Recursive Bayes estimates for aggregate FRPs

[CamFreshwater]

@ann-marieH passed me off posterior estimates of parameters for Larkin and Ricker stocks from recursive Bayes models. However I am wondering whether the harvest control rule FRPs (or OCPs) should also reflect non-stationary productivity. In other words should I fit a recursive Bayes model to the aggregate data to estimate alpha/beta so that I can then use the most recent estimates to calculate aggregate 0.4Smsy, 0.8Smsy and Umsy? Or is this not necessary?

If the former, could you send me your script Ann-Marie and I'll use it with the Summer MU aggregated recruitment data?

Thanks!

[CamFreshwater]

This slipped down my to-do list, but is still relevant. Thoughts on whether it's necessary to parameterize the generic multistock HCR with SR data that reflects declines in aggregate productivity or can we stick with stationary estimates of alpha at the aggregate level?

[ann-marieH]

Aside from the fact that I have totally forgotten what we're using the msy estimates for (sorry!), I think it might depend on what the purpose is: if it's to see how a stationary HCR interacts with a changing stock, then that's one HCR; if it's to figure out how to develop an HCR that responds to changes in productivity, then that's a different MP altogether.

[krHolt]

I don't have a definitive answer, but I think using the stationary estimates could make more sense given that the paper is focused on the single-mixed fishery split. Looking at HCRs that respond to changing productivity is a good question, but I'm wondering if it's too much to add to this paper. Also - I seem to recall that the single-stock HCRs are stationary (percentile benchmarks estimated only once at the beginning of the simulation), so using stationary estimates for mixed-stock would be consistent.

[CamFreshwater]

Sorry, I could have been a bit clearer. I'm definitely not suggesting that we incorporate a time-varying HCR (ack!). Just that we use account for non-stationary productivity when estimating stock recruit parameters at the aggregate level (remember that this process is necessary to calculate u_msy and s_msy for the multistock HCR).

As is the multistock HCR applies fairly aggressive exploitation rates because u_msy is high, which is in turn driven by aggregate productivity being estimated as high since it's the median over the entire time series. If we accounted for temporal variability when estimating aggregate stock recruit benchmarks this probably wouldn't be the case. I'll keep it simple for now and use the stationary estimate of alpha, but perhaps keep it in mind when you read the next manuscript draft (coming shortly).

FWIW I've also considered switching back to using stock recruit BMs for the single-stock HCR because we're already using 0.4s_msy and 0.8s_msy as FRPs in the multistock HCR. In terms of consistency, it makes sense to me because presumably if alpha and beta can be estimated at the MU level, they can also be estimated at the CU level (but perhaps not?). Either way we can peg that one for future discussion.

[carrieholt]

I don’t necessarily recommend accounting for time-varying productivity in estimating operational control points at either the MU or CU level (if stock-recruitment based benchmarks are used at the CU level). Two reasons (a) they aren’t actually used in practice and adds an additional complexity in the analyses that is not needed, (b) observed declines in productivity for most stocks means that estimates of SMSY will be relatively low if we use the most current estimate of productivity (i.e., relatively optimistic status assessment) which is not precautionary. Though you’re correct about UMSY perhaps being too high under long-term average productivity . However, our application of this PA harvest control rule is theoretical anyways…..