BK: Beddington and Kirkwood life-history MP
In DLMtool/DLMtool: Data-Limited Methods Toolkit

Description Usage Arguments Details Value Functions Required Data Rendered Equations Note Author(s) References Examples

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)

`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).

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_∞}

where K is the von Bertalanffy growth coefficient, L_c is the length at first capture, and L_∞ is the von Bertalanffy asymptotic length

Abundance (A) is either assumed known (BK) or estimated (BK_CC and BK_ML):

A = \frac{\bar{C}}{≤ft(1-e^{-F}\right)}

where \bar{C} is the mean catch, and F is estimated. See Functions section below for the estimation of F.

An object of class Rec with the TAC slot populated with a numeric vector of length reps

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.

See Data 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

See Online Documentation for correctly rendered equations

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.

T. Carruthers.

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.

## Not run: 
BK(1, DLMtool::SimulatedData, reps=1000, plot=TRUE)

## End(Not run)

## Not run: 
BK_CC(1, DLMtool::SimulatedData, reps=1000, plot=TRUE)

## End(Not run)

## Not run: 
BK_ML(1, DLMtool::SimulatedData, reps=100, plot=TRUE)

## End(Not run)