divergent productivity

[CamFreshwater]

I've added a divergent productivity option that assigns CUs within the model either increasing, decreasing or stable trends. Right now this is pretty simple and has the following structure:

• Increasing/decreasing trends are equivalent; final alpha value is equal to 0.65 and 1.35 scalar applied to reference alpha (based on Fraser River recursive Bayes estimates)
• Applied over the entire simulation period so that the final alpha value is reached in the last simulation year
• Assigned randomly at beginning of simulation period (i.e. the same CUs are inc., dec. or stable for all MC trials)
• Covariance is still uniform among CUs (i.e. inc. and dec. CUs covary with one another)

So far the results suggest that at the aggregate level using a divergent operating model leads to approximately equivalent results as the reference, which isn't really surprising since via random assignment you'll get a fairly even mix of each trend. Of course the CU-specific trends are more interesting, but they're entirely driven by which trend a CU is assigned, which as structured isn't really meaningful.

I think the most obvious way to make this more interesting is to assign trends a priori, rather than randomly. Obviously this is more realistic and could be fairly simple (e.g. just pull trends from Catherine Michaelsens and Carrie's most recent analysis or Peterman and Dorner 2012), however I'm not really sure what to do about the cyclic stocks. I also don't really know how this could then be applied to non-Fraser River aggregates where these relatively complex analyses haven't been applied.

So should I go down the rabbit hole of identifying and justifying CU-specific trends for the purpose of the single-stock manuscript? Alternatively does anyone have any suggestions on how else to structure these trends?

[ann-marieH]

It IS a rabbit hole, isn't it?!??

For single stock, maybe structure the assignment of incr/decr/no pattern productivity to reflect some "what ifs" that may be of concern/interest for accessing harvest? e.g. I'm thinking the following might be real life concerns:

• "one of these is not like the others"
  • large stock with increasing prod'y, while all others are decreasing or staying the same (harrison)
  • small stock with decreasing prod'y, while all others are staying the same (cultus)
• "none of these is like the others"
  • similar size stocks - one incr, one decr, one stays the same (pretty sure this is happening somewhere in the ESum aggregate!)

...by framing things out this way, I'm thinking they are drawn from FR SK examples, but:

1. are not slavishly replicating them
2. will be broadly applicable to other stocks & systems.

re: applying trend to the entire forward simulation - I have some thoughts, but they aren't terribly coherent at the moment:

• there will be some [insert word that starts with "c" re: not being able to tell what's affecting what] between gradual change in productivity & lingering effects of starting SPN pattern in the first 3 generations or so
• after first 3 gens, can see the effects of the OM
• I have yet to tease out how much of an effect the HCR has on where things are at after 48 yrs, compared to all of the various bits of the OM (e.g. S/R model, prod'y, en-route mort) - initial explorations are that S/R model overrides HCR (as long as HCR isn't something silly like Fixed90 ER)

[CamFreshwater]

So I spent some more time tweaking these around and developed the following productivity OMs:

• lowProd: everyone drops to 65% reference alpha
• divergent: CUs are randomly assigned an increasing or decreasing trend
• divergentSmall: small CUs (i.e. any CU with a median recruitment in the lower 50% of the aggregate distribution) gets a decreasing trend
• oneUp: one CU increases (for exploratory purposes Harrison)
• oneDown: one CU decreases (for exploratory purposes Cultus)

While each OM impacts performance metrics in different ways (e.g. low productivity reduces spawner abundance, oneUp increases the performance of the CU with increasing productivity), as long as total exploitation rates are low or moderate they don't alter the relationship between single-stock allocations and aggregate performance (First figure). The one exception to this is the proportion of CUs extinct, which increases as mixed stock allocations increase with the divergent productivity OMs. When productivity is at reference or low this same pattern doesn't occur. I still need to fully explore why, but it seems to be driven by greater variability in realized exploitation rates among trials. My guess is that outcome uncertainty results in depleted CUs with low productivity trends blinking out due to exploitation in mixed stock fisheries.

Interestingly the interaction between the proportion of CUs above their lower/upper benchmarks and mixed-stock allocations also aren't impacted by productivity regime. This appears to be driven by a) depleted CUs getting only modest benefits from single stock fisheries (i.e. they grow but not much) and b) a small number of CUs exhibiting evidence of overescapement effects when single stock fisheries are closed. Specifically Stellako and Harrison recruit and spawner abundance increases significantly there is moderate exploitation. Counter-intuitively mixed stock fisheries solve this problem because the single stock harvest control rule closes those CU's fisheries because they rarely exceed their lower BM.

When total exploitation rates increase the difference between mixed and single stock allocations is magnified (mixed stock fisheries tend to overexploit), but the divergent productivity trends are basically intermediate to reference and low.

We can discuss whether the proportion of CUs extinct result during our next call, but for now I'll stick with a simple low productivity scenario as the alternative OM.

[carrieholt]

I wonder if the divergent trends in ppnCUExtant and ppnCULower/ppnCUUpper in the first set of plots (low exploitation) are because, the quasi-extinction threshold for ppnCUExtant is a fixed number, but benchmarks vary with productivity. Under low productivity they tend to decline (upper benchmark at least, and the lower benchmark sometimes), so that the probability of depleting below the benchmark is relatively stable as productivity declines. Here are my recent Kalman Filter Ricker a estimates for 12 stocks of Fraser Sockeye. Interestingly, Cultus is stable, at least until 2000 when hatchery started. I can send the CU-stock name translation if you'd like.

[CamFreshwater]

Right. I hadn't considered that because I was so focused on the uptick in spawner and return abundance but it may also be a driver. I guess that's another argument for a normative period like we were discussing...