Description Usage Arguments Details Value Functions Required Data Rendered Equations Note Author(s) References See Also Examples
This group of MPs calculates a catch limit (dcac; intended as an MSY proxy) based on average historical catch while accounting for the windfall catch that got the stock down to its current depletion level (D).
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x 
A position in a datalimited methods data object 
Data 
A datalimited methods data object 
reps 
The number of stochastic samples of the MP recommendation(s) 
plot 
Logical. Show the plot? 
The method calculates the depletioncorrected average catch (dcac) as:
\textrm{dcac} = \frac{∑_{y=1}^{n}{C_y}}{n+(1D)/Y_{\textrm{pot}}}
where
Y_{\textrm{pot}} = \frac{B_{\textrm{MSY}}}{B_0}\frac{F_{\textrm{MSY}}}{M}M
and C is the historical catches; i.e C does not change in the future projections in the MSE
The methods differ in the assumptions of current depletion (D). See the Functions section below for details.
An object of class Rec
with the TAC
slot populated with a numeric vector of length reps
DCACs
: Depletion is not updated in the future projections.
The TAC is static and not updated in the future years. This represents
an application of the DCAC method where a catch limit is calculated based on
current estimate of depletion and timeseries of catch from the beginning
of the fishery, and the TAC is fixed at this level for all future projections.
DCAC
: Depletion is estimated each management interval and used to
update the catch limit recommendation based on the historical catch (which is
not updated in the future projections).
DCAC_40
: Current stock biomass is assumed to be exactly at 40 per cent
of unfished levels. The 40 percent depletion assumption may not
really affect DCAC that much as it already makes TAC recommendations that are
quite MSYlike.
DCAC4010
: The dynamic DCAC (depletion is updated) is paired with the 4010 rule that throttles
back the OFL to zero at 10 percent of unfished stock size (the OFL is not subject to downward
adjustment above 40 percent unfished). DCAC can overfish below BMSY levels. The 4010
harvest control rule largely resolves this problem providing an MP with surprisingly good
performance even at low stock levels.
DCAC_ML
: This variant uses the mean length estimator to calculate current stock
depletion. The mean length extension was programmed by Gary Nelson as part of his
excellent R package 'fishmethods'.
DAAC
: Depletion Adjusted Average Catch: essentially DCAC (with updated Depletion)
divided by BMSY/B0 (Bpeak) (Harford and Carruthers, 2017).
HDAAC
: Hybrid Depletion Adjusted Average Catch: essentially DCAC (with updated Depletion)
divided by BMSY/B0 (Bpeak) when below BMSY,
and DCAC above BMSY (Harford and Carruthers 2017).
See Data for information on the Data
object
DCACs
: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, t, Year
DCAC
: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, t, Year
DCAC_40
: AvC, BMSY_B0, FMSY_M, LHYear, Mort, t, Year
DCAC4010
: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, t, Year
DCAC_ML
: AvC, CAL, Cat, Lbar, Lc, LHYear, Mort, t, vbK, vbLinf, Year
DAAC
: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, t, Year
HDAAC
: AvC, BMSY_B0, Dt, FMSY_M, LHYear, Mort, t, Year
See Online Documentation for correctly rendered equations
It's probably worth noting that DCAC TAC recommendations do not tend to zero as depletion tends to zero. It adjusts for depletion only in calculating historical average catch. It follows that at stock levels much below BMSY, DCAC tends to chronically overfish.
T. Carruthers
MacCall, A.D., 2009. Depletioncorrected average catch: a simple formula for estimating sustainable yields in datapoor situations. ICES J. Mar. Sci. 66, 22672271.
Harford W. and Carruthers, T. 2017. Interim and longterm performance of static and adaptive management procedures. Fish. Res. 190, 8494.
Other Average Catch MPs: AvC_MLL
,
AvC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  DCACs(1, DLMtool::Atlantic_mackerel, plot=TRUE)
DCAC(1, DLMtool::Atlantic_mackerel, plot=TRUE)
DCAC_40(1, DLMtool::Atlantic_mackerel, plot=TRUE)
Data < DLMtool::Atlantic_mackerel
Data@LHYear < 2005
DCAC4010(1, Data, plot=TRUE)
DCAC_ML(1, DLMtool::SimulatedData, plot=TRUE)
Data < DLMtool::Atlantic_mackerel
Data@LHYear < 2005
DAAC(1, Data, plot=TRUE)
Data < DLMtool::Atlantic_mackerel
Data@LHYear < 2005
HDAAC(1, Data, plot=TRUE)

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