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

`Lratio_BHI.Rd`

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

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

## 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).

## 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

## 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

## Examples

```
Lratio_BHI(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1401.608
Lratio_BHI2(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1460.572
Lratio_BHI3(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 2097.509
```