# Length Target TAC MP

`Ltarget1.Rd`

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.

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

## 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`

\(L_\textrm{ave}\).

## 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

## 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)
#> TAC (median)
#> 1972.638
Ltarget2(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1774.109
Ltarget3(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1695.918
Ltarget4(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1369.049
L95target(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 855.973
```