# Delay - Difference Stock Assessment

`DD.Rd`

A simple delay-difference assessment with UMSY and MSY as leading parameters that estimates the TAC using a time-series of catches and a relative

## 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

This DD model is observation error only and has does not estimate process error (recruitment deviations). Assumption is that knife-edge selectivity occurs at the age of 50% maturity. Similar to many other assessment models it depends on a whole host of dubious assumptions such as temporally stationary productivity and proportionality between the abundance index and real abundance. Unsurprisingly the extent to which these assumptions are violated tends to be the biggest driver of performance for this method.

The method is conditioned on effort and estimates catch. The effort is calculated as the ratio of catch and index. Thus, to get a complete effort time series, a full time series of catch and index is also needed. Missing values are linearly interpolated.

A detailed description of the delay-difference model can be found in Chapter 9 of Hilborn and Walters (1992).

## Functions

`DD`

: Base version where the TAC = UMSY * Current Biomass.`DD4010`

: A 40-10 rule is imposed over the TAC recommendation.

## Required Data

See `Data-class`

for information on the `Data`

object

`DD`

: Cat, Ind, L50, MaxAge, Mort, vbK, vbLinf, vbt0, wla, wlb

`DD4010`

: Cat, Ind, L50, MaxAge, Mort, vbK, vbLinf, vbt0, wla, wlb

## Rendered Equations

See Online Documentation for correctly rendered equations

## References

Carruthers, T, Walters, C.J,, and McAllister, M.K. 2012. Evaluating methods that classify fisheries stock status using only fisheries catch data. Fisheries Research 119-120:66-79.

Hilborn, R., and Walters, C. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York.

## See also

Other Delay-Difference MPs:
`DDe()`

## Examples

```
DD(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 1.947672
DD4010(1, Data=MSEtool::Atlantic_mackerel, plot=TRUE)
#> TAC (median)
#> 0.4334987
```