# Index Target based on natural mortality rate

`ITM.Rd`

An index target MP where the TAC is modified according to current index
levels (mean index over last number of years determined by natural mortality
(*M*)) relative to a target level.

## 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?

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

## Details

The TAC is caluclated as:
$$\textrm{TAC}_y = \textrm{TAC}_{y-1} \delta I$$
where \(\delta I\) is the ratio of the mean index over \(4\frac{1}{M}^{1/4}\) years
to the reference index (`Data@Iref`

).

The maximum fractional change in TAC is determined by \(mc\), defined as \(mc = \textrm{max}\left(\frac{5 + 25M}{100}, 0.2\right)\)

## Rendered Equations

See Online Documentation for correctly rendered equations

## Examples

```
ITM(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 1950.633
```