An adaptive MP that uses trajectory in inferred suplus production and fishing mortality rate to update a TAC
Fadapt(x, Data, reps = 100, plot = FALSE, yrsmth = 7, gg = 1)A position in a data-limited methods data object
A data-limited methods data object
The number of stochastic samples of the MP recommendation(s)
Logical. Show the plot?
Years over which to smooth recent estimates of surplus production
A gain parameter controlling the speed in update in TAC.
An object of class Rec with the TAC slot populated with a numeric vector of length reps
A numeric vector of quota recommendations
See '>Data for information on the Data object
Fadapt: Abun, Cat, FMSY_M, Ind, Mort, Year
See Online Documentation for correctly rendered equations
Fishing rate is modified each year according to the gradient of surplus production with biomass (aims for zero). F is bounded by FMSY/2 and 2FMSY and walks in the logit space according to dSP/dB. This is derived from the theory of Maunder 2014.
The TAC is calculated as:
$$\textrm{TAC}_y= F_y B_{y-1}$$
where \(B_{y-1}\) is the most recent biomass, estimated with a loess smoother
of the most recent yrsmth years from the index of abundance (Data@Ind)
and estimate of current abundance (Data@Abun), and
$$F_y = F_{\textrm{lim}_1} + \left(\frac{\exp^{F_{\textrm{mod}_2}}} {1 + \exp^{F_{\textrm{mod}_2}}} F_{\textrm{lim}_3} \right) $$
where \(F_{\textrm{lim}_1} = 0.5 \frac{F_\textrm{MSY}}{M}M\),
\(F_{\textrm{lim}_2} = 2 \frac{F_\textrm{MSY}}{M}M\), \(F_{\textrm{lim}_3}\) is \(F_{\textrm{lim}_2} - F_{\textrm{lim}_1}\),
\(F_{\textrm{mod}_2}\) is
$$F_{\textrm{mod}_1} + g -G$$
where \(g\) is gain parameter gg, G is the predicted surplus production given current abundance,
and:
$$F_{\textrm{mod}_1} =
\left\{\begin{array}{ll}
-2 & \textrm{if } F_\textrm{old} < F_{\textrm{lim}_1} \\
2 & \textrm{if } F_\textrm{old} > F_{\textrm{lim}_2} \\
\log{\frac{F_\textrm{frac}}{1-F_\textrm{frac}}} & \textrm{if } F_{\textrm{lim}_1} \leq F_\textrm{old} \leq F_{\textrm{lim}_2} \\
\end{array}\right.
$$
where \(-F_{\textrm{frac}} = \frac{F_{\textrm{old}} - F_{\textrm{lim}_1}}{F_{\textrm{lim}_3}} \),
\(F_\textrm{old} = \sum{\frac{C_\textrm{hist}}{B_\textrm{hist}}}/n\)
where \(C_\textrm{hist}\) and \(B_\textrm{hist}\) are smooth catch and biomass over last yrsmth,
and \(n\) is yrsmth.
Tested in Carruthers et al. 2015.
Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.
Maunder, M. 2014. http://www.iattc.org/Meetings/Meetings2014/MAYSAC/PDFs/SAC-05-10b-Management-Strategy-Evaluation.pdf
Other Fmsy/M methods: DynF,
Fratio
Other Surplus production MPs: Rcontrol,
SPMSY, SPSRA,
SPmod, SPslope
# NOT RUN {
Fadapt(1, Data=DLMtool::Atlantic_mackerel, plot=TRUE)
# }
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