# Intrinsic rate of Increase MP

`Rcontrol.Rd`

An MP proposed by Carl Walters that modifies the TAC according to trends in apparent surplus production that includes information from a demographically derived prior for intrinsic rate of increase

## 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 years for smoothing catch and biomass data

- gg
A gain parameters

- glim
Limits for the change in TAC among years

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

## Details

The TAC is calculated as:
$$\textrm{TAC} = \textrm{SP} (1-gG)$$
where \(g\) is a gain parameter, \(\textrm{SP}\) is estimated surplus production,
and \(G\) is:
For `Rcontrol`

: \(G = r (1-2D)\) where \(r\) is the estimated intrinsic rate
of increase, and \(D\) is assumed depletion.

For `Rcontrol2`

: \(G = r - 2bB_\textrm{hist}\) where \(B_\textrm{hist}\)
is the smoothed biomass overlast `yrsmth`

years and:
$$b = \sum{\frac{\textrm{SP}}{B_\textrm{hist}} - r} \frac{\sum{B_\textrm{hist}}}{\sum{B_\textrm{hist}^2}} $$.

The TAC is subject to conditions limit the maximum change from the smoothed catch
over the last `yrsmth`

years by the `glim`

argument, e.g, default values of `glim = c(0.5, 2)`

means that maximum decrease in TAC is 50% of average catch and maximum increase
is 2 x average catch.

## Functions

`Rcontrol`

: Base version`Rcontrol`

`Rcontrol2`

: This is different from`Rcontrol`

because it includes a quadratic approximation of recent trend in surplus production given biomass

## Required Data

See `Data-class`

for information on the `Data`

object

`Rcontrol`

: Abun, Cat, Dep, FMSY_M, Ind, L50, MaxAge, Mort, Year, steep, vbK, vbLinf, vbt0, wla, wlb

## Rendered Equations

See Online Documentation for correctly rendered equations

## Examples

```
Rcontrol(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 6.529254
Rcontrol2(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 6.529254
```