Package 'DLMtool'

Average Catch

Description

A simple average catch MP that is included to demonstrate a 'status quo' management option

Usage

AvC(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

The average catch method is very simple. The mean historical catch is calculated and used to set a constant catch limit (TAC). If reps > 1 then the reps samples are drawn from a log-normal distribution with mean TAC and standard deviation (in log-space) of 0.2.

For completeness, the TAC is calculated by:

$\textrm{TAC} =\frac{\sum_{y=1}^{\textrm{n}}{C_y}}{\textrm{n}}$

where $\textrm{TAC}$ is the the mean catch recommendation, $n$ is the number of historical years, and $C_y$ is the catch in historical year $y$

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

AvC: Cat, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

See Also

Other Average Catch MPs: AvC_MLL(), DCACs()

Examples

Rec <- AvC(1, MSEtool::Cobia, reps=1000, plot=TRUE) # 1,000 log-normal samples with CV = 0.2

---

Average Catch with a size limit

Description

A example mixed control MP that uses the average catch output control MP together with a minimul size limit set at the size of maturity.

Usage

AvC_MLL(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

The average catch method is very simple. The mean historical catch is calculated and used to set a constant catch limit (TAC). If reps > 1 then the reps samples are drawn from a log-normal distribution with mean TAC and standard deviation (in log-space) of 0.2.

For completeness, the TAC is calculated by:

$\textrm{TAC} =\frac{\sum_{y=1}^{\textrm{n}}{C_y}}{\textrm{n}}$

where $\textrm{TAC}$ is the the mean catch recommendation, $n$ is the number of historical years, and $C_y$ is the catch in historical year $y$.

The size of retention is set to the length of maturity.

This MP has been included for demonstration purposes of a mixed control MP.

Value

An object of class Rec-class with the TAC, Retention slot(s) populated

Required Data

See Data-class for information on the Data object

AvC_MLL: Cat, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

See Also

Other Average Catch MPs: AvC(), DCACs()

Examples

Rec <- AvC_MLL(1, MSEtool::Cobia, reps=1000, plot=TRUE) # 1,000 log-normal samples with CV = 0.2

---

Beddington and Kirkwood life-history MP

Description

Family of management procedures that sets the TAC by approximation of Fmax based on the length at first capture relative to asymptotic length and the von Bertalanffy growth parameter K.

Usage

BK(x, Data, reps = 100, plot = FALSE)

BK_CC(x, Data, reps = 100, plot = FALSE, Fmin = 0.005)

BK_ML(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
Fmin	The minimum fishing mortality rate that is derived from the catch-curve (interval censor).

Details

The TAC is calculated as:

$\textrm{TAC} = A F_{\textrm{max}}$

where $A$ is (vulnerable) stock abundance, and $F_{\textrm{max}}$ is calculated as:

$F_{\textrm{max}} = \frac{0.6K}{0.67-L_c/L_\infty}$

where $K$ is the von Bertalanffy growth coefficient, $L_c$ is the length at first capture, and $L_\infty$ is the von Bertalanffy asymptotic length

Abundance (A) is either assumed known (BK) or estimated (BK_CC and BK_ML):

$A = \frac{\bar{C}}{\left(1-e^{-F}\right)}$

where $\bar{C}$ is the mean catch, and F is estimated. See Functions section below for the estimation of F.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• BK: Assumes that abundance is known, i.e. Data@Abun and Data@CV_abun contain values

• BK_CC: Abundance is estimated using an age-based catch curve to estimate Z and F, and abundance estimated from recent catches and F.

• BK_ML: Abundance is estimated using mean length to estimate Z and F, and abundance estimated from recent catches and F.

Required Data

See Data-class for information on the Data object

BK: Abun, LFC, vbK, vbLinf

BK_CC: CAA, Cat, LFC, vbK, vbLinf

BK_ML: CAL, Cat, LFC, Lbar, Lc, Mort, vbK, vbLinf

Rendered Equations

See Online Documentation for correctly rendered equations

Note

Note that the Beddington-Kirkwood method is designed to estimate $F_\textrm{max}$, that is, the fishing mortality that produces the maximum yield assuming constant recruitment independent of spawning biomass.

Beddington and Kirkwood (2005) recommend estimating F using other methods (e.g., a catch curve) and comparing the estimated F to the estimated $F_\textrm{max}$ and adjusting exploitation accordingly. These MPs have not been implemented that way.

Author(s)

T. Carruthers.

References

Beddington, J.R., Kirkwood, G.P., 2005. The estimation of potential yield and stock status using life history parameters. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360, 163-170.

Examples

## Not run: 
BK(1, MSEtool::SimulatedData, reps=1000, plot=TRUE)

## End(Not run)

## Not run: 
BK_CC(1, MSEtool::SimulatedData, reps=1000, plot=TRUE)

## End(Not run)

## Not run: 
BK_ML(1, MSEtool::SimulatedData, reps=100, plot=TRUE)

## End(Not run)

---

Geromont and Butterworth (2015) Constant Catch

Description

The TAC is the average historical catch over the last yrsmth (default 5) years, multiplied by (1-xx)

Usage

CC1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0)

CC2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.1)

CC3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.2)

CC4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.3)

CC5(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.4)

CurC(x, Data, reps = 100, plot = FALSE, yrsmth = 1, xx = 0)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate mean catches
xx	Parameter controlling the TAC. Mean catches are multiplied by (1-xx)

Details

The TAC is calculated as:

$\textrm{TAC} = (1-x)C_{\textrm{ave}}$

where x lies between 0 and 1, and $C_{\textrm{ave}}$ is average historical catch over the previous yrsmth years.

The TAC is constant for all future projections.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• CC1: TAC is average historical catch from recent yrsmth years

• CC2: TAC is average historical catch from recent yrsmth years reduced by 10\

• CC3: TAC is average historical catch from recent yrsmth years reduced by 20\

• CC4: TAC is average historical catch from recent yrsmth years reduced by 30\

• CC5: TAC is average historical catch from recent yrsmth years reduced by 40\

• CurC: TAC is fixed at last historical catch

Required Data

See Data-class for information on the Data object

CC1: Cat, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Geromont, H. F., and D. S. Butterworth. 2015. Generic Management Procedures for Data-Poor Fisheries: Forecasting with Few Data. ICES Journal of Marine Science: Journal Du Conseil 72 (1). 251-61.

See Also

Other Constant Catch MPs: GB_CC()

Examples

CC1(1, MSEtool::Cobia, plot=TRUE)

CC2(1, MSEtool::Cobia, plot=TRUE)

CC3(1, MSEtool::Cobia, plot=TRUE)

CC4(1, MSEtool::Cobia, plot=TRUE)

CC5(1, MSEtool::Cobia, plot=TRUE)

CurC(1, MSEtool::Cobia, plot=TRUE)

---

Age-Composition Stock-Reduction Analysis

Description

A stock reduction analysis (SRA) model is fitted to the age-composition from the last 3 years (or less if fewer data are available)

Usage

CompSRA(x, Data, reps = 100, plot = FALSE)

CompSRA4010(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

A stock reduction analysis (SRA) model is fitted to the age-composition from the last 3 years (or less if fewer data are available) assuming a constant total mortality rate (Z) and used to estimate current stock depletion (D), $F_\textrm{MSY}$, and stock abundance (A).

Abundance is estimated in the SRA. $F_{\textrm{MSY}}$ is calculated assuming knife-edge vulnerability at the age of full selection.

The TAC is calculated as $F_\textrm{MSY} A$. CompSRA4010 uses a 40-10 harvest control rule to reduce TAC at low biomass.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• CompSRA: TAC is FMSY x Abundance

• CompSRA4010: With a 40-10 control rule based on estimated depletion

Required Data

See Data-class for information on the Data object

CompSRA: CAA, Cat, L50, LFC, LFS, MaxAge, Mort, steep, vbK, vbLinf, vbt0, wla, wlb

CompSRA4010: CAA, Cat, L50, LFC, LFS, MaxAge, Mort, steep, vbK, vbLinf, vbt0, wla, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

Examples

## Not run: 
CompSRA(1, MSEtool::SimulatedData, plot=TRUE)

## End(Not run)

CompSRA4010(1, MSEtool::SimulatedData, plot=TRUE)

---

Fishing at current effort levels

Description

Constant fishing effort set at final year of historical simulations subject to changes in catchability determined by OM@qinc and interannual variability in catchability determined by OM@qcv. This MP is intended to represent a 'status quo' management approach.

Usage

curE(x, Data, reps, plot = FALSE)

curE75(x, Data, reps, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• curE: Set effort to 100\

• curE75: Set effort to 75\

Required Data

See Data-class for information on the Data object

curE:

curE75:

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers.

Examples

curE(1, MSEtool::Atlantic_mackerel, plot=TRUE)
curE75(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Depletion-Based Stock Reduction Analysis

Description

Depletion-Based Stock Reduction Analysis (DB-SRA) is a method designed for determining a catch limit and management reference points for data-limited fisheries where catches are known from the beginning of exploitation. User prescribed BMSY/B0, M, FMSY/M are used to find B0 and therefore the a catch limit by back-constructing the stock to match a user specified level of stock depletion.

Usage

DBSRA(x, Data, reps = 100, plot = FALSE)

DBSRA_40(x, Data, reps = 100, plot = FALSE)

DBSRA4010(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

DB-SRA assumes that a complete time-series of catch from the beginning of exploitation is available. Users prescribe estimates of current depletion $(D)$, biomass at MSY relative to unfished $\left(\frac{B_\textrm{MSY}}{B_0}\right)$, the natural mortality rate $(M)$, and the ratio fishing mortality at MSY to M $\left(\frac{F_{\textrm{MSY}}}{M}\right)$.

You may have noticed that you -the user- specify three of the factors that make the quota recommendation. So this can be quite a subjective method. In the MSE the MSY reference points (e.g., $\left(\frac{F_\textrm{MSY}}{M}\right)$) are taken as the true value calculate in the MSE with added uncertainty specified in the Obs object (e.g Obs@FMSY_Mbiascv).

The catch limit, for the Base Version, is calculated as:

$\textrm{TAC} = M \frac{F_{\textrm{MSY}}}{M} D B_0$

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• DBSRA: Base Version. TAC is calculated assumed MSY harvest rate multiplied by the estimated current abundance (estimated B0 x Depletion)

• DBSRA_40: Same as the Base Version but assumes 40 percent current depletion (Bcurrent/B0 = 0.4), which is more or less the most optimistic state for a stock (ie very close to BMSY/B0 for many stocks).

• DBSRA4010: Base version paired with the 40-10 rule that linearly throttles back the TAC when depletion is below 0.4 down to zero at 10 percent of unfished biomass.

Required Data

See Data-class for information on the Data object

DBSRA: BMSY_B0, Cat, Dep, FMSY_M, L50, vbK, vbLinf, vbt0

DBSRA_40: BMSY_B0, Cat, FMSY_M, L50, vbK, vbLinf, vbt0

DBSRA4010: BMSY_B0, Cat, Dep, FMSY_M, L50, vbK, vbLinf, vbt0

Rendered Equations

See Online Documentation for correctly rendered equations

Note

The DB-SRA method of this package isn't exactly the same as the original method of Dick and MacCall (2011) because it has to work for simulated depletions above BMSY/B0 and even on occasion over B0. It also doesn't have the modification for flatfish life histories that has previously been applied by Dick and MacCall (2011).

Author(s)

T. Carruthers

References

Dick, E.J., MacCall, A.D., 2010. Estimates of sustainable yield for 50 data-poor stocks in the Pacific Coast groundfish fishery management plan. Technical memorandum. Southwest fisheries Science Centre, Santa Cruz, CA. National Marine Fisheries Service, National Oceanic and Atmospheric Administration of the U.S. Department of Commerce. NOAA-TM-NMFS-SWFSC-460.

Dick, E.J., MacCall, A.D., 2011. Depletion-Based Stock Reduction Analysis: A catch-based method for determining sustainable yields for data-poor fish stocks. Fish. Res. 110, 331-341.

Examples

DBSRA(1, MSEtool::ourReefFish, plot=TRUE)

DBSRA_40(1, MSEtool::ourReefFish, plot=TRUE)
DBSRA4010(1, MSEtool::ourReefFish, plot=TRUE)

---

Depletion Corrected Average Catch

Description

This group of MPs calculates a catch limit (dcac; intended as an MSY proxy) based on average historical catch while accounting for the windfall catch that got the stock down to its current depletion level (D).

Usage

DCACs(x, Data, reps = 100, plot = FALSE)

DCAC(x, Data, reps = 100, plot = FALSE)

DCAC_40(x, Data, reps = 100, plot = FALSE)

DCAC4010(x, Data, reps = 100, plot = FALSE)

DCAC_ML(x, Data, reps = 100, plot = FALSE)

DAAC(x, Data, reps = 100, plot = FALSE)

HDAAC(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

The method calculates the depletion-corrected average catch (dcac) as:

$\textrm{dcac} = \frac{\sum_{y=1}^{n}{C_y}}{n+(1-D)/Y_{\textrm{pot}}}$

where

$Y_{\textrm{pot}} = \frac{B_{\textrm{MSY}}}{B_0}\frac{F_{\textrm{MSY}}}{M}M$

and $C$ is the historical catches; i.e $C$ does not change in the future projections in the MSE

The methods differ in the assumptions of current depletion (D). See the Functions section below for details.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• DCACs: Depletion is not updated in the future projections. The TAC is static and not updated in the future years. This represents an application of the DCAC method where a catch limit is calculated based on current estimate of depletion and time-series of catch from the beginning of the fishery, and the TAC is fixed at this level for all future projections.

• DCAC: Depletion is estimated each management interval and used to update the catch limit recommendation based on the historical catch (which is not updated in the future projections).

• DCAC_40: Current stock biomass is assumed to be exactly at 40 per cent of unfished levels. The 40 percent depletion assumption may not really affect DCAC that much as it already makes TAC recommendations that are quite MSY-like.

• DCAC4010: The dynamic DCAC (depletion is updated) is paired with the 40-10 rule that throttles back the OFL to zero at 10 percent of unfished stock size (the OFL is not subject to downward adjustment above 40 percent unfished). DCAC can overfish below BMSY levels. The 40-10 harvest control rule largely resolves this problem providing an MP with surprisingly good performance even at low stock levels.

• DCAC_ML: This variant uses the mean length estimator to calculate current stock depletion. The mean length extension was programmed by Gary Nelson as part of his excellent R package 'fishmethods'.

• DAAC: Depletion Adjusted Average Catch: essentially DCAC (with updated Depletion) divided by BMSY/B0 (Bpeak) (Harford and Carruthers, 2017).

• HDAAC: Hybrid Depletion Adjusted Average Catch: essentially DCAC (with updated Depletion) divided by BMSY/B0 (Bpeak) when below BMSY, and DCAC above BMSY (Harford and Carruthers 2017).

Required Data

See Data-class for information on the Data object

DCACs: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, Year, t

DCAC: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, Year, t

DCAC_40: AvC, BMSY_B0, FMSY_M, LHYear, Mort, Year, t

DCAC4010: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, Year, t

DCAC_ML: AvC, CAL, Cat, LHYear, Lbar, Lc, Mort, Year, t, vbK, vbLinf

DAAC: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, Year, t

HDAAC: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, Year, t

Rendered Equations

See Online Documentation for correctly rendered equations

Note

It's probably worth noting that DCAC TAC recommendations do not tend to zero as depletion tends to zero. It adjusts for depletion only in calculating historical average catch. It follows that at stock levels much below BMSY, DCAC tends to chronically overfish.

Author(s)

T. Carruthers

References

MacCall, A.D., 2009. Depletion-corrected average catch: a simple formula for estimating sustainable yields in data-poor situations. ICES J. Mar. Sci. 66, 2267-2271.

Harford W. and Carruthers, T. 2017. Interim and long-term performance of static and adaptive management procedures. Fish. Res. 190, 84-94.

See Also

Other Average Catch MPs: AvC_MLL(), AvC()

Examples

DCACs(1, MSEtool::Atlantic_mackerel, plot=TRUE)

DCAC(1, MSEtool::Atlantic_mackerel, plot=TRUE)

DCAC_40(1, MSEtool::Atlantic_mackerel, plot=TRUE)

Data <- MSEtool::Atlantic_mackerel
Data@LHYear <- 2005
DCAC4010(1, Data, plot=TRUE)

DCAC_ML(1, MSEtool::SimulatedData, plot=TRUE)

Data <- MSEtool::Atlantic_mackerel
Data@LHYear <- 2005
DAAC(1, Data, plot=TRUE)

Data <- MSEtool::Atlantic_mackerel
Data@LHYear <- 2005
HDAAC(1, Data, plot=TRUE)

---

Delay - Difference Stock Assessment

Description

A simple delay-difference assessment with UMSY and MSY as leading parameters that estimates the TAC using a time-series of catches and a relative

Usage

DD(x, Data, reps = 100, plot = FALSE)

DD4010(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

This DD model is observation error only and has does not estimate process error (recruitment deviations). Assumption is that knife-edge selectivity occurs at the age of 50% maturity. Similar to many other assessment models it depends on a whole host of dubious assumptions such as temporally stationary productivity and proportionality between the abundance index and real abundance. Unsurprisingly the extent to which these assumptions are violated tends to be the biggest driver of performance for this method.

The method is conditioned on effort and estimates catch. The effort is calculated as the ratio of catch and index. Thus, to get a complete effort time series, a full time series of catch and index is also needed. Missing values are linearly interpolated.

A detailed description of the delay-difference model can be found in Chapter 9 of Hilborn and Walters (1992).

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• DD: Base version where the TAC = UMSY * Current Biomass.

• DD4010: A 40-10 rule is imposed over the TAC recommendation.

Required Data

See Data-class for information on the Data object

DD: Cat, Ind, L50, MaxAge, Mort, vbK, vbLinf, vbt0, wla, wlb

DD4010: Cat, Ind, L50, MaxAge, Mort, vbK, vbLinf, vbt0, wla, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers, T, Walters, C.J,, and McAllister, M.K. 2012. Evaluating methods that classify fisheries stock status using only fisheries catch data. Fisheries Research 119-120:66-79.

Hilborn, R., and Walters, C. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York.

See Also

Other Delay-Difference MPs: DDe()

Examples

DD(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
DD4010(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Effort-based Delay - Difference Stock Assessment

Description

A simple delay-difference assessment with UMSY and MSY as leading parameters that estimates $E_{\textrm{MSY}}$ using a time-series of catches and a relative abundance index.

Usage

DDe(x, Data, reps = 100, plot = FALSE)

DDes(x, Data, reps = 100, plot = FALSE, LB = 0.9, UB = 1.1)

DDe75(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
LB	The lowest permitted factor of previous fishing effort
UB	The highest permitted factor of previous fishing effort

Details

This DD model is observation error only and has does not estimate process error (recruitment deviations). Assumption is that knife-edge selectivity occurs at the age of 50% maturity. Similar to many other assessment models it depends on a whole host of dubious assumptions such as temporally stationary productivity and proportionality between the abundance index and real abundance. Unsurprisingly the extent to which these assumptions are violated tends to be the biggest driver of performance for this method.

The method is conditioned on effort and estimates catch. The effort is calculated as the ratio of catch and index. Thus, to get a complete effort time series, a full time series of catch and index is also needed. Missing values are linearly interpolated.

A detailed description of the delay-difference model can be found in Chapter 9 of Hilborn and Walters (1992).

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• DDe: Effort-control version. The recommended effort is EMSY.

• DDes: Variant of DDe that limits the maximum change in effort to 10 percent.

• DDe75: Variant of DDe where the recommended effort is 75\

Required Data

See Data-class for information on the Data object

DDe: Cat, Ind, L50, MPeff, MaxAge, Mort, vbK, vbLinf, vbt0, wla, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

See Also

Other Delay-Difference MPs: DD()

Examples

DDe(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
DDes(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
DDe75(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Effort searching MP aiming for a fixed stock depletion

Description

Effort is adjusted using a simple rule that aims for a specified level of depletion.

Usage

DTe40(x, Data, reps = 100, plot = FALSE, alpha = 0.4, LB = 0.9, UB = 1.1)

DTe50(x, Data, reps = 100, plot = FALSE, alpha = 0.5, LB = 0.9, UB = 1.1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
alpha	The target level of depletion
LB	The lowest permitted factor of previous fishing effort
UB	The highest permitted factor of previous fishing effort

Details

The TAE is calculated as:

$\textrm{TAE}_y = \frac{D}{\alpha} \textrm{TAE}_{y-1}$

where $D$ is estimated current level of depletion and $\alpha$ is argument alpha specifying the target level of depletion.

The maximum fractional change in TAE is specified with arguments LB and UB

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• DTe40: Effort is adjusted to reach 40 percent stock depletion

• DTe50: Effort is adjusted to reach 50 percent stock depletion

Required Data

See Data-class for information on the Data object

DTe40: Dep, MPeff

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

Examples

DTe40(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Dynamic Fratio MP

Description

The Fratio MP with a controller that changes the level of F according to the estimated relationship between surplus production and biomass. Ie lower F when dSP/dB is positive and higher F when dSP/dB is negative.

Usage

DynF(x, Data, reps = 100, plot = FALSE, yrsmth = 10, gg = 2)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	The number of historical recent years used for smoothing catch and biomass data
gg	A gain parameter that modifies F according to the gradient in surplus production with biomass

Details

The method smoothes historical catches and biomass and then infers the relationship between surplus production and biomass (as suggested by Mark Maunder and Carl Walters). The approach then regulates a F based policy according to this gradient in which F may range between two different fractions of natural mortality rate.

The core advantage is the TAC(t) is not strongly determined by TAC(t-1) and therefore errors are not as readily propagated. The result is method that tends to perform alarmingly well and therefore requires debunking ASAP.

The catch limit (TAC) is calculated as:

$\textrm{TAC}=F B$

where $F$ is fishing mortality and $B$ is the estimated current biomass.

$F$ is calculated as:

$F = F_{\textrm{MSY}} \exp{-gG}$

where $F_{\textrm{MSY}}$ is calculated from assumed values of $\frac{F_{\textrm{MSY}}}{M}$ and $M$, g is a gain parameter and G is the estimated gradient in surplus production (SP) as a function of biomass (B). Surplus production for year y is calculated as:

$SP_y = B_{y+1} - B_y + C_y$

Trends in historical catch (C) and biomass (B) are both estimated using a loess smoother, over the last yrsmth years, of available catch and a time-series of abundance, calculated from an index of abundance (Data@Ind) and an estimate of abundance (Data@Abun) for the current year.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

DynF: Abun, Cat, FMSY_M, Ind, Mort, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Made-up for this package.

See Also

Other Fmsy/M methods: Fadapt(), Fratio()

Examples

DynF(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Effort Target Optimum Length

Description

This MP adjusts effort limit based on the ratio of recent mean length (over last yrsmth years) and a target length defined as $L_{\textrm{opt}}$. Effort MP: adjust effort up/down if mean length above/below Ltarget

Usage

EtargetLopt(x, Data, reps = 100, plot = FALSE, yrsmth = 3, buffer = 0.1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Number of years to calculate average length
buffer	Parameter controlling the fraction of calculated effor - acts as a precautionary buffer

Details

The TAE is calculated as:

$\textrm{TAE}_y = \textrm{TAE}_{y-1} \left((1-\textrm{buffer}) (w + (1-w)r) \right)$

where $\textrm{buffer}$ is specified in argument buffer, $w$ is fixed at 0.5, and:

$r = \frac{L_{\textrm{recent}}}{L_{\textrm{opt}}}$

where $L_{\textrm{recent}}$is mean length over last yrmsth years, and:

$L_{\textrm{opt}} = \frac{L_\infty W_b}{\frac{M}{K} + W_b }$

where $L_\infty$ is von Bertalanffy asymptotic length, $W_b$ is exponent of the length-weight relationship, $M$ is natural mortality, and $K$ is von Bertalanffy growth coefficient.#'

Value

An object of class Rec-class with the TAE slot(s) populated

Required Data

See Data-class for information on the Data object

EtargetLopt: ML, MPeff, Mort, Year, vbK, vbLinf, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

HF Geromont

Examples

EtargetLopt(1, MSEtool::SimulatedData, plot=TRUE)

---

Adaptive Fratio

Description

An adaptive MP that uses trajectory in inferred suplus production and fishing mortality rate to update a TAC

Usage

Fadapt(x, Data, reps = 100, plot = FALSE, yrsmth = 7, gg = 1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to smooth recent estimates of surplus production
gg	A gain parameter controlling the speed in update in TAC.

Details

Fishing rate is modified each year according to the gradient of surplus production with biomass (aims for zero). F is bounded by FMSY/2 and 2FMSY and walks in the logit space according to dSP/dB. This is derived from the theory of Maunder 2014.

The TAC is calculated as:

$\textrm{TAC}_y= F_y B_{y-1}$

where $B_{y-1}$ is the most recent biomass, estimated with a loess smoother of the most recent yrsmth years from the index of abundance (Data@Ind) and estimate of current abundance (Data@Abun), and

$F_y = F_{\textrm{lim}_1} + \left(\frac{\exp^{F_{\textrm{mod}_2}}} {1 + \exp^{F_{\textrm{mod}_2}}} F_{\textrm{lim}_3} \right)$

where $F_{\textrm{lim}_1} = 0.5 \frac{F_\textrm{MSY}}{M}M$, $F_{\textrm{lim}_2} = 2 \frac{F_\textrm{MSY}}{M}M$, $F_{\textrm{lim}_3}$ is $F_{\textrm{lim}_2} - F_{\textrm{lim}_1}$, $F_{\textrm{mod}_2}$ is

$F_{\textrm{mod}_1} + g -G$

where $g$ is gain parameter gg, G is the predicted surplus production given current abundance, and:

$F_{\textrm{mod}_1} = \left\{\begin{array}{ll} -2 & \textrm{if } F_\textrm{old} < F_{\textrm{lim}_1} \\ 2 & \textrm{if } F_\textrm{old} > F_{\textrm{lim}_2} \\ \log{\frac{F_\textrm{frac}}{1-F_\textrm{frac}}} & \textrm{if } F_{\textrm{lim}_1} \leq F_\textrm{old} \leq F_{\textrm{lim}_2} \\ \end{array}\right.$

where $-F_{\textrm{frac}} = \frac{F_{\textrm{old}} - F_{\textrm{lim}_1}}{F_{\textrm{lim}_3}}$, $F_\textrm{old} = \sum{\frac{C_\textrm{hist}}{B_\textrm{hist}}}/n$ where $C_\textrm{hist}$ and $B_\textrm{hist}$ are smooth catch and biomass over last yrsmth, and $n$ is yrsmth.

Tested in Carruthers et al. 2015.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

A numeric vector of quota recommendations

Required Data

See Data-class for information on the Data object

Fadapt: Abun, Cat, FMSY_M, Ind, Mort, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Maunder, M. 2014. http://www.iattc.org/Meetings/Meetings2014/MAYSAC/PDFs/SAC-05-10b-Management-Strategy-Evaluation.pdf

See Also

Other Fmsy/M methods: DynF(), Fratio()

Other Surplus production MPs: Rcontrol(), SPMSY(), SPSRA(), SPmod(), SPslope()

Examples

Fadapt(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Demographic FMSY method

Description

FMSY is calculated as r/2 where r is calculated from a demographic approach (inc steepness). Coupled with an estimate of current abundance that gives you the OFL.

Usage

Fdem(x, Data, reps = 100, plot = FALSE)

Fdem_CC(x, Data, reps = 100, plot = FALSE, Fmin = 0.005)

Fdem_ML(x, Data, reps = 100, plot = FALSE, Fmin = 0.005)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
Fmin	The minimum fishing mortality rate derived from the catch-curve analysis

Details

The TAC is calculated as:

$\textrm{TAC} = F_{\textrm{MSY}} A$

where A is an estimate of current abundance, and $F_{\textrm{MSY}}$ is estimated as $r/2$, where $r$ is the intrinsic rate of population growth, estimated from the life-history parameters using the methods of McAllister et al. (2001).

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Fdem: Current abundance is assumed to be known (i.e Data@Abun)

• Fdem_CC: Current abundance is estimated from catch curve analysis

• Fdem_ML: Current abundance is estimated from mean length

Required Data

See Data-class for information on the Data object

Fdem: Abun, FMSY_M, L50, MaxAge, Mort, steep, vbK, vbLinf, vbt0, wla, wlb

Fdem_CC: CAA, Cat, FMSY_M, L50, MaxAge, Mort, steep, vbK, vbLinf, vbt0, wla, wlb

Fdem_ML: CAL, Cat, FMSY_M, L50, Lbar, Lc, MaxAge, Mort, steep, vbK, vbLinf, vbt0, wla, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

McAllister, M.K., Pikitch, E.K., and Babcock, E.A. 2001. Using demographic methods to construct Bayesian priors for the intrinsic rate of increase in the Schaefer model and implications for stock rebuilding. Can. J. Fish. Aquat. Sci. 58: 1871-1890.

Examples

Fdem(1, MSEtool::SimulatedData, plot=TRUE)
Fdem_CC(1, MSEtool::SimulatedData, plot=TRUE)
Fdem_ML(1, MSEtool::SimulatedData, plot=TRUE)

---

FMSY/M ratio methods

Description

Calculates the OFL based on a fixed ratio of FMSY to M multiplied by a current estimate of abundance.

Usage

Fratio(x, Data, reps = 100, plot = FALSE)

Fratio4010(x, Data, reps = 100, plot = FALSE)

DepF(x, Data, reps = 100, plot = FALSE)

Fratio_CC(x, Data, reps = 100, plot = FALSE, Fmin = 0.005)

Fratio_ML(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
Fmin	Minimum current fishing mortality rate for the catch-curve analysis

Details

A simple method that tends to outperform many other approaches alarmingly often even when current biomass is relatively poorly known. The low stock crash potential is largely due to the quite large difference between Fmax and FMSY for most stocks.

The TAC is calculated as:

$\textrm{TAC} = F_{\textrm{MSY}} A$

where $F_{\textrm{MSY}}$ is calculated as $\frac{F_\textrm{MSY}}{M} M$ and A is estimate of current abundance.

The MP variants differ in the assumption of current abundance (see Functions section below)

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Fratio: Requires an estimate of current abundance (i.e Data@Abun)

• Fratio4010: Paired with the 40-10 rule that throttles back the OFL to zero at 10 percent of unfished biomass. Requires an estimate of current depletion.

• DepF: Depletion Corrected Fratio: the Fratio MP with a harvest control rule that reduces F according to the production curve given an estimate of current stock depletion (made-up for this package).

• Fratio_CC: Current abundance is estimated using average catch and estimate of F from an age-based catch curve

• Fratio_ML: Current abundance is estimated using average catch and estimate of F from mean lengths

Required Data

See Data-class for information on the Data object

Fratio: Abun, FMSY_M, Mort

Fratio4010: Abun, Dep, FMSY_M, Mort

DepF: Abun, Dep, FMSY_M, Mort

Fratio_CC: CAA, Cat, FMSY_M, Mort

Fratio_ML: CAL, Cat, FMSY_M, Lbar, Lc, Mort, vbK, vbLinf

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Gulland, J.A., 1971. The fish resources of the ocean. Fishing News Books, West Byfleet, UK.

Martell, S., Froese, R., 2012. A simple method for estimating MSY from catch and resilience. Fish Fish. doi: 10.1111/j.1467-2979.2012.00485.x.

See Also

Other Fmsy/M methods: DynF(), Fadapt()

Examples

Fratio(1, MSEtool::Atlantic_mackerel, plot=TRUE)
Fratio4010(1, MSEtool::Atlantic_mackerel, plot=TRUE)
Fratio_CC(1, MSEtool::SimulatedData, plot=TRUE)
Fratio_ML(1, MSEtool::SimulatedData, plot=TRUE)

---

Geromont and Butterworth Constant Catch Harvest Control Rule

Description

A simple MP that aims for a reference catch (as a proxy for MSY) subject to imperfect information.

Usage

GB_CC(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

Note that this is my interpretation of their MP and is now stochastic. Currently it is generalized and is not 'tuned' to more detailed assessment data which might explain why in some cases it leads to stock declines.

The TAC is calculated as:

$\textrm{TAC} = C_\textrm{ref}$

where $C_\textrm{ref}$ is a reference catch assumed to be a proxy for MSY. In the MSE $C_\textrm{ref}$ is the calculated MSY subject to observation error defined in Obs@CV_Cref.

The TAC is subject to the following conditions:

1. if next TAC > 1.2 last catch, then TAC = 1.2 last catch

2. if next TAC < 0.8 last catch, then TAC = 0.8 last catch

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

GB_CC: Cref

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Geromont, H.F. and Butterworth, D.S. 2014. Complex assessment or simple management procedures for efficient fisheries management: a comparative study. ICES J. Mar. Sci. doi:10.1093/icesjms/fsu017

See Also

Other Constant Catch MPs: CC1()

Examples

GB_CC(1, MSEtool::SimulatedData, plot=TRUE)

---

Geromont and Butterworth index slope Harvest Control Rule

Description

An MP similar to SBT1 that modifies a time-series of catch recommendations and aims for a stable catch rates.

Usage

GB_slope(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Number of years for evaluating slope in relative abundance index
lambda	A gain parameter

Details

The TAC is calculated as:

$\textrm{TAC}_y= C_{y-1} \left(1+\lambda I\right)$

where $C_{y-1}$ is catch from the previous year, $\lambda$ is a gain parameter, and $I$ is the slope of the linear regression of log Index (Data@Ind) over the last yrsmth years.

The TAC is subject to the following conditions:

1. if next TAC > 1.2 last catch, then TAC = 1.2 last catch

2. if next TAC < 0.8 last catch, then TAC = 0.8 last catch

Note that this is my interpretation of their approach and is now stochastic. Currently it is generalized and is not 'tuned' to more detailed assessment data which might explain why in some cases it leads to stock declines.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

GB_slope: Cat, Ind, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Geromont, H.F. and Butterworth, D.S. 2014. Complex assessment or simple management procedures for efficient fisheries management: a comparative study. ICES J. Mar. Sci. doi:10.1093/icesjms/fsu017

See Also

Other Index methods: GB_target(), Gcontrol(), ICI(), Iratio(), Islope1(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

GB_slope(1, MSEtool::SimulatedData, plot=TRUE)

---

Geromont and Butterworth target CPUE and catch MP

Description

An MP similar to SBT2 that modifies a time-series of catch recommendations and aims for target catch rate and catch level based on BMSY/B0 and MSY, respectively.

Usage

GB_target(x, Data, reps = 100, plot = FALSE, w = 0.5)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
w	A gain parameter

Details

The TAC is calculated as: If $I_\textrm{recent} \geq I_0$:

$\textrm{TAC}= C_\textrm{ref} \left(w + (1-w)\frac{I_\textrm{rec}-I_0}{I_\textrm{target}-I_0} \right)$

else:

$\textrm{TAC}= wC_\textrm{ref} \frac{I_\textrm{rec}}{I_0}^2$

where $C_\textrm{ref}$ is a reference catch assumed to be a proxy for MSY (Data@Cref), w is a gain parameter, $I_\textrm{rec}$ is the average index over the last 4 years, $I_\textrm{target}$ is the target Index (Data@Iref), and $I_0$ is 0.2 x the average index over the past 5 years.

In the MSE $C_\textrm{ref}$ is the calculated MSY subject to observation error defined in Obs@CV_Cref, and $I_\textrm{target}$ is assumed to be the index at MSY subject to observation error (Obs@CV_Iref). Consequently, the performance of this method in the MSE is strongly determined by the specified uncertainty for these parameters.

The TAC is subject to the following conditions:

1. if next TAC > 1.2 last catch, then TAC = 1.2 last catch

2. if next TAC < 0.8 last catch, then TAC = 0.8 last catch

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

GB_target: Cref, Ind, Iref

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Geromont, H.F. and Butterworth, D.S. 2014. Complex assessment or simple management procedures for efficient fisheries management: a comparative study. ICES J. Mar. Sci. doi:10.1093/icesjms/fsu017

See Also

Other Index methods: GB_slope(), Gcontrol(), ICI(), Iratio(), Islope1(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

GB_target(1, MSEtool::SimulatedData, plot=TRUE)

---

G-control MP

Description

A harvest control rule proposed by Carl Walters that uses trajectory in inferred surplus production to make upward/downward adjustments to TAC recommendations

Usage

Gcontrol(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 10,
  gg = 2,
  glim = c(0.5, 2)
)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	The number of years over which to smooth catch and biomass data
gg	A gain parameter
glim	A constraint limiting the maximum level of change in quota recommendations

Details

The TAC is calculated as:

$\textrm{TAC} = \textrm{SP} \left(1-gG\right)$

where $\textrm{SP}$ is the predicted surplus production for the next year, g is a gain parameter, and G is the slope of surplus production as a function of biomass over the last yrsmth years.

The change in TAC is bounded by the glim argument, which by default does not allow the TAC to decrease by more than half or increase more than twice the last annual catch.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

Gcontrol: Abun, Cat, Ind, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

C. Walters and T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

See Also

Other Index methods: GB_slope(), GB_target(), ICI(), Iratio(), Islope1(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

Gcontrol(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Index Confidence Interval

Description

The MP adjusts catch based on the value of the index in the current year relative to the time series mean and standard error.

Usage

ICI(x, Data, reps = 100, plot = FALSE)

ICI2(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

The TAC is calculated as:

$\textrm{TAC}_y=C_{y-1} \alpha$

where $C_{y-1}$ is the catch from the previous year, and $\alpha$ is defined as:

$\alpha = \left\{\begin{array}{ll} d & \textrm{if } I < \textrm{CI}_L \\ u & \textrm{if } I > \textrm{CI}_H \\ 1 & \textrm{if } \textrm{CI}_L \leq I \leq \textrm{CI}_H \\ \end{array}\right.$

where $I$ is the index in the most recent year, $d$ is 0.75 for ICI and ICI2, $u$ is 1.05 and 1.25 forICI and ICI2 respectively, and $\textrm{CI}_L$ and $\textrm{CI}_L$ are the lower and upper bound of the confidence interval of mean historical index. The confidence interval is calculated using Z-scores described in the Functions section below.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• ICI: The catch is reduced by 0.75 if the Z-score of the current year's index is less than -0.44. The catch is increased by 1.05 if the Z-score of the current year's index is greater than 1.96. Otherwise, the catch is held constant.

• ICI2: This method is less precautionary of the two ICI MPs by allowing for a larger increase in TAC and a lower threshold of the index to decrease the TAC. The catch is reduced by 0.75 if the Z-score of the current year's index is less than -1.96. The catch is increased by 1.25 if the Z-score of the current year's index is greater than 1.96. Otherwise, the catch is held constant.

Required Data

See Data-class for information on the Data object

ICI: Cat, Ind

ICI2: Cat, Ind

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

Coded by Q. Huynh. Developed by Jardim et al. (2015)

References

Ernesto Jardim, Manuela Azevedo, Nuno M. Brites, Harvest control rules for data limited stocks using length-based reference points and survey biomass indices, Fisheries Research, Volume 171, November 2015, Pages 12-19, ISSN 0165-7836, https://doi.org/10.1016/j.fishres.2014.11.013

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), Iratio(), Islope1(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

ICI(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

ICI2(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)

---

Mean Index Ratio

Description

The TAC is adjusted by the ratio alpha, where the numerator being the mean index in the most recent two years of the time series and the denominator being the mean index in the three years prior to those in the numerator. This MP is the stochastic version of Method 3.2 used by ICES for Data-Limited Stocks (ICES 2012).

Usage

Iratio(x, Data, reps = 100, plot = FALSE, yrs = c(2, 5))

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrs	Vector of length 2 specifying the reference years

Details

The TAC is calculated as:

$\textrm{TAC}_y = \alpha C_{y-1}$

where $C_{y-1}$ is the catch from the previous year, and $\alpha$ is the ratio of the mean index in the most recent two years of the time series and the mean index in 3-5 years before current time (reference years are specified as yrs argument.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

Iratio: Cat, Ind

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

Coded by Q. Huynh. Developed by Jardim et al. (2015)

References

Ernesto Jardim, Manuela Azevedo, Nuno M. Brites, Harvest control rules for data limited stocks using length-based reference points and survey biomass indices, Fisheries Research, Volume 171, November 2015, Pages 12-19, ISSN 0165-7836, https://doi.org/10.1016/j.fishres.2014.11.013

ICES. 2012. ICES Implementation of Advice for Data-limited Stocks in 2012 in its 2012 Advice. ICES CM 2012/ACOM 68. 42 pp.

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), ICI(), Islope1(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

Iratio(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Index Slope Tracking MP

Description

A management procedure that incrementally adjusts the TAC to maintain a constant CPUE or relative abundance index.

Usage

Islope1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.2)

Islope2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.3)

Islope3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.4)

Islope4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.2, xx = 0.4)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate index
lambda	A gain parameter controlling the speed in update in TAC.
xx	Parameter controlling the fraction of mean catch to start using in first year

Details

The TAC is calculated as:

$\textrm{TAC} = \textrm{TAC}^* \left(1+\lambda I \right)$

where $\textrm{TAC}^*$ is $1-xx$ multiplied by the mean catch from the past yrsmth years for the first year and catch from the previous year in projection years, $\lambda$ is a gain parameter, and $I$ is the slope of log index over the past yrsmth years.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Islope1: The least biologically precautionary of the Islope methods

• Islope2: More biologically precautionary. Reference TAC is 0.7 average catch

• Islope3: More biologically precautionary. Reference TAC is 0.6 average catch

• Islope4: The most biologically precautionary of the Islope methods. Reference TAC is 0.6 average catch and gain parameter is 0.2

Required Data

See Data-class for information on the Data object

Islope1: Cat, Ind, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), ICI(), Iratio(), Itarget1_MPA(), Itarget1(), ItargetE1()

Examples

Islope1(1, MSEtool::SimulatedData, plot=TRUE)
Islope2(1, MSEtool::SimulatedData, plot=TRUE)
Islope3(1, MSEtool::SimulatedData, plot=TRUE)
Islope4(1, MSEtool::SimulatedData, plot=TRUE)

---

Iterative Index Target MP

Description

An index target MP where the TAC is modified according to current index levels (mean index over last 5 years) relative to a target level.

Usage

IT5(x, Data, reps = 100, plot = FALSE, yrsmth = 5, mc = 0.05)

IT10(x, Data, reps = 100, plot = FALSE, yrsmth = 5, mc = 0.1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	The number of historical years over which to average the index
mc	The maximum fractional change in the TAC among years.

Details

The TAC is calculated as:

$\textrm{TAC}_y = C_{y-1} I_\delta$

where $C_{y-1}$ is the catch from the previous year and $I_\delta$ is the ratio of the mean index over the past yrsmth years to a reference index level. The maximum allowable change in TAC is determined by mc: e.g mc=0.05 means that the maximum change in TAC from the previous catch is 5%.

The reference index level (Data@Iref) is assumed to be a proxy for MSY. In the MSE Iref is the index at MSY subject to observation error (Obs@Irefbiascv). Consequently the performance of these methods in MSE is strongly determined by the uncertainty the in reference index.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• IT5: Maximum annual changes in TAC are 5 per cent.

• IT10: Maximum annual changes are 10 per cent.

Required Data

See Data-class for information on the Data object

IT5: Ind, Iref, MPrec

IT10: Ind, Iref, MPrec

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

Examples

IT5(1, MSEtool::SimulatedData, plot=TRUE)
IT10(1, MSEtool::SimulatedData, plot=TRUE)

---

Incremental Index Target MP

Description

A management procedure that incrementally adjusts the TAC (starting from reference level that is a fraction of mean recent catches) to reach a target CPUE / relative abundance index

Usage

Itarget1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, Imulti = 1.5)

Itarget2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, Imulti = 2)

Itarget3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, Imulti = 2.5)

Itarget4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.3, Imulti = 2.5)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which the average index is calculated.
xx	Parameter controlling the fraction of mean catch to start using in first year
Imulti	Parameter controlling how much larger target CPUE / index is compared with recent levels.

Details

Four index/CPUE target MPs proposed by Geromont and Butterworth 2014. Tested by Carruthers et al. 2015.

The TAC is calculated as: If $I_\textrm{recent} \geq I_0$:

$\textrm{TAC}= 0.5 \textrm{TAC}^* \left[1+\left(\frac{I_\textrm{recent} - I_0}{I_\textrm{target} - I_0}\right)\right]$

else:

$\textrm{TAC}= 0.5 \textrm{TAC}^* \left[\frac{I_\textrm{recent}}{I_0}^2\right]$

where $I_0$ is $0.8 I_{\textrm{ave}}$ (the average index over the 2 x yrsmth years prior to the projection period), $I_\textrm{recent}$ is the average index over the past yrsmth years, and $I_\textrm{target}$ is Imulti times $I_{\textrm{ave}}$, and $\textrm{TAC}^*$ is:

$(1-x)C$

where $x$ is argument xx and C is the average catch over the last 5 years of the historical period.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Itarget1: The less precautionary TAC-based MP

• Itarget2: Increasing biologically precautionary TAC-based MP

• Itarget3: Increasing biologically precautionary TAC-based MP

• Itarget4: The most biologically precautionary TAC-based MP

Required Data

See Data-class for information on the Data object

Itarget1: Cat, Ind, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. 72, 251-261. doi:10.1093/icesjms/fst232

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), ICI(), Iratio(), Islope1(), Itarget1_MPA(), ItargetE1()

Examples

Itarget1(1, MSEtool::Atlantic_mackerel, plot=TRUE)
Itarget2(1, MSEtool::Atlantic_mackerel, plot=TRUE)
Itarget3(1, MSEtool::Atlantic_mackerel, plot=TRUE)
Itarget4(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Itarget1 with an MPA

Description

A example mixed control MP that uses the Itarget1 output control MP together with a spatial closure.

Usage

Itarget1_MPA(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  xx = 0,
  Imulti = 1.5
)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to smooth recent estimates of surplus production
xx	Parameter controlling the fraction of mean catch to start using in first year
Imulti	Parameter controlling how much larger target CPUE / index is compared with recent levels.

Details

The TAC is calculated as: If $I_\textrm{recent} \geq I_0$:

$\textrm{TAC}= 0.5 \textrm{TAC}^* \left[1+\left(\frac{I_\textrm{recent} - I_0}{I_\textrm{target} - I_0}\right)\right]$

else:

$\textrm{TAC}= 0.5 \textrm{TAC}^* \left[\frac{I_\textrm{recent}}{I_0}^2\right]$

where $I_0$ is $0.8 I_{\textrm{ave}}$ (the average index over the 2 x yrsmth years prior to the projection period), $I_\textrm{recent}$ is the average index over the past yrsmth years, and $I_\textrm{target}$ is Imulti times $I_{\textrm{ave}}$, and $\textrm{TAC}^*$ is:

$(1-x)C$

where $x$ is argument xx and C is the average catch over the last 5 years of the historical period.

This mixed control MP also closes Area 1 to fishing.

This MP has been included for demonstration purposes of a mixed control MP.

Value

An object of class Rec-class with the TAC, Spatial slot(s) populated

Required Data

See Data-class for information on the Data object

Itarget1_MPA: Cat, Ind, LHYear, Year

Rendered Equations

See Online Documentation for correctly rendered equations

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), ICI(), Iratio(), Islope1(), Itarget1(), ItargetE1()

Examples

Itarget1_MPA(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Incremental Index Target MP - Effort-Based

Description

A management procedure that incrementally adjusts the fishing effort to reach a target CPUE / relative abundance index

Usage

ItargetE1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, Imulti = 1.5)

ItargetE2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, Imulti = 2)

ItargetE3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, Imulti = 2.5)

ItargetE4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, Imulti = 2.5)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which the average index is calculated.
Imulti	Parameter controlling how much larger target CPUE / index is compared with recent levels.

Details

Four index/CPUE target MPs proposed by Geromont and Butterworth 2014.

The TAE is calculated as: If $I_\textrm{recent} \geq I_0$:

$\textrm{TAE}_y = 0.5 \textrm{TAE}_{y-1} \left[1+ \left( \frac{I_{\textrm{recent}} - I_0}{I_{\textrm{target}} - I_0} \right)\right]$

else:

$\textrm{TAE}_y= 0.5 \textrm{TAE}_{y-1} \left( \frac{I_{\textrm{recent}}}{I_0}^2 \right)$

where $I_0$ is $0.8 I_{\textrm{ave}}$ (the average index over the 2 x yrsmth years prior to the projection period), $I_\textrm{recent}$ is the average index over the past yrsmth years, and $I_\textrm{target}$ is Imulti times $I_{\textrm{ave}}$.

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• ItargetE1: The less precautionary TAE-based MP

• ItargetE2: Increasing biologically precautionary TAE-based MP

• ItargetE3: Increasing biologically precautionary TAE-based MP

• ItargetE4: The most biologically precautionary TAE-based MP

Required Data

See Data-class for information on the Data object

ItargetE1: Ind, LHYear, MPeff, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. 72, 251-261. doi:10.1093/icesjms/fst232

See Also

Other Index methods: GB_slope(), GB_target(), Gcontrol(), ICI(), Iratio(), Islope1(), Itarget1_MPA(), Itarget1()

Examples

ItargetE1(1, MSEtool::Atlantic_mackerel, plot=TRUE)
ItargetE2(1, MSEtool::Atlantic_mackerel, plot=TRUE)
ItargetE3(1, MSEtool::Atlantic_mackerel, plot=TRUE)
ItargetE4(1, MSEtool::Atlantic_mackerel, plot=TRUE)

---

Index Target Effort-Based

Description

An index target MP where the Effort is modified according to current index levels (mean index over last 5 years) relative to a target level.

Usage

ITe5(x, Data, reps = 100, plot = FALSE, yrsmth = 5, mc = 0.05)

ITe10(x, Data, reps = 100, plot = FALSE, yrsmth = 5, mc = 0.1)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	The number of historical years over which to average the index
mc	The maximum fractional change in the effort among years.

Details

The TAE is calculated as:

$\textrm{TAE}_y = \textrm{TAE}_{y-1} \delta$

where $\delta$ is $\frac{I} {I_{\textrm{ref}}}$ averaged over last yrsmth years. $I_{\textrm{ref}}$ is the index target (Data@Iref).

The maximum fractional change in TAE is specified in mc.

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• ITe5: Maximum annual changes are 5 per cent.

• ITe10: Maximum annual changes are 10 per cent.

Required Data

See Data-class for information on the Data object

ITe5: Ind, Iref, MPeff

ITe10: Ind, Iref, MPeff

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

Examples

ITe5(1, MSEtool::SimulatedData, plot=TRUE)
ITe10(1, MSEtool::SimulatedData, plot=TRUE)

---

Index Target based on natural mortality rate

Description

An index target MP where the TAC is modified according to current index levels (mean index over last number of years determined by natural mortality (M)) relative to a target level.

Usage

ITM(x, Data, reps = 100, plot = FALSE)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?

Details

The TAC is caluclated as:

$\textrm{TAC}_y = \textrm{TAC}_{y-1} \delta I$

where $\delta I$ is the ratio of the mean index over $4\frac{1}{M}^{1/4}$ years to the reference index (Data@Iref).

The maximum fractional change in TAC is determined by $mc$, defined as $mc = \textrm{max}\left(\frac{5 + 25M}{100}, 0.2\right)$

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Required Data

See Data-class for information on the Data object

ITM: Ind, Iref, MPrec, Mort

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

Examples

ITM(1, Data=MSEtool::SimulatedData, plot=TRUE)

---

Length-Based SPR MPs

Description

The spawning potential ratio (SPR) is estimated using the LBSPR method and compared to a target of 0.4.

Usage

LBSPR(
  x,
  Data,
  reps = 1,
  plot = FALSE,
  SPRtarg = 0.4,
  theta1 = 0.3,
  theta2 = 0.05,
  maxchange = 0.3,
  n = 5,
  smoother = TRUE,
  R = 0.2
)

LBSPR_MLL(
  x,
  Data,
  reps = 1,
  plot = FALSE,
  SPRtarg = 0.4,
  n = 5,
  smoother = TRUE,
  R = 0.2
)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
SPRtarg	The target SPR
theta1	Control parameter for the harvest control rule
theta2	Control parameter for the harvest control rule
maxchange	Maximum change in effort
n	Last number of years to run the model on.
smoother	Logical. Should the SPR estimates be smoothed?
R	variance of sampling noise for smoother

Details

Effort is modified according to the harvest control rules described in Hordyk et al. (2015b):

Value

An object of class Rec-class with the TAE slot populated

Functions

• LBSPR_MLL: Fishing retention-at-length is set equivalent to slightly higher than the maturity curve if SPR < 0.4

Required Data

See Data-class for information on the Data object

LBSPR: CAL, CAL_bins, L50, L95, LHYear, MPeff, Mort, Year, vbK, vbLinf, wlb

Rendered Equations

See Online Documentation for correctly rendered equations

References

Hordyk, A., Ono, K., Valencia, S., Loneragan, N., and Prince J (2015a). A novel length-based empirical estimation method of spawning potential ratio (SPR), and tests of its performance, for small-scale, data-poor fisheries, ICES Journal of Marine Science, 72 (1), 217-231

Hordyk, A. R., Loneragan, N. R., & Prince, J. D. (2015b). An evaluation of an iterative harvest strategy for data-poor fisheries using the length-based spawning potential ratio assessment methodology. Fisheries Research, 171, 20-32. https://doi.org/10.1016/j.fishres.2014.12.018

Examples

LBSPR(1, Data=MSEtool::SimulatedData, plot=TRUE)
LBSPR_MLL(1, Data=MSEtool::SimulatedData, plot=FALSE)

---

Mean length-based indicator MP of Jardim et al. 2015

Description

The TAC is calculated as the most recent catch, modified by the ratio alpha, where the numerator is the mean length of the catch (of lengths larger than Lc) and the denominator is the mean length expected at MSY. Here, Lc is the length at full selection (LFS).

Usage

Lratio_BHI(x, Data, reps = 100, plot = FALSE, yrsmth = 3)

Lratio_BHI2(x, Data, reps = 100, plot = FALSE, yrsmth = 3)

Lratio_BHI3(x, Data, reps = 100, plot = FALSE, yrsmth = 3)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	The most recent years of data to smooth the calculation of the mean length

Details

The TAC is calculated as:

$\textrm{TAC}_y = C_{y-1} \frac{L}{L_\textrm{ref}}$

where $C_{y-1}$ is the catch from the previous year, $L$ is the mean length of the catch over the last yrsmth years (of lengths larger than Lc) and $L_\textrm{ref}$ is the mean length expected at MSY. Here, Lc is the length at full selection (LFS).

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Lratio_BHI: Assumes M/K = 1.5 and FMSY/M = 1. Natural mortality M and von Bertalanffy K are not used in this MP (see Appendix A of Jardim et al. 2015).

• Lratio_BHI2: More general version that calculates the reference mean length as a function of M, K, and presumed FMSY/M.

• Lratio_BHI3: A modified version of Lratio_BHI2 where mean length is calculated for lengths > modal length (Lc)

Required Data

See Data-class for information on the Data object

Lratio_BHI: CAL, CAL_bins, Cat, LFS, vbLinf

Lratio_BHI2: CAL, CAL_bins, Cat, FMSY_M, LFS, Mort, vbK, vbLinf

Lratio_BHI3: CAL, CAL_bins, Cat, FMSY_M, LFS, Mort, vbK, vbLinf

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

Coded by Q. Huynh. Developed by Jardim et al. (2015)

References

Ernesto Jardim, Manuela Azevedo, Nuno M. Brites, Harvest control rules for data limited stocks using length-based reference points and survey biomass indices, Fisheries Research, Volume 171, November 2015, Pages 12-19, ISSN 0165-7836, https://doi.org/10.1016/j.fishres.2014.11.013

See Also

Other Length target MPs: Ltarget1(), LtargetE1()

Examples

Lratio_BHI(1, Data=MSEtool::SimulatedData, plot=TRUE)

Lratio_BHI2(1, Data=MSEtool::SimulatedData, plot=TRUE)

Lratio_BHI3(1, Data=MSEtool::SimulatedData, plot=TRUE)

---

Step-wise Constant Catch

Description

A management procedure that incrementally adjusts the TAC according to the mean length of recent catches.

Usage

LstepCC1(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  xx = 0,
  stepsz = 0.05,
  llim = c(0.96, 0.98, 1.05)
)

LstepCC2(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  xx = 0.1,
  stepsz = 0.05,
  llim = c(0.96, 0.98, 1.05)
)

LstepCC3(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  xx = 0.2,
  stepsz = 0.05,
  llim = c(0.96, 0.98, 1.05)
)

LstepCC4(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  xx = 0.3,
  stepsz = 0.05,
  llim = c(0.96, 0.98, 1.05)
)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate mean length.
xx	Parameter controlling the fraction of mean catch to start using in first year
stepsz	Parameter controlling the size of update increment in TAC or effort.
llim	A vector of length reference points that determine the conditions for increasing, maintaining or reducing the TAC or effort.

Details

The TAC is calculated as:

$\textrm{TAC} = \left\{\begin{array}{ll} \textrm{TAC}^* - 2 S\textrm{TAC}^* & \textrm{if } r < 0.96 \\ \textrm{TAC}^* - S \textrm{TAC}^* & \textrm{if } r < 0.98 \\ \textrm{TAC}^* & \textrm{if } > 1.058 \\ \end{array}\right.$

where $\textrm{TAC}^*$ is (1-xx) times average catch in the first year, and previous catch in all projection years, $S$ is step-size determined by stepsz, and $r$ is the ratio of $L_\textrm{recent}$ and $L_\textrm{ave}$ which are mean length over the most recent yrsmth years and 2 x yrsmth historical years respectively.

The conditions are specified in the llim argument to the function.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• LstepCC1: The least biologically precautionary TAC-based MP.

• LstepCC2: More biologically precautionary than LstepCC1 (xx = 0.1)

• LstepCC3: More biologically precautionary than LstepCC2 (xx = 0.2)

• LstepCC4: The most precautionary TAC-based MP.

Required Data

See Data-class for information on the Data object

LstepCC1: Cat, LHYear, ML, Year

LstepCC2: Cat, LHYear, ML, Year

LstepCC3: Cat, LHYear, ML, Year

LstepCC4: Cat, LHYear, ML, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

Examples

LstepCC1(1, Data=MSEtool::SimulatedData, plot=TRUE)

LstepCC2(1, Data=MSEtool::SimulatedData, plot=TRUE)
LstepCC3(1, Data=MSEtool::SimulatedData, plot=TRUE)
LstepCC4(1, Data=MSEtool::SimulatedData, plot=TRUE)

---

Step-wise Constant Effort

Description

A management procedure that incrementally adjusts the total allowable effort (TAE) according to the mean length of recent catches.

Usage

LstepCE1(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  stepsz = 0.05,
  llim = c(0.96, 0.98, 1.05)
)

LstepCE2(
  x,
  Data,
  reps = 100,
  plot = FALSE,
  yrsmth = 5,
  stepsz = 0.1,
  llim = c(0.96, 0.98, 1.05)
)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate trend in mean length.
stepsz	Parameter controlling the size of update increment in effort.
llim	A vector of length reference points that determine the conditions for increasing, maintaining or reducing the effort.

Details

The TAE is calculated as:

$\textrm{TAE} = \left\{\begin{array}{ll} \textrm{TAE}^* - 2 S\textrm{TAE}^* & \textrm{if } r < 0.96 \\ \textrm{TAE}^* - S \textrm{TAE}^* & \textrm{if } r < 0.98 \\ \textrm{TAE}^* & \textrm{if } > 1.058 \\ \end{array}\right.$

where $\textrm{TAE}^*$ is effort in the previous year, $S$ is step-size determined by stepsz, and $r$ is the ratio of $L_\textrm{recent}$ and $L_\textrm{ave}$ which are mean length over the most recent yrsmth years and 2 x yrsmth historical years respectively.

The conditions are specified in the llim argument to the function.

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• LstepCE1: The least biologically precautionary effort-based MP.

• LstepCE2: Step size is increased to 0.1

Required Data

See Data-class for information on the Data object

LstepCE1: LHYear, ML, MPeff, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

See Also

LstepCC1

Examples

LstepCE1(1, Data=MSEtool::SimulatedData, plot=TRUE)
LstepCE2(1, Data=MSEtool::SimulatedData, plot=TRUE)

---

Length Target TAC MP

Description

A management procedure that incrementally adjusts the TAC to reach a target mean length in catches.

Usage

Ltarget1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, xL = 1.05)

Ltarget2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, xL = 1.1)

Ltarget3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, xL = 1.15)

Ltarget4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0.2, xL = 1.15)

L95target(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xx = 0, xL = 1.05)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate mean length.
xx	Parameter controlling the fraction of mean catch to start using in first year
xL	Parameter controlling the magnitude of the target mean length of catches relative to average length in catches.

Details

Four target length MPs proposed by Geromont and Butterworth 2014. Tested by Carruthers et al. 2015.

The TAC is calculated as:

If $L_\textrm{recent} \geq L_0$:

$\textrm{TAC} = 0.5 \textrm{TAC}^* \left[1+\left(\frac{L_\textrm{recent}-L_0}{L_\textrm{target}-L_0}\right)\right]$

else:

$\textrm{TAC} = 0.5 \textrm{TAC}^* \left[\frac{L_\textrm{recent}}{L_0}^2\right]$

where $\textrm{TAC}^*$ is (1 - xx) mean catches from the last yrsmth historical years (pre-projection), $L_\textrm{recent}$ is mean length in last yrmsth years, $L_0$ is (except for L95target) 0.9 average catch in the last 2 x yrsmth historical (pre-projection years) ($L_\textrm{ave}$), and $L_\textrm{target}$ is (except for L95target) xL $L_\textrm{ave}$.

Value

An object of class Rec-class with the TAC slot populated with a numeric vector of length reps

Functions

• Ltarget1: The least biologically precautionary TAC-based MP.

• Ltarget2: Increasingly biologically precautionary (xL = 1.1).

• Ltarget3: Increasingly biologically precautionary (xL = 1.1).

• Ltarget4: The most biologically precautionary TAC-based MP (xL = 1.1, xx=0.2).

• L95target: Same as Ltarget1 but here the target and limit mean lengths are based on the length at maturity distribution rather than an arbitrary multiplicative of the mean length

Required Data

See Data-class for information on the Data object

Ltarget1: Cat, LHYear, ML, Year

Ltarget2: Cat, LHYear, ML, Year

Ltarget3: Cat, LHYear, ML, Year

Ltarget4: Cat, LHYear, ML, Year

L95target: Cat, L50, LHYear, ML, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

See Also

Other Length target MPs: Lratio_BHI(), LtargetE1()

Examples

Ltarget1(1, Data=MSEtool::SimulatedData, plot=TRUE)
Ltarget2(1, Data=MSEtool::SimulatedData, plot=TRUE)
Ltarget3(1, Data=MSEtool::SimulatedData, plot=TRUE)
Ltarget4(1, Data=MSEtool::SimulatedData, plot=TRUE)
L95target(1, Data=MSEtool::SimulatedData, plot=TRUE)

---

Length Target TAE MP

Description

A management procedure that incrementally adjusts the TAE to reach a target mean length in catches.

Usage

LtargetE1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xL = 1.05)

LtargetE4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, xL = 1.15)

Arguments

x	A position in the data object
Data	A data object
reps	The number of stochastic samples of the MP recommendation(s)
plot	Logical. Show the plot?
yrsmth	Years over which to calculate mean length
xL	Parameter controlling the magnitude of the target mean length of catches relative to average length in catches.

Details

Four target length MPs proposed by Geromont and Butterworth 2014. Tested by Carruthers et al. 2015.

The TAE is calculated as:

If $L_\textrm{recent} \geq L_0$:

$\textrm{TAE} = 0.5 \textrm{TAE}^* \left[1+\left(\frac{L_\textrm{recent}-L_0}{L_\textrm{target}-L_0}\right)\right]$

else:

$\textrm{TAE} = 0.5 \textrm{TAE}^* \left[\frac{L_\textrm{recent}}{L_0}^2\right]$

where $\textrm{TAE}^*$ is the effort in the previous year, $L_\textrm{recent}$ is mean length in last yrmsth years, $L_0$ is (except for L95target) 0.9 average catch in the last 2 x yrsmth historical (pre-projection years) ($L_\textrm{ave}$), and $L_\textrm{target}$ is (except for L95target) xL $L_\textrm{ave}$.

Value

An object of class Rec-class with the TAE slot(s) populated

Functions

• LtargetE1: The least biologically precautionary TAE-based MP.

• LtargetE4: The xL argument is increased to 1.15.

Required Data

See Data-class for information on the Data object

LtargetE1: LHYear, ML, MPeff, Year

Rendered Equations

See Online Documentation for correctly rendered equations

Author(s)

T. Carruthers

References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

See Also

Other Length target MPs: Lratio_BHI(), Ltarget1()

Examples

LtargetE1(1, Data=MSEtool::SimulatedData, plot=TRUE)
LtargetE4(1, Data=MSEtool::SimulatedData, plot=TRUE)

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