BK.RdFamily 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). |
An object of class Rec with the TAC slot populated with a numeric vector of length reps
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.
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 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.
See Data for information on the Data object
BK: Abun, LFC, vbK, vbLinf
BK_CC: CAA, Cat, LFC, vbK, vbLinf
BK_ML: CAL, Cat, Lbar, Lc, LFC, Mort, vbK, vbLinf
See Online Documentation for correctly rendered equations
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.
if (FALSE) { BK(1, DLMtool::SimulatedData, reps=1000, plot=TRUE) } if (FALSE) { BK_CC(1, DLMtool::SimulatedData, reps=1000, plot=TRUE) } if (FALSE) { BK_ML(1, DLMtool::SimulatedData, reps=100, plot=TRUE) }