The Fratio MP with a controller that changes the level of F according to the estimated relationship between surplus production and biomass. Ie lower F when dSP/dB is positive and higher F when dSP/dB is negative.

DynF(x, Data, reps = 100, plot = FALSE, yrsmth = 10, gg = 2)

## Arguments

x A position in the data object A data object The number of stochastic samples of the MP recommendation(s) Logical. Show the plot? The number of historical recent years used for smoothing catch and biomass data A gain parameter that modifies F according to the gradient in surplus production with biomass

## Value

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

## Details

The method smoothes historical catches and biomass and then infers the relationship between surplus production and biomass (as suggested by Mark Maunder and Carl Walters). The approach then regulates a F based policy according to this gradient in which F may range between two different fractions of natural mortality rate.

The core advantage is the TAC(t) is not strongly determined by TAC(t-1) and therefore errors are not as readily propagated. The result is method that tends to perform alarmingly well and therefore requires debunking ASAP.

The catch limit (TAC) is calculated as: $$\textrm{TAC}=F B$$ where $$F$$ is fishing mortality and $$B$$ is the estimated current biomass.

$$F$$ is calculated as: $$F = F_{\textrm{MSY}} \exp{-gG}$$ where $$F_{\textrm{MSY}}$$ is calculated from assumed values of $$\frac{F_{\textrm{MSY}}}{M}$$ and $$M$$, g is a gain parameter and G is the estimated gradient in surplus production (SP) as a function of biomass (B). Surplus production for year y is calculated as: $$SP_y = B_{y+1} - B_y + C_y$$ Trends in historical catch (C) and biomass (B) are both estimated using a loess smoother, over the last yrsmth years, of available catch and a time-series of abundance, calculated from an index of abundance (Data@Ind) and an estimate of abundance (Data@Abun) for the current year.

## Required Data

See Data-class for information on the Data object

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

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Other Fmsy/M methods: Fadapt(), Fratio()
DynF(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#>     4.873551