Impacts of Priors on Beta

[CamFreshwater]

To try to deal with overcompensation we decide to refit the stock-recruit models for Fraser w/ more informative priors on beta, specifically by constraining the distribution by observed spawner abundance. When I revisited the models I realized that Gotfried and Ann-Marie actually already had done that, but with a relative large cap (3x max observed escapement).

So I tried a few alternatives:

1. More conservative caps of 1 and 1.5
2. More restrictive priors on tau (0.01 instead of 0.001)
3. Uniform as well as truncated log-normal distribution

The attached plot shows the first two alternatives (using a uniform distribution didn't dramatically impact the results) for the Ricker CUs in the aggregate. As you can see reducing the cap results in larger beta values, however for most CUs the changes are pretty modest and I doubt they'll reverse the overcompensation trends we currently see for stocks like Harrison and Stellako.

Any other ideas on what to tweak? Do any of you have a strong preference on which parameterization is more appropriate?

Given how uncertain these parameter estimates are I was thinking that resampling the SR parameters for each MC trial may be realistic and result in more pessimistic outcomes. However it will really increase the uncertainty among trials and perhaps just swamp out other model components, which is why we dropped that strategy a ~year ago.

[carrieholt]

What is the impact of this increase in beta (lower cap on prior) on dynamics of Harrison and Stellako? Is over compensation really the problem, or is it something else? What if you fixed beta at (1/maximum observed value)? Yes, you could resample SR parameters for each MC trial, which is perhaps more realistic, but I don't think will solve this problem (other than swamping it).

[ann-marieH]

fyi, I've been re-estimating Ricker pars for more recent time periods (2002-2011BY = DNA years & 2000-2011BY = 3generations)

• surprisingly to me, there is very little difference in Harrison betas when solved with all years vs shorter years - means w/in 5%, medians w/in 10%. Alphas saw the most change with shorter time series - up 20-30% from all yr values
• Stellako is also showing most difference in alphas when using shorter time series: down 45-50%. Betas up 10-30%.

[CamFreshwater]

Sorry for the delay, wanted to dig into some forward simulated time series before replying. That's interesting about the larger increases in alpha Ann-Marie. Not sure I know enough about the guts of the models to determine why one parameter would be more sensitive than the other, but good to know.

Carrie, the lower cap results in a 7% increase in beta for Harrison and a 2% increase for Stellako. When you forward simulate this tamps down the large positive recruitment deviations a bit, but you still get a jump in recruit abundance.

The attached figure shows an example from one trial run for Harrison. The panels rperesent mixed stock allocations (0 to 1) with a fixed exploitation rate of 0.3. The solid line represents a high beta treatment where it was inflated by 25% (i.e. this shows a larger effect than we will see if we use the newly estimated betas). The horizontal lines represent mean recruitment through time for that trial for each MP/OM.

Obviously the patterns change quite a bit across trials, and the 100% mixed stock certainly isn't always bigger, it just is on average. Typically the difference between the beta OMs is also greatest with 100% mixed stock (regardless of CU). This makes me think that it is being driven by an interaction between realized exploitation rate and the beta parameter, but I think it's definitely a function of the shape of the curve (i.e. alpha and beta) rather than one or the other.

I'll keep digging into this, however I'm not sure if there's an obvious solution other than to try to explain the emergent patterns as clearly as possible in the manuscript.

[carrieholt]

Okay. If nothing else comes up in your digging Cam, then let's leave it at explaining the behaviour with over-compensation, which presumably goes away with high exploitation rates and/or low productivity. Ann-Marie, I'd be caution about interpreting the prod/Smax estimates too much with the shorter data sets, especially Stellako (as I think the long time-series of Harrison essentially acts like a short time-series with the long string of very low values).

[CamFreshwater]

Yeah after chatting this morning I did some runs with different alpha and beta scalars plus a range of exploitation rates. The wonkiness disappears when you ramp up fishing or ramp down productivity, as expected, so I'd put my money on it being a symptom of overcompensation. I also plotted CU-specific relationships between realized exploitation rates and median recruitment, which was really helpful. Theres much more variation among CUs in what those curves look like than I was expecting, which I guess really speaks to the complexities of managing aggregates. There's Rmd's with all those figures if anyone's keen to look.

Finally I tried to tweak the code so that I could adjust initial spawner abundance values, but that's going to take more time than I originally thought to put back in. It's on the to-do list, I'd just like to get some preliminary Nass runs taken care of first!