# Dynamic Fratio MP

`DynF.Rd`

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.

## 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

## Examples

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