# Beddington and Kirkwood life-history MP

`BK.Rd`

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).

## 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: $$\textrm{TAC} = A F_{\textrm{max}}$$ 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*.

## 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*.

## 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.

## 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

## 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

```
if (FALSE) {
BK(1, MSEtool::SimulatedData, reps=1000, plot=TRUE)
}
if (FALSE) {
BK_CC(1, MSEtool::SimulatedData, reps=1000, plot=TRUE)
}
if (FALSE) {
BK_ML(1, MSEtool::SimulatedData, reps=100, plot=TRUE)
}
```