult   SBTi
#>  231678.1 117285.94 2023 116828.68 0.5042716   f  mult   SBTi
#>  232017.6 117221.69 2024 116999.89 0.5042716   f  mult   SBTi
#>  245893.8 166434.93 2020 123997.27 0.5042716   f   add  SBTii
#>  280926.3 169290.56 2021 141663.18 0.5042716   f   add  SBTii
#>  303065.7 169478.80 2022 152827.44 0.5042716   f   add  SBTii
#>  316186.8 169034.93 2023 159444.05 0.5042716   f   add  SBTii
#>  323673.9 168602.80 2024 163219.56 0.5042716   f   add  SBTii
#>  238671.5 148348.21 2020 120355.25 0.5042716   f  mult  SBTii
#>  258493.0 142000.73 2021 130350.67 0.5042716   f  mult  SBTii
#>  266564.0 138912.59 2022 134420.65 0.5042716   f  mult  SBTii
#>  269650.1 137657.06 2023 135976.87 0.5042716   f  mult  SBTii
#>  270800.8 137178.44 2024 136557.15 0.5042716   f  mult  SBTii
#>  209338.0  74889.21 2020 105563.21 0.5042716   f   add SBTiii
#>  187040.4  80397.88 2021  94319.15 0.5042716   f   add SBTiii
#>  176664.6  82256.79 2022  89086.97 0.5042716   f   add SBTiii
#>  171508.8  83005.49 2023  86487.02 0.5042716   f   add SBTiii
#>  168863.2  83343.36 2024  85152.94 0.5042716   f   add SBTiii
#>  216761.4  93479.31 2020 109306.60 0.5042716   f  mult SBTiii
#>  204528.7  94500.01 2021 103138.02 0.5042716   f  mult SBTiii
#>  197773.4  94858.78 2022  99731.48 0.5042716   f  mult SBTiii
#>  193936.6  94995.80 2023  97796.69 0.5042716   f  mult SBTiii
#>  191722.3  95052.50 2024  96680.11 0.5042716   f  mult SBTiii
#>  219870.3 123439.71 2020 133049.19 0.6051259 f12   add   SBTi
#>  212534.8 123548.77 2021 128610.29 0.6051259 f12   add   SBTi
#>  208642.5 123531.93 2022 126254.97 0.6051259 f12   add   SBTi
#>  206540.1 123500.94 2023 124982.74 0.6051259 f12   add   SBTi
#>  205393.5 123477.51 2024 124288.91 0.6051259 f12   add   SBTi
#>  218343.6 119462.62 2020 132125.38 0.6051259 f12  mult   SBTi
#>  209047.1 120569.63 2021 126499.84 0.6051259 f12  mult   SBTi
#>  204648.9 120972.11 2022 123838.36 0.6051259 f12  mult   SBTi
#>  202512.5 121138.97 2023 122545.56 0.6051259 f12  mult   SBTi
#>  201461.5 121214.11 2024 121909.56 0.6051259 f12  mult   SBTi
#>  237486.6 169332.41 2020 143709.28 0.6051259 f12   add  SBTii
#>  258279.2 172253.49 2021 156291.42 0.6051259 f12   add  SBTii
#>  270997.9 173463.14 2022 163987.83 0.6051259 f12   add  SBTii
#>  278469.6 173977.36 2023 168509.18 0.6051259 f12   add  SBTii
#>  282756.2 174208.22 2024 171103.13 0.6051259 f12   add  SBTii
#>  230254.6 150492.14 2020 139333.01 0.6051259 f12  mult  SBTii
#>  238062.5 148514.59 2021 144057.80 0.6051259 f12  mult  SBTii
#>  241153.1 147652.24 2022 145927.97 0.6051259 f12  mult  SBTii
#>  242344.6 147307.86 2023 146649.01 0.6051259 f12  mult  SBTii
#>  242799.3 147174.70 2024 146924.16 0.6051259 f12  mult  SBTii
#>  201849.7  76493.83 2020 122144.47 0.6051259 f12   add SBTiii
#>  169262.6  82901.62 2021 102425.17 0.6051259 f12   add SBTiii
#>  154786.4  84236.51 2022  93665.27 0.6051259 f12   add SBTiii
#>  147658.0  84523.66 2023  89351.69 0.6051259 f12   add SBTiii
#>  143970.1  84572.33 2024  87120.06 0.6051259 f12   add SBTiii
#>  208649.7  94208.84 2020 126259.37 0.6051259 f12  mult SBTiii
#>  184394.3  95121.34 2021 111581.75 0.6051259 f12  mult SBTiii
#>  171631.0  94792.20 2022 103858.36 0.6051259 f12  mult SBTiii
#>  164501.1  94350.29 2023  99543.89 0.6051259 f12  mult SBTiii
#>  160382.4  94007.69 2024  97051.54 0.6051259 f12  mult SBTiii
#>  236292.2 118558.67 2020  95324.34 0.4034173 f08   add   SBTi
#>  254662.0 116240.52 2021 102735.07 0.4034173 f08   add   SBTi
#>  265158.9 114458.03 2022 106969.70 0.4034173 f08   add   SBTi
#>  270925.9 113341.74 2023 109296.18 0.4034173 f08   add   SBTi
#>  274026.3 112702.17 2024 110546.93 0.4034173 f08   add   SBTi
#>  235455.1 116546.95 2020  94986.67 0.4034173 f08  mult   SBTi
#>  251814.2 112744.10 2021 101586.21 0.4034173 f08  mult   SBTi
#>  260141.9 110443.21 2022 104945.74 0.4034173 f08  mult   SBTi
#>  264212.4 109231.46 2023 106587.86 0.4034173 f08  mult   SBTi
#>  266162.5 108630.98 2024 107374.54 0.4034173 f08  mult   SBTi
#>  254823.6 163097.49 2020 102800.25 0.4034173 f08   add  SBTii
#>  305451.2 164182.24 2021 123224.30 0.4034173 f08   add  SBTii
#>  338446.1 161566.77 2022 136534.99 0.4034173 f08   add  SBTii
#>  358147.8 158854.58 2023 144482.99 0.4034173 f08   add  SBTii
#>  369315.7 156952.61 2024 148988.33 0.4034173 f08   add  SBTii
#>  247590.6 145713.62 2020  99882.34 0.4034173 f08  mult  SBTii
#>  280421.5 132957.39 2021 113126.89 0.4034173 f08  mult  SBTii
#>  294142.5 126273.64 2022 118662.17 0.4034173 f08  mult  SBTii
#>  299340.2 123542.97 2023 120759.02 0.4034173 f08  mult  SBTii
#>  301232.2 122522.35 2024 121522.29 0.4034173 f08  mult  SBTii
#>  217314.1  72946.46 2020  87668.26 0.4034173 f08   add SBTiii
#>  206418.2  76202.68 2021  83272.67 0.4034173 f08   add SBTiii
#>  201123.8  77618.09 2022  81136.83 0.4034173 f08   add SBTiii
#>  198473.1  78284.81 2023  80067.49 0.4034173 f08   add SBTiii
#>  197126.1  78612.77 2024  79524.09 0.4034173 f08   add SBTiii
#>  225439.3  92474.70 2020  90946.11 0.4034173 f08  mult SBTiii
#>  226645.7  92317.06 2021  91432.80 0.4034173 f08  mult SBTiii
#>  227342.8  92224.00 2022  91714.03 0.4034173 f08  mult SBTiii
#>  227744.6  92169.71 2023  91876.12 0.4034173 f08  mult SBTiii
#>  227975.8  92138.25 2024  91969.40 0.4034173 f08  mult SBTiii
#> 
#>

Case of considering multicovariate environmental models

In case of multicovar=TRUE in knobi_env, the env argument must be a list in which each item is a data frame containing the values of the variables for a specific environmental scenario. In the following scenario we have two scenarios, “climate_1” and “climate_2”, and each of them we provide values of the two covariables, “AMO” and “NAO”, which are the ones included in the environmental fit.

env <- list( climate_1 = data.frame( AMO=c(0.2,0.2,0.3,0.3,0.4),
                                     NAO=c(0.2,0.2,0.3,0.3,0.4)),
             climate_2 = data.frame( AMO=c(0.2,0.3,0.4,0.5,0.6),
                                     NAO=c(0.2,0.3,0.4,0.5,0.6)))

multiproj <- knobi_proj( hake_n_results, hake_n_multi, c=C, env=env)

multiproj
#> 
#>  Projections: 
#>  
#>       SSB        SP Year        C         F      Sc Model     EnvSc
#>  235508.2 108904.40 2020  87238.0 0.3704245   catch  base      <NA>
#>  256339.7 107234.53 2021  87238.0 0.3403219   catch  base      <NA>
#>  275106.4 104775.01 2022  87238.0 0.3171064   catch  base      <NA>
#>  291242.7 101973.58 2023  87238.0 0.2995371   catch  base      <NA>
#>  304589.9  99196.75 2024  87238.0 0.2864113   catch  base      <NA>
#>  243962.5 108365.38 2020  69790.4 0.2860702 catch08  base      <NA>
#>  280323.4 103937.24 2021  69790.4 0.2489639 catch08  base      <NA>
#>  311323.0  97642.81 2022  69790.4 0.2241736 catch08  base      <NA>
#>  335916.5  91124.99 2023  69790.4 0.2077611 catch08  base      <NA>
#>  354385.5  85393.72 2024  69790.4 0.1969336 catch08  base      <NA>
#>  226957.6 109250.89 2020 104685.6 0.4612561 catch12  base      <NA>
#>  231444.6 109094.31 2021 104685.6 0.4523138 catch12  base      <NA>
#>  235752.0 108891.57 2022 104685.6 0.4440497 catch12  base      <NA>
#>  239838.4 108652.39 2023 104685.6 0.4364840 catch12  base      <NA>
#>  243672.5 108387.04 2024 104685.6 0.4296160 catch12  base      <NA>
#>  236170.3 110228.58 2020  87238.0 0.3693860   catch   add climate_1
#>  258251.3 108409.51 2021  87238.0 0.3378027   catch   add climate_1
#>  279117.2 107798.15 2022  87238.0 0.3125498   catch   add climate_1
#>  298011.7 104467.00 2023  87238.0 0.2927334   catch   add climate_1
#>  314709.1 103403.73 2024  87238.0 0.2772020   catch   add climate_1
#>  236426.6 110741.16 2020  87238.0 0.3689856   catch  mult climate_1
#>  258446.6 107774.92 2021  87238.0 0.3375475   catch  mult climate_1
#>  278431.0 106669.91 2022  87238.0 0.3133200   catch  mult climate_1
#>  295700.0 102343.93 2023  87238.0 0.2950220   catch  mult climate_1
#>  310025.2 100782.54 2024  87238.0 0.2813900   catch  mult climate_1
#>  236170.3 110228.58 2020  87238.0 0.3693860   catch   add climate_2
#>  259234.8 110376.43 2021  87238.0 0.3365212   catch   add climate_2
#>  281989.1 109608.18 2022  87238.0 0.3093666   catch   add climate_2
#>  303659.7 108209.02 2023  87238.0 0.2872887   catch   add climate_2
#>  323771.2 106489.97 2024  87238.0 0.2694434   catch   add climate_2
#>  236426.6 110741.16 2020  87238.0 0.3689856   catch  mult climate_2
#>  259771.3 110424.27 2021  87238.0 0.3358262   catch  mult climate_2
#>  282070.9 108651.02 2022  87238.0 0.3092768   catch  mult climate_2
#>  302143.0 105969.13 2023  87238.0 0.2887308   catch  mult climate_2
#>  319378.3 102977.50 2024  87238.0 0.2731494   catch  mult climate_2
#>  244549.9 109540.21 2020  69790.4 0.2853831 catch08   add climate_1
#>  281987.2 104915.11 2021  69790.4 0.2474950 catch08   add climate_1
#>  314937.4 100566.12 2022  69790.4 0.2216009 catch08   add climate_1
#>  342108.4  93356.77 2023  69790.4 0.2040008 catch08   add climate_1
#>  363737.0  89481.26 2024  69790.4 0.1918705 catch08   add climate_1
#>  244677.7 109795.81 2020  69790.4 0.2852340 catch08  mult climate_1
#>  281398.6 103226.80 2021  69790.4 0.2480126 catch08  mult climate_1
#>  311994.2  97545.10 2022  69790.4 0.2236914 catch08  mult climate_1
#>  335670.4  89388.23 2023  69790.4 0.2079135 catch08  mult climate_1
#>  352967.3  84786.33 2024  69790.4 0.1977248 catch08  mult climate_1
#>  244549.9 109540.21 2020  69790.4 0.2853831 catch08   add climate_2
#>  283008.8 106958.39 2021  69790.4 0.2466015 catch08   add climate_2
#>  317887.3 102379.32 2022  69790.4 0.2195445 catch08   add climate_2
#>  347889.7  97206.40 2023  69790.4 0.2006107 catch08   add climate_2
#>  372907.4  92409.72 2024  69790.4 0.1871521 catch08   add climate_2
#>  244677.7 109795.81 2020  69790.4 0.2852340 catch08  mult climate_2
#>  282631.0 105691.58 2021  69790.4 0.2469312 catch08  mult climate_2
#>  315230.9  99088.97 2022  69790.4 0.2213946 catch08  mult climate_2
#>  341026.6  92083.36 2023  69790.4 0.2046479 catch08  mult climate_2
#>  360292.8  86029.79 2024  69790.4 0.1937047 catch08  mult climate_2
#>  227696.1 110727.79 2020 104685.6 0.4597602 catch12   add climate_1
#>  233626.6 110504.35 2021 104685.6 0.4480895 catch12   add climate_1
#>  240255.2 112124.16 2022 104685.6 0.4357266 catch12   add climate_1
#>  247459.8 111656.13 2023 104685.6 0.4230409 catch12   add climate_1
#>  255153.2 113102.03 2024 104685.6 0.4102852 catch12   add climate_1
#>  228076.5 111488.69 2020 104685.6 0.4589933 catch12  mult climate_1
#>  234596.9 110923.16 2021 104685.6 0.4462361 catch12  mult climate_1
#>  241911.2 113076.67 2022 104685.6 0.4327439 catch12  mult climate_1
#>  249776.5 112025.20 2023 104685.6 0.4191171 catch12  mult climate_1
#>  257951.0 113694.98 2024 104685.6 0.4058352 catch12  mult climate_1
#>  227696.1 110727.79 2020 104685.6 0.4597602 catch12   add climate_2
#>  234571.9 112395.10 2021 104685.6 0.4462836 catch12   add climate_2
#>  243058.9 113950.12 2022 104685.6 0.4307005 catch12   add climate_2
#>  253018.3 115339.79 2023 104685.6 0.4137471 catch12   add climate_2
#>  264259.6 116513.98 2024 104685.6 0.3961468 catch12   add climate_2
#>  228076.5 111488.69 2020 104685.6 0.4589933 catch12  mult climate_2
#>  236006.5 113742.49 2021 104685.6 0.4435708 catch12  mult climate_2
#>  245973.6 115562.82 2022 104685.6 0.4255969 catch12  mult climate_2
#>  257477.2 116815.67 2023 104685.6 0.4065820 catch12  mult climate_2
#>  269915.5 117432.14 2024 104685.6 0.3878458 catch12  mult climate_2
#> 
#>

References

Schaefer, M.B. (1954). Some Aspects of the Dynamics of Populations Important to the Management of the Commercial Marine Fisheries. Bulletin of the Inter-American Tropical Tuna Commission. 1:26-56.

Pella, J.J., Tomlinson, P.K. (1969). A generalized stock-production model. Bulletin of the Inter-American Tropical Tuna Commission. 13:421–58.

MacCall, A. (2002). Use of Known-Biomass Production Models to Determine Productivity of West Coast Groundfish Stocks. North American Journal of Fisheries Management, 22, 272-279.