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

## Author

T. Carruthers

## Examples

#> TAC (median)
#> 4.873551