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.

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 A data object The number of stochastic samples of the MP recommendation(s) Logical. Show the plot? 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.

T. Carruthers.

## 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)
}