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.

SPMSY(x, Data, reps = 100, plot = FALSE)

## 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

## See also

## Author

T. Carruthers

## Examples

#> TAC (median)
#> 1067.542