Question on MSY estimates

[Giancarlo M. Correa]

Hi SS community. 

I have tried to replicate how SS estimates MSY benchmarks (Fmsy, SSB_MSY, etc) in R with simple SS models. I succeeded sometimes but failed some others, depending on the SS parameters (e.g., steepness), and I cannot find the reason for the failures. I suspect it has something to do with the shape of the SPR/YPR curve (any kind of 'correction'?).

I have tracked the SS_benchfore.tpl file, and the Do_Equil_Calc and Equil_Spawn_Recr_Fxn functions, and coded part of them in R to estimate MSY on my own.

I have tried two examples. For both, I always get the same values as in the SPR/YPR_Profile table in the Report.sso for SRloop == 0, 1, or 2. However, in some cases, the estimated MSY quantities are different. Some more details are below.

Example 1: I managed to get the same MSY estimates as in SS when steepness <= 0.8. When steepness > 0.8, I can get the same values in the SPR/YPR_Profile, but the MSY quantities differ.

Example 2: I always got the same MSY estimates regardless of the steepness value.

You can find the inputs files and Report.sso here: https://github.com/GiancarloMCorrea/SS_examples_MSY

I would appreciate any insights on this. Thanks!

--

Giancarlo M. Correa, PhD

Personal Website

[Richard Methot - NOAA Federal]

Hi Giancarlo,

I think I can explain what is happening.

As steepness gets larger and/or as right-shifted selectivity protects a large fraction of the SSB from F, the search for FMSY will go towards higher F.  When I look at the warning.sso for the h=0.9 run, I see these two lines which are an indication of the problem:

Warning 1 : poor convergence in Fmsy, final dy/dy2= -0.284552
Warning 2 : Fmsy.mey is close to max allowed; check for convergence 

Those warning lines do not appear in the h=0.8 run.

It was a good idea for you to compare the Fmsy estimate to the SPR/YPR profile.  When I do that, I see a good match when h=0.8 and the profile has a well-defined maximum.

But with h=0.9, the profile is quite flat in the region F=2 to F=3.  That is why the FMSY iterative search is reporting poor convergence.

The Fmsy search itself can be seen in forecast-report.sso.  This is not a user-friendly report and not read into r4ss, but it does contain more detain on the benchmark iterative searches and then the forecast.

There you can see that SS3 searches over a fixed number (20) of iterations for MSY.  Look under "find_Fmsy_to_maximize_dead_catch".  It shows a reasonably negative curvature for the search, but the gradient at iteration 20 is not near zero, so SS3 reports poor convergence.

You'll also see that SS3 starts the FMSY search at the final F from the search that produces the target SSB/SSBzero, which you have set to 0.4.  That F value is 0.61.  So perhaps if you set the target SSB/SSBzero to a smaller value like 0.25, then the FMSY search will begin at a larger F and have a better chance of reaching convergence.

I hope this helps explain the results you are seeing.

Rick

[Giancarlo M. Correa]

Thanks a lot, Rick. This makes sense. I will be careful with those poor convergence situations.