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:
knobi_fit: fits the KBPM model (main function).knobi_env: analyzes the production changes in response to environmental fluctuations.knobi_retro: carries out the retrospective analysis.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.
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.
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.
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.
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 SSB and SP
observations (first plot) and with the catch and SP 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 0.6303396
#> 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.
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:
- The correlation analysis between the environmental variable(s) and the KBPM residuals through the Pearson’s correlation or autoregressive models;
- The selection of which lagged environmental variable(s) is included in the environmental KBPM models fit;
- 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 two columns containing the
values of 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
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.
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 0.6846295
#> K 450802.6
#> p 0.25
#> c 0.178514
#>
#>
#> Additive model:
#> SP_t = (r/p)*B_t*(1-(B_t/K)^p)+c*X_t*B_t
#>
#> Parameter estimates:
#> r 0.7340582
#> K 393745.8
#> p 0.25
#> c 0.140194A 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 $BRPs provides the BRPs
estimates for a value of the centered environmental variable equal to
the mean of the time series, i.e. , which cancels out the environmental
effect in the equations defining both models, i.e. the effect of the
parameter .
More options
There is the possibility of obtaining 3D plots reporting the surplus
production curve conditioned to a grid of environmental values using the
argument control$plot3d=TRUE. In this case, a list named
plots3D is added to the output list of
knobi_env with the 3D plots objects.
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
the two variables, “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.
control <- list( lag=c(2,3), multicovar=TRUE)
hake_n_multi <- knobi_env( hake_n_results, data, 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)
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.
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.
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 0.5042717 109395.1 0.2065497
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048596 113174.0 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 0.6303396 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310745 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 0.25There 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.
#> $BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 529631.1 216936.88 0.5042717 109395.12 0.2065497
#> 1978 - 2005 154479.7 63274.88 0.9052966 57282.54 0.3708095
#> 1978 - 2010 1059574.9 434001.88 0.4182296 181512.45 0.1713069
#> 1978 - 2015 625579.8 256237.47 0.4807142 123177.00 0.1969005
#>
#> $params
#> r K p
#> 1978 - 2019 0.6303396 529631.1 0.25
#> 1978 - 2005 1.1316207 154479.7 0.25
#> 1978 - 2010 0.5227870 1059574.9 0.25
#> 1978 - 2015 0.6008928 625579.8 0.25
#> $BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 529631.1 216936.88 0.5042717 109395.12 0.2065497
#> 1990 - 2005 164718.6 67468.74 0.8630042 58225.81 0.3534865
#> 1995 - 2010 391203.7 210004.26 0.8258184 173425.39 0.4433122
#> 1995 - 2015 422793.8 195255.58 0.6960105 135899.92 0.3214331
#>
#> $params
#> r K p
#> 1978 - 2019 0.6303396 529631.1 0.2500000
#> 1990 - 2005 1.0787553 164718.6 0.2500000
#> 1995 - 2010 2.0000000 391203.7 1.4218399
#> 1995 - 2015 1.1425156 422793.8 0.6415208The 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.
#> $base
#> $base$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 529631.1 216936.9 0.5042717 109395.1 0.2065497
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048596 113174.0 0.2067905
#> 1978 - 2016 585744.5 239921.0 0.4944368 118625.8 0.2025213
#>
#> $base$params
#> r K p
#> 1978 - 2019 0.6303396 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310745 547288.4 0.25
#> 1978 - 2016 0.6180460 585744.5 0.25
#>
#>
#> $add
#> $add$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 393745.8 161278.3 0.5872466 94710.11 0.2405362
#> 1978 - 2018 396766.2 162515.4 0.5869989 95396.39 0.2404348
#> 1978 - 2017 406535.6 166517.0 0.5841814 97276.13 0.2392807
#> 1978 - 2016 427141.1 174957.0 0.5735868 100353.02 0.2349411
#>
#> $add$params
#> r K p c
#> 1978 - 2019 0.7340582 393745.8 0.25 0.1401940
#> 1978 - 2018 0.7337487 396766.2 0.25 0.1391139
#> 1978 - 2017 0.7302268 406535.6 0.25 0.1342291
#> 1978 - 2016 0.7169834 427141.1 0.25 0.1338208
#>
#>
#> $mult
#> $mult$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 450802.6 184648.7 0.5477036 101132.8 0.2243394
#> 1978 - 2018 453630.1 185806.9 0.5491147 102029.3 0.2249174
#> 1978 - 2017 461292.5 188945.4 0.5508720 104084.7 0.2256372
#> 1978 - 2016 484226.1 198339.0 0.5423817 107575.4 0.2221595
#>
#> $mult$params
#> r K p c
#> 1978 - 2019 0.6846295 450802.6 0.25 0.1785140
#> 1978 - 2018 0.6863933 453630.1 0.25 0.1775464
#> 1978 - 2017 0.6885900 461292.5 0.25 0.1731753
#> 1978 - 2016 0.6779771 484226.1 0.25 0.1704043
#> $BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 529631.1 216936.9 0.5042717 109395.1 0.2065497
#> 1978 - 2018 534350.5 218870.0 0.5047717 110479.4 0.2067545
#> 1978 - 2017 547288.4 224169.3 0.5048596 113174.0 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 0.6303396 529631.1 0.25
#> 1978 - 2018 0.6309646 534350.5 0.25
#> 1978 - 2017 0.6310745 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
#> $base
#> $base$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 529631.1 216936.88 0.5042717 109395.12 0.2065497
#> 1990 - 2005 164718.6 67468.74 0.8630042 58225.81 0.3534865
#> 1995 - 2010 391203.7 210004.26 0.8258184 173425.39 0.4433122
#> 1995 - 2015 422793.8 195255.58 0.6960105 135899.92 0.3214331
#>
#> $base$params
#> r K p
#> 1978 - 2019 0.6303396 529631.1 0.2500000
#> 1990 - 2005 1.0787553 164718.6 0.2500000
#> 1995 - 2010 2.0000000 391203.7 1.4218399
#> 1995 - 2015 1.1425156 422793.8 0.6415208
#>
#>
#> $add
#> $add$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 516488.3 211553.60 0.5067794 107211.01 0.2075769
#> 1990 - 2005 111640.1 55621.52 1.0092475 56135.88 0.5028292
#> 1995 - 2010 405142.5 215900.38 0.8428851 181979.21 0.4491734
#> 1995 - 2015 456976.9 214188.60 0.7175495 153690.92 0.3363210
#>
#> $add$params
#> r K p c1 c2
#> 1978 - 2019 0.6334743 516488.3 0.2500000 0.01699067 -0.004395079
#> 1990 - 2005 2.0000000 111640.1 0.9816744 -0.12416757 0.002753431
#> 1995 - 2010 2.0000000 405142.5 1.3728028 -0.07141606 0.019703123
#> 1995 - 2015 1.2206167 456976.9 0.7010907 -0.07483213 0.049012357
#>
#>
#> $mult
#> $mult$BRPs
#> K B_MSY F_MSY MSY MSYoverK
#> 1978 - 2019 498824.2 204318.37 0.5217789 106609.01 0.2137206
#> 1990 - 2005 114444.0 57363.85 0.9936034 56996.92 0.4980331
#> 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 0.6522236 498824.2 0.2500000 0.05169040 -0.006546061
#> 1990 - 2005 2.0000000 114444.0 1.0128755 -0.09494592 0.001506820
#> 1995 - 2010 2.0000000 396365.5 1.3688343 -0.05364248 0.025982666
#> 1995 - 2015 1.3168214 422155.9 0.7703032 -0.06813650 0.0900824682.4. 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.
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 108904.39 2020 87238.0 0.3704245 catch base
#> 256339.7 107234.52 2021 87238.0 0.3403219 catch base
#> 275106.4 104775.00 2022 87238.0 0.3171064 catch base
#> 291242.7 101973.57 2023 87238.0 0.2995371 catch base
#> 304589.9 99196.74 2024 87238.0 0.2864114 catch base
#> 315290.2 96680.05 2025 87238.0 0.2766911 catch base
#> 323660.2 94535.92 2026 87238.0 0.2695357 catch base
#> 330084.1 92787.89 2027 87238.0 0.2642902 catch base
#> 243962.5 108365.37 2020 69790.4 0.2860702 catch08 base
#> 280323.4 103937.23 2021 69790.4 0.2489639 catch08 base
#> 311323.0 97642.80 2022 69790.4 0.2241736 catch08 base
#> 335916.5 91124.98 2023 69790.4 0.2077612 catch08 base
#> 354385.4 85393.72 2024 69790.4 0.1969336 catch08 base
#> 367707.9 80832.01 2025 69790.4 0.1897985 catch08 base
#> 377046.9 77426.72 2026 69790.4 0.1850974 catch08 base
#> 383464.5 74989.39 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 108891.56 2022 104685.6 0.4440497 catch12 base
#> 239838.3 108652.38 2023 104685.6 0.4364840 catch12 base
#> 243672.5 108387.04 2024 104685.6 0.4296161 catch12 base
#> 247233.2 108105.55 2025 104685.6 0.4234287 catch12 base
#> 250508.9 107817.08 2026 104685.6 0.4178918 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 AMO equal to last year’s AMO; (ii) constant AMO equal to last year’s AMO with a 50% increment; and (iii) constant AMO equal to last year’s AMO with a 50% decrease.
last_AMO <- Env$AMO[length(Env$AMO)]
env <- data.frame( AMOi=rep(last_AMO,5),
AMOii=rep(last_AMO*1.5,5),
AMOiii=rep(last_AMO*0.5,5))
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
#>
#> Projections:
#>
#> SSB SP Year C F Sc Model EnvSc
#> 235508.2 108904.39 2020 87238.0 0.3704245 catch base <NA>
#> 256339.7 107234.52 2021 87238.0 0.3403219 catch base <NA>
#> 275106.4 104775.00 2022 87238.0 0.3171064 catch base <NA>
#> 291242.7 101973.57 2023 87238.0 0.2995371 catch base <NA>
#> 304589.9 99196.74 2024 87238.0 0.2864114 catch base <NA>
#> 243962.5 108365.37 2020 69790.4 0.2860702 catch08 base <NA>
#> 280323.4 103937.23 2021 69790.4 0.2489639 catch08 base <NA>
#> 311323.0 97642.80 2022 69790.4 0.2241736 catch08 base <NA>
#> 335916.5 91124.98 2023 69790.4 0.2077612 catch08 base <NA>
#> 354385.4 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 108891.56 2022 104685.6 0.4440497 catch12 base <NA>
#> 239838.3 108652.38 2023 104685.6 0.4364840 catch12 base <NA>
#> 243672.5 108387.04 2024 104685.6 0.4296161 catch12 base <NA>
#> 236966.1 111820.26 2020 87238.0 0.3681454 catch add AMOi
#> 259385.4 107494.21 2021 87238.0 0.3363258 catch add AMOi
#> 277361.0 102932.98 2022 87238.0 0.3145288 catch add AMOi
#> 291014.8 98850.79 2023 87238.0 0.2997717 catch add AMOi
#> 300976.4 95548.33 2024 87238.0 0.2898500 catch add AMOi
#> 237731.7 113351.45 2020 87238.0 0.3669599 catch mult AMOi
#> 260930.8 107522.69 2021 87238.0 0.3343339 catch mult AMOi
#> 278416.0 101923.73 2022 87238.0 0.3133369 catch mult AMOi
#> 290817.4 97355.01 2023 87238.0 0.2999752 catch mult AMOi
#> 299245.2 93976.58 2024 87238.0 0.2915268 catch mult AMOi
#> 242182.5 122252.96 2020 87238.0 0.3602160 catch add AMOii
#> 274466.6 116791.25 2021 87238.0 0.3178456 catch add AMOii
#> 300716.5 110184.67 2022 87238.0 0.2901004 catch add AMOii
#> 320564.0 103986.24 2023 87238.0 0.2721391 catch add AMOii
#> 334787.8 98937.37 2024 87238.0 0.2605770 catch add AMOii
#> 241313.5 120514.92 2020 87238.0 0.3615132 catch mult AMOii
#> 270340.1 112014.39 2021 87238.0 0.3226972 catch mult AMOii
#> 291150.7 104082.83 2022 87238.0 0.2996317 catch mult AMOii
#> 304963.5 98018.79 2023 87238.0 0.2860604 catch mult AMOii
#> 313674.2 93878.53 2024 87238.0 0.2781166 catch mult AMOii
#> 231709.1 101306.10 2020 87238.0 0.3764980 catch add AMOiii
#> 244400.1 98551.91 2021 87238.0 0.3569475 catch add AMOiii
#> 254440.6 96005.27 2022 87238.0 0.3428619 catch add AMOiii
#> 262126.8 93842.97 2023 87238.0 0.3328084 catch add AMOiii
#> 267865.7 92110.84 2024 87238.0 0.3256782 catch add AMOiii
#> 234322.8 106533.57 2020 87238.0 0.3722984 catch mult AMOiii
#> 251752.5 102801.95 2021 87238.0 0.3465228 catch mult AMOiii
#> 265497.4 99163.77 2022 87238.0 0.3285832 catch mult AMOiii
#> 275857.4 96032.30 2023 87238.0 0.3162431 catch mult AMOiii
#> 283408.2 93545.29 2024 87238.0 0.3078174 catch mult AMOiii
#> 244521.6 109483.58 2020 69790.4 0.2854161 catch08 add AMOi
#> 280033.9 101121.77 2021 69790.4 0.2492213 catch08 add AMOi
#> 306990.4 92372.18 2022 69790.4 0.2273374 catch08 add AMOi
#> 325922.4 85072.58 2023 69790.4 0.2141319 catch08 add AMOi
#> 338523.4 79710.15 2024 69790.4 0.2061612 catch08 add AMOi
#> 245575.5 111591.48 2020 69790.4 0.2841912 catch08 mult AMOi
#> 281921.7 100681.57 2021 69790.4 0.2475525 catch08 mult AMOi
#> 307664.9 90385.73 2022 69790.4 0.2268390 catch08 mult AMOi
#> 324384.2 82633.61 2023 69790.4 0.2151474 catch08 mult AMOi
#> 334648.6 77476.00 2024 69790.4 0.2085483 catch08 mult AMOi
#> 249681.6 119803.61 2020 69790.4 0.2795176 catch08 add AMOii
#> 294961.1 110336.25 2021 69790.4 0.2366088 catch08 add AMOii
#> 329963.8 99249.79 2022 69790.4 0.2115093 catch08 add AMOii
#> 354614.8 89633.05 2023 69790.4 0.1968062 catch08 add AMOii
#> 370894.6 82507.41 2024 69790.4 0.1881677 catch08 add AMOii
#> 249055.5 118551.39 2020 69790.4 0.2802203 catch08 mult AMOii
#> 290680.0 104278.44 2021 69790.4 0.2400936 catch08 mult AMOii
#> 318715.4 91373.17 2022 69790.4 0.2189740 catch08 mult AMOii
#> 335770.4 82317.66 2023 69790.4 0.2078515 catch08 mult AMOii
#> 345514.8 76751.82 2024 69790.4 0.2019896 catch08 mult AMOii
#> 239323.1 99086.58 2020 69790.4 0.2916158 catch08 add AMOiii
#> 265221.4 92290.92 2021 69790.4 0.2631401 catch08 add AMOiii
#> 284525.6 85898.18 2022 69790.4 0.2452869 catch08 add AMOiii
#> 298070.1 80771.74 2023 69790.4 0.2341409 catch08 add AMOiii
#> 307183.4 77035.62 2024 69790.4 0.2271946 catch08 add AMOiii
#> 242259.6 104959.52 2020 69790.4 0.2880811 catch08 mult AMOiii
#> 273357.8 96817.84 2021 69790.4 0.2553078 catch08 mult AMOiii
#> 296410.9 88869.15 2022 69790.4 0.2354515 catch08 mult AMOiii
#> 312304.2 82498.12 2023 69790.4 0.2234693 catch08 mult AMOiii
#> 322732.2 77938.71 2024 69790.4 0.2162486 catch08 mult AMOiii
#> 229324.9 113985.40 2020 104685.6 0.4564947 catch12 add AMOi
#> 237987.3 112710.65 2021 104685.6 0.4398789 catch12 add AMOi
#> 245374.1 111434.00 2022 104685.6 0.4266368 catch12 add AMOi
#> 251525.8 110240.62 2023 104685.6 0.4162023 catch12 add AMOi
#> 256550.4 109179.75 2024 104685.6 0.4080509 catch12 add AMOi
#> 229786.0 114907.59 2020 104685.6 0.4555787 catch12 mult AMOi
#> 239085.9 113063.33 2021 104685.6 0.4378578 catch12 mult AMOi
#> 246604.2 111344.48 2022 104685.6 0.4245086 catch12 mult AMOi
#> 252517.2 109852.80 2023 104685.6 0.4145682 catch12 mult AMOi
#> 257069.1 108622.15 2024 104685.6 0.4072275 catch12 mult AMOi
#> 234600.9 124537.38 2020 104685.6 0.4462285 catch12 add AMOii
#> 253273.1 122178.29 2021 104685.6 0.4133309 catch12 add AMOii
#> 269335.1 119316.86 2022 104685.6 0.3886816 catch12 add AMOii
#> 282517.6 116419.36 2023 104685.6 0.3705454 catch12 add AMOii
#> 292937.4 113791.32 2024 104685.6 0.3573651 catch12 add AMOii
#> 233467.6 122270.85 2020 104685.6 0.4483945 catch12 mult AMOii
#> 249176.9 118518.81 2021 104685.6 0.4201257 catch12 mult AMOii
#> 261253.4 115005.47 2022 104685.6 0.4007052 catch12 mult AMOii
#> 270116.3 112091.57 2023 104685.6 0.3875575 catch12 mult AMOii
#> 276404.6 109856.29 2024 104685.6 0.3787404 catch12 mult AMOii
#> 224005.7 103346.99 2020 104685.6 0.4673345 catch12 add AMOiii
#> 222770.7 103554.32 2021 104685.6 0.4699253 catch12 add AMOiii
#> 221725.2 103725.76 2022 104685.6 0.4721412 catch12 add AMOiii
#> 220836.7 103868.47 2023 104685.6 0.4740408 catch12 add AMOiii
#> 220079.3 103987.96 2024 104685.6 0.4756722 catch12 add AMOiii
#> 226286.4 107908.36 2020 104685.6 0.4626244 catch12 mult AMOiii
#> 229267.2 107424.50 2021 104685.6 0.4566096 catch12 mult AMOiii
#> 231789.4 106991.02 2022 104685.6 0.4516411 catch12 mult AMOiii
#> 233904.6 106610.60 2023 104685.6 0.4475569 catch12 mult AMOiii
#> 235665.4 106282.25 2024 104685.6 0.4442128 catch12 mult AMOiii
#>
#> 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 109340.41 2020 112500.47 0.5042717 f base <NA>
#> 220585.4 109375.86 2021 111234.96 0.5042717 f base <NA>
#> 219105.6 109388.31 2022 110488.75 0.5042717 f base <NA>
#> 218228.5 109392.70 2023 110046.46 0.5042717 f base <NA>
#> 217707.0 109394.26 2024 109783.48 0.5042717 f base <NA>
#> 214475.7 109386.30 2020 129784.84 0.6051260 f12 base <NA>
#> 198627.8 108897.43 2021 120194.82 0.6051260 f12 base <NA>
#> 189718.7 108283.08 2022 114803.74 0.6051260 f12 base <NA>
#> 184530.5 107808.37 2023 111664.20 0.6051260 f12 base <NA>
#> 181445.9 107484.40 2024 109797.66 0.6051260 f12 base <NA>
#> 232338.5 109056.43 2020 93729.39 0.4034173 f08 base <NA>
#> 244779.5 108303.12 2021 98748.28 0.4034173 f08 base <NA>
#> 252451.6 107632.75 2022 101843.35 0.4034173 f08 base <NA>
#> 257070.6 107155.32 2023 103706.73 0.4034173 f08 base <NA>
#> 259811.7 106846.13 2024 104812.53 0.4034173 f08 base <NA>
#> 225365.8 115027.26 2020 113645.60 0.5042717 f add AMOi
#> 226430.5 114930.05 2021 114182.46 0.5042717 f add AMOi
#> 227005.9 114875.95 2022 114472.64 0.5042717 f add AMOi
#> 227316.2 114846.32 2023 114629.10 0.5042717 f add AMOi
#> 227483.2 114830.23 2024 114713.34 0.5042717 f add AMOi
#> 225607.5 115632.43 2020 113767.46 0.5042717 f mult AMOi
#> 227003.1 115397.58 2021 114471.25 0.5042717 f mult AMOi
#> 227695.3 115278.40 2022 114820.31 0.5042717 f mult AMOi
#> 228037.4 115218.84 2023 114992.80 0.5042717 f mult AMOi
#> 228206.1 115189.30 2024 115077.89 0.5042717 f mult AMOi
#> 229710.1 125906.52 2020 115836.30 0.5042717 f add AMOii
#> 237587.7 125493.67 2021 119808.74 0.5042717 f add AMOii
#> 242001.6 125177.39 2022 122034.54 0.5042717 f add AMOii
#> 244431.8 124977.61 2023 123260.03 0.5042717 f add AMOii
#> 245757.0 124861.07 2024 123928.28 0.5042717 f add AMOii
#> 228641.9 123231.38 2020 115297.62 0.5042717 f mult AMOii
#> 234507.1 122051.95 2021 118255.28 0.5042717 f mult AMOii
#> 237296.4 121443.74 2022 119661.84 0.5042717 f mult AMOii
#> 238601.7 121148.75 2023 120320.06 0.5042717 f mult AMOii
#> 239207.9 121009.51 2024 120625.76 0.5042717 f mult AMOii
#> 220997.2 104087.02 2020 111442.62 0.5042717 f add AMOiii
#> 215416.2 104821.99 2021 108628.30 0.5042717 f add AMOiii
#> 212511.8 105161.11 2022 107163.68 0.5042717 f add AMOiii
#> 210979.1 105327.96 2023 106390.78 0.5042717 f add AMOiii
#> 210164.3 105413.22 2024 105979.92 0.5042717 f add AMOiii
#> 222737.0 108443.90 2020 112319.95 0.5042717 f mult AMOiii
#> 219804.7 108852.68 2021 110841.26 0.5042717 f mult AMOiii
#> 218295.7 109051.05 2022 110080.35 0.5042717 f mult AMOiii
#> 217513.5 109150.67 2023 109685.88 0.5042717 f mult AMOiii
#> 217106.4 109201.64 2024 109480.60 0.5042717 f mult AMOiii
#> 217382.4 116958.55 2020 131543.74 0.6051260 f12 add AMOi
#> 206343.6 117371.48 2021 124863.88 0.6051260 f12 add AMOi
#> 200608.7 117416.08 2022 121393.53 0.6051260 f12 add AMOi
#> 197545.5 117391.13 2023 119539.95 0.6051260 f12 add AMOi
#> 195885.1 117363.22 2024 118535.20 0.6051260 f12 add AMOi
#> 217348.9 116871.18 2020 131523.45 0.6051260 f12 mult AMOi
#> 206568.1 118090.41 2021 124999.71 0.6051260 f12 mult AMOi
#> 201424.3 118508.81 2022 121887.07 0.6051260 f12 mult AMOi
#> 198894.5 118674.99 2023 120356.25 0.6051260 f12 mult AMOi
#> 197631.8 118748.07 2024 119592.17 0.6051260 f12 mult AMOi
#> 221616.2 127988.24 2020 134105.75 0.6051260 f12 add AMOii
#> 216915.2 127976.41 2021 131261.02 0.6051260 f12 add AMOii
#> 214379.3 127939.45 2022 129726.52 0.6051260 f12 add AMOii
#> 212996.1 127910.17 2023 128889.51 0.6051260 f12 add AMOii
#> 212237.1 127891.35 2024 128430.17 0.6051260 f12 add AMOii
#> 220340.9 124665.80 2020 133334.01 0.6051260 f12 mult AMOii
#> 214032.3 125567.65 2021 129516.54 0.6051260 f12 mult AMOii
#> 211138.2 125925.87 2022 127765.23 0.6051260 f12 mult AMOii
#> 209785.7 126081.16 2023 126946.80 0.6051260 f12 mult AMOii
#> 209148.2 126151.66 2024 126561.03 0.6051260 f12 mult AMOii
#> 213125.4 105868.55 2020 128967.73 0.6051260 f12 add AMOiii
#> 195912.8 107226.00 2021 118551.96 0.6051260 f12 add AMOiii
#> 187318.2 107487.70 2022 113351.10 0.6051260 f12 add AMOiii
#> 182825.2 107509.83 2023 110632.30 0.6051260 f12 add AMOiii
#> 180419.9 107488.64 2024 109176.79 0.6051260 f12 add AMOiii
#> 214523.6 109511.04 2020 129813.81 0.6051260 f12 mult AMOiii
#> 199441.1 110824.87 2021 120687.02 0.6051260 f12 mult AMOiii
#> 191995.9 111153.50 2022 116181.74 0.6051260 f12 mult AMOiii
#> 188167.9 111237.38 2023 113865.28 0.6051260 f12 mult AMOiii
#> 186158.3 111257.88 2024 112649.21 0.6051260 f12 mult AMOiii
#> 233864.3 112723.46 2020 94344.90 0.4034173 f08 add AMOi
#> 248279.4 110611.80 2021 100160.20 0.4034173 f08 add AMOi
#> 256365.9 109143.81 2022 103422.43 0.4034173 f08 add AMOi
#> 260760.4 108262.89 2023 105195.25 0.4034173 f08 add AMOi
#> 263107.5 107768.74 2024 106142.12 0.4034173 f08 add AMOi
#> 234408.1 114030.46 2020 94564.28 0.4034173 f08 mult AMOi
#> 249220.9 110699.39 2021 100540.01 0.4034173 f08 mult AMOi
#> 256837.5 108686.48 2022 103612.68 0.4034173 f08 mult AMOi
#> 260613.7 107614.86 2023 105136.10 0.4034173 f08 mult AMOi
#> 262452.1 107075.74 2024 105877.73 0.4034173 f08 mult AMOi
#> 238323.2 123440.19 2020 96143.72 0.4034173 f08 add AMOii
#> 260056.0 121080.27 2021 104911.11 0.4034173 f08 add AMOii
#> 272675.6 119072.08 2022 110002.07 0.4034173 f08 add AMOii
#> 279678.7 117763.31 2023 112827.22 0.4034173 f08 add AMOii
#> 283468.0 116998.51 2024 114355.91 0.4034173 f08 add AMOii
#> 237475.8 121403.57 2020 95801.87 0.4034173 f08 mult AMOii
#> 256695.9 116394.08 2021 103555.59 0.4034173 f08 mult AMOii
#> 266146.7 113431.22 2022 107368.19 0.4034173 f08 mult AMOii
#> 270569.5 111935.08 2023 109152.44 0.4034173 f08 mult AMOii
#> 272591.0 111228.34 2024 109967.95 0.4034173 f08 mult AMOii
#> 229379.7 101945.17 2020 92535.75 0.4034173 f08 add AMOiii
#> 236647.7 100594.46 2021 95467.80 0.4034173 f08 add AMOiii
#> 240579.6 99791.03 2022 97053.98 0.4034173 f08 add AMOiii
#> 242670.9 99343.19 2023 97897.65 0.4034173 f08 add AMOiii
#> 243773.2 99101.45 2024 98342.34 0.4034173 f08 add AMOiii
#> 231500.3 107041.82 2020 93391.23 0.4034173 f08 mult AMOiii
#> 242014.7 105011.23 2021 97632.94 0.4034173 f08 mult AMOiii
#> 247639.4 103773.05 2022 99902.02 0.4034173 f08 mult AMOiii
#> 250574.7 103085.66 2023 101086.16 0.4034173 f08 mult AMOiii
#> 252086.7 102720.65 2024 101696.13 0.4034173 f08 mult AMOiii
#>
#> 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 108904.39 2020 87238.0 0.3704245 catch base <NA>
#> 256339.7 107234.52 2021 87238.0 0.3403219 catch base <NA>
#> 275106.4 104775.00 2022 87238.0 0.3171064 catch base <NA>
#> 291242.7 101973.57 2023 87238.0 0.2995371 catch base <NA>
#> 304589.9 99196.74 2024 87238.0 0.2864114 catch base <NA>
#> 243962.5 108365.37 2020 69790.4 0.2860702 catch08 base <NA>
#> 280323.4 103937.23 2021 69790.4 0.2489639 catch08 base <NA>
#> 311323.0 97642.80 2022 69790.4 0.2241736 catch08 base <NA>
#> 335916.5 91124.98 2023 69790.4 0.2077612 catch08 base <NA>
#> 354385.4 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 108891.56 2022 104685.6 0.4440497 catch12 base <NA>
#> 239838.3 108652.38 2023 104685.6 0.4364840 catch12 base <NA>
#> 243672.5 108387.04 2024 104685.6 0.4296161 catch12 base <NA>
#> 236170.3 110228.58 2020 87238.0 0.3693860 catch add climate_1
#> 258251.3 108409.50 2021 87238.0 0.3378027 catch add climate_1
#> 279117.2 107798.15 2022 87238.0 0.3125498 catch add climate_1
#> 298011.7 104466.99 2023 87238.0 0.2927334 catch add climate_1
#> 314709.1 103403.73 2024 87238.0 0.2772020 catch add climate_1
#> 236426.6 110741.14 2020 87238.0 0.3689856 catch mult climate_1
#> 258446.6 107774.90 2021 87238.0 0.3375475 catch mult climate_1
#> 278431.0 106669.89 2022 87238.0 0.3133200 catch mult climate_1
#> 295699.9 102343.91 2023 87238.0 0.2950221 catch mult climate_1
#> 310025.1 100782.52 2024 87238.0 0.2813901 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 108209.03 2023 87238.0 0.2872887 catch add climate_2
#> 323771.2 106489.99 2024 87238.0 0.2694433 catch add climate_2
#> 236426.6 110741.14 2020 87238.0 0.3689856 catch mult climate_2
#> 259771.3 110424.25 2021 87238.0 0.3358262 catch mult climate_2
#> 282070.9 108651.00 2022 87238.0 0.3092769 catch mult climate_2
#> 302143.0 105969.12 2023 87238.0 0.2887309 catch mult climate_2
#> 319378.3 102977.49 2024 87238.0 0.2731495 catch mult climate_2
#> 244549.9 109540.21 2020 69790.4 0.2853831 catch08 add climate_1
#> 281987.2 104915.10 2021 69790.4 0.2474950 catch08 add climate_1
#> 314937.4 100566.12 2022 69790.4 0.2216009 catch08 add climate_1
#> 342108.4 93356.76 2023 69790.4 0.2040008 catch08 add climate_1
#> 363737.0 89481.26 2024 69790.4 0.1918705 catch08 add climate_1
#> 244677.7 109795.78 2020 69790.4 0.2852340 catch08 mult climate_1
#> 281398.6 103226.78 2021 69790.4 0.2480126 catch08 mult climate_1
#> 311994.1 97545.08 2022 69790.4 0.2236914 catch08 mult climate_1
#> 335670.3 89388.21 2023 69790.4 0.2079135 catch08 mult climate_1
#> 352967.2 84786.32 2024 69790.4 0.1977249 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 102379.33 2022 69790.4 0.2195445 catch08 add climate_2
#> 347889.7 97206.41 2023 69790.4 0.2006107 catch08 add climate_2
#> 372907.4 92409.73 2024 69790.4 0.1871521 catch08 add climate_2
#> 244677.7 109795.78 2020 69790.4 0.2852340 catch08 mult climate_2
#> 282631.0 105691.56 2021 69790.4 0.2469312 catch08 mult climate_2
#> 315230.8 99088.94 2022 69790.4 0.2213946 catch08 mult climate_2
#> 341026.6 92083.34 2023 69790.4 0.2046480 catch08 mult climate_2
#> 360292.7 86029.78 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 113102.04 2024 104685.6 0.4102852 catch12 add climate_1
#> 228076.5 111488.67 2020 104685.6 0.4589933 catch12 mult climate_1
#> 234596.8 110923.14 2021 104685.6 0.4462362 catch12 mult climate_1
#> 241911.1 113076.65 2022 104685.6 0.4327440 catch12 mult climate_1
#> 249776.5 112025.18 2023 104685.6 0.4191172 catch12 mult climate_1
#> 257950.9 113694.96 2024 104685.6 0.4058353 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
#> 243059.0 113950.13 2022 104685.6 0.4307004 catch12 add climate_2
#> 253018.3 115339.81 2023 104685.6 0.4137471 catch12 add climate_2
#> 264259.6 116514.00 2024 104685.6 0.3961468 catch12 add climate_2
#> 228076.5 111488.67 2020 104685.6 0.4589933 catch12 mult climate_2
#> 236006.5 113742.47 2021 104685.6 0.4435708 catch12 mult climate_2
#> 245973.5 115562.80 2022 104685.6 0.4255970 catch12 mult climate_2
#> 257477.2 116815.65 2023 104685.6 0.4065821 catch12 mult climate_2
#> 269915.5 117432.13 2024 104685.6 0.3878459 catch12 mult climate_2
#>
#>