### Description

An adaptive MP that uses trajectory in inferred suplus production and fishing mortality rate to update a TAC

### Usage

Fadapt(x, Data, reps = 100, plot = FALSE, yrsmth = 7, gg = 1)


### Arguments

 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? yrsmth Years over which to smooth recent estimates of surplus production gg A gain parameter controlling the speed in update in TAC.

### Details

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} + ≤ft(\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:

where -F_{\textrm{frac}} = \frac{F_{\textrm{old}} - F_{\textrm{lim}_1}}{F_{\textrm{lim}_3}} , F_\textrm{old} = ∑{\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.

### Value

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

A numeric vector of quota recommendations

### Required Data

See Data-class for information on the Data object

Fadapt: Abun, Cat, FMSY_M, Ind, Mort, Year

### Rendered Equations

See Online Documentation for correctly rendered equations

T. Carruthers

### References

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()
Fadapt(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)