`SPslope.Rd`

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

- 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 smooth recent estimates of surplus production

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

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

An object of class `Rec-class`

with the `TAC`

slot populated with a numeric vector of length `reps`

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

The TAC is calculated as:
$$\textrm{TAC}_y =
\left\{\begin{array}{ll}
M \bar{C} & \textrm{if } r < \alpha_1 \\
\bar{C} & \textrm{if } \alpha_1 < r < \alpha_2 \\
\textrm{bet}_2 \textrm{SP} & \textrm{if } r > \alpha_2 \\
\end{array}\right.
$$
where \(r\) is the ratio of predicted biomass in next year to biomass in
current year \(\bar{C}\) is the mean catch over the last `yrmsth`

years, \(\alpha_1\)
and \(\alpha_2\) are specified in `alp`

, \(\textrm{bet}_1\) and \(\textrm{bet}_2\)
are specified in `bet`

, \(\textrm{SP}\) is estimated surplus production in most recent year,
and:
$$M = 1-\textrm{bet}_1 \frac{B_y - \tilde{B}_y}{B_y}$$
where \(B_y\) is the most recent estimate of biomass and \(\tilde{B}\)
is the predicted biomass in the next year.

See Online Documentation for correctly rendered equations

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

```
SPslope(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 13.90378
```