# Index Slope Tracking MP

`Islope1.Rd`

A management procedure that incrementally adjusts the TAC to maintain a constant CPUE or relative abundance index.

## Usage

```
Islope1(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.2)
Islope2(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.3)
Islope3(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.4, xx = 0.4)
Islope4(x, Data, reps = 100, plot = FALSE, yrsmth = 5, lambda = 0.2, xx = 0.4)
```

## 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
Years over which to calculate index

- lambda
A gain parameter controlling the speed in update in TAC.

- xx
Parameter controlling the fraction of mean catch to start using in first year

## 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:
$$\textrm{TAC} = \textrm{TAC}^* \left(1+\lambda I \right)$$
where \(\textrm{TAC}^*\) is \(1-xx\) multiplied by the mean catch from the past `yrsmth`

years for the
first year and catch from the previous year in projection years,
\(\lambda\) is a gain parameter, and \(I\) is the slope of log index over the past `yrsmth`

years.

## Functions

`Islope1`

: The least biologically precautionary of the Islope methods`Islope2`

: More biologically precautionary. Reference TAC is 0.7 average catch`Islope3`

: More biologically precautionary. Reference TAC is 0.6 average catch`Islope4`

: The most biologically precautionary of the Islope methods. Reference TAC is 0.6 average catch and gain parameter is 0.2

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Carruthers et al. 2015. Performance evaluation of simple management procedures. ICES J. Mar Sci. 73, 464-482.

Geromont, H.F., Butterworth, D.S. 2014. Generic management procedures for data-poor fisheries; forecasting with few data. ICES J. Mar. Sci. doi:10.1093/icesjms/fst232

## Examples

```
Islope1(1, MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1636.087
Islope2(1, MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1629.304
Islope3(1, MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1644.498
Islope4(1, MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1677.275
```