# Catch trend Surplus Production MSY MP

`SPMSY.Rd`

An MP that uses Martell and Froese (2012) method for estimating MSY to determine the OFL. Since their approach estimates stock trajectories based on catches and a rule for intrinsic rate of increase it also returns depletion. Given their surplus production model predicts K, r and depletion it is straight forward to calculate the OFL based on the Schaefer productivity curve.

## 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 calculated as: $$\textrm{TAC} = D K \frac{r}{2}$$ where \(D\) is depletion, \(K\) is unfished biomass, and \(r\) is intrinsic rate of increasase, all estimated internally by the method based on trends in the catch data and life-history information.

Requires the assumption that catch is proportional to abundance, and a catch time-series from the beginning of exploitation.

Occasionally the rule that limits r and K ranges does not allow r-K pairs to be found that lead to the depletion inferred by the catch trajectories. In this case this method widens the search.

## Required Data

See `Data-class`

for information on the `Data`

object

`SPMSY`

: Cat, L50, MaxAge, vbK, vbLinf, vbt0

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Martell, S. and Froese, R. 2012. A simple method for estimating MSY from catch and resilience. Fish and Fisheries. DOI: 10.1111/j.1467-2979.2012.00485.x

## Examples

```
SPMSY(1, Data=MSEtool::SimulatedData, plot=TRUE)
#> TAC (median)
#> 2484.297
```