A simple yield per recruit approximation to FMSY (F01) which is the position
of the ascending YPR curve for which dYPR/dF = 0.1(dYPR/d0)

YPR(x, Data, reps = 100, plot = FALSE)
YPR_CC(x, Data, reps = 100, plot = FALSE, Fmin = 0.005)
YPR_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 inferred from the catch-curve
analysis |

## 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:
$$\textrm{TAC} = F_{0.1} A$$
where \(F_{0.1}\) is the fishing mortality (*F*) where the slope of the yield-per-recruit
(YPR) curve is 10\

The YPR curve is calculated using an equilibrium age-structured model with life-history and
selectivity parameters sampled from the `Data`

object.

The variants of the YPR MP differ in the method to estimate current abundance (see Functions section below). #'

## Functions

`YPR`

: Requires an external estimate of abundance.

`YPR_CC`

: A catch-curve analysis is used to determine recent Z which given M (Mort)
gives F and thus abundance = Ct/(1-exp(-F))

`YPR_ML`

: A mean-length estimate of recent Z is used to infer current
abundance.

## Note

Based on the code of Meaghan Bryan

## Required Data

See `Data-class`

for information on the `Data`

object

`YPR`

: Abun, LFS, MaxAge, vbK, vbLinf, vbt0

`YPR_CC`

: CAA, Cat, LFS, MaxAge, vbK, vbLinf, vbt0

`YPR_ML`

: CAL, Cat, LFS, Lbar, Lc, MaxAge, Mort, vbK, vbLinf, vbt0

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Beverton and Holt. 1954.

## Author

Meaghan Bryan and Tom Carruthers

## Examples

#> TAC (median)
#> 1814.77

#> TAC (median)
#> 4203.757

#> TAC (median)
#> 5373.718