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

Data

A data object

reps

The number of stochastic samples of the MP recommendation(s)

plot

Logical. Show the plot?

yrsmth

The number of historical recent years used for smoothing catch and biomass data

gg

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

Made-up for this package.

See also

Other Fmsy/M methods: Fadapt(), Fratio()

Author

T. Carruthers

Examples

DynF(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median) #> 4.873551