# Ltarget1: Length Target TAC MP In DLMtool: Data-Limited Methods Toolkit

## Description

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

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 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} ≥q L_0:

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

else:

\textrm{TAC} = 0.5 \textrm{TAC}^* ≤ft[\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 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 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

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

Other Length target MPs: Lratio_BHI, LtargetE1
 1 2 3 4 5 Ltarget1(1, Data=DLMtool::SimulatedData, plot=TRUE) Ltarget2(1, Data=DLMtool::SimulatedData, plot=TRUE) Ltarget3(1, Data=DLMtool::SimulatedData, plot=TRUE) Ltarget4(1, Data=DLMtool::SimulatedData, plot=TRUE) L95target(1, Data=DLMtool::SimulatedData, plot=TRUE)