# Surplus production based catch-limit modifier

`SPmod.Rd`

An MP that makes incremental adjustments to TAC recommendations based on the apparent trend in surplus production. Based on the theory of Mark Maunder (IATTC)

## 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?

- alp
Condition for modifying the TAC (bounds on change in abundance)

- bet
Limits for how much the TAC can change among years

## Value

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

A numeric vector of TAC recommendations

## Details

Note that this isn't exactly what Mark has previously suggested and is stochastic in this implementation.

The TAC is calculated as:
$$\textrm{TAC}_y =
\left\{\begin{array}{ll}
C_{y-1} \textrm{bet}_1 & \textrm{if } r < \alpha_1 \\
C_{y-1} & \textrm{if } \alpha_1 < r < \alpha_2 \\
\textrm{bet}_2 (b_2 - b_1 + C_{y-2} ) & \textrm{if } r > \alpha_2 \\
\end{array}\right.
$$
where \(\textrm{bet}_1\) and \(\textrm{bet}_2\) are elements in `bet`

,
\(r\) is the ratio of the index in the most recent two years, \(C_{y-1}\)
is catch in the previous year, \(b_1\) and \(b_2\) are ratio of index
in \(y-2\) and \(y-1\) over the estimate of catchability \(\left(\frac{I}{A}\right)\),
and \(\alpha_1\), \(\alpha_2\), and \(\alpha_3\) are specified in argument
`alp`

.

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

http://www.iattc.org/Meetings/Meetings2014/MAYSAC/PDFs/SAC-05-10b-Management-Strategy-Evaluation.pdf

## Examples

```
SPmod(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 15.92228
```