# SPslope: Slope in surplus production MP In DLMtool: Data-Limited Methods Toolkit

## Description

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)

## Usage

 1 2 SPslope(x, Data, reps = 100, plot = FALSE, yrsmth = 4, alp = c(0.9, 1.1), bet = c(1.5, 0.9)) 

## 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 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

## Details

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

The TAC is calculated as:

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, α_1 and α_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.

## Value

An object of class Rec with the TAC slot populated with a numeric vector of length reps

## Required Data

See Data for information on the Data object

SPslope: Abun, Cat, Ind, Year

## Rendered Equations

See Online Documentation for correctly rendered equations

T. Carruthers

## References

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

Other Surplus production MPs: Fadapt, Rcontrol, SPMSY, SPSRA, SPmod
 1 SPslope(1, Data=DLMtool::Atlantic_mackerel, plot=TRUE)