[Feature]: Likelihood profiles for current depletion and current spawning biomass for two-area models

[BMC1986]

Describe the solution you would like.

From Brett Crisafulli in Western Australia

In a recent review of our stock assessments, Andre Punt notes that Stock Synthesis appears unable to construct likelihood profiles for current depletion and current spawning biomass for two-area models. The method we used for single-area models utilises a depletion fleet (special survey type 34) for the depletion profile and a Current Biomass fleet (special survey type 30) for the spawning biomass profile. We acknowledge the SS manual notes this approach is untested in multi-area models and may present challenges. Could we please ask the SS team to consider testing this feature for multi-area models.

Describe alternatives you have considered

NA

Statistical validity, if applicable

No response

Describe if this is needed for a management application

No response

Additional context

No response

[Rick-Methot-NOAA]

Hi Brett,
My recollection is that the SS3 calculations are correct, but with multiple areas there could be ambiguity in the result. Something like the depletion profile is for total SSB and with multiple areas the distribution of SSB between areas gives SS3 flexibility to adjust to the forced degree of depletion. Do you have an example that demonstrates the problem? Where in the manual did you find that comment?

Rick

[BMC1986]

Repsonse to Rick

Thanks for the clarification Rick,
An example that demonstrates the issue is our 2-area model for a tropical lutjanid (ReK2_250604_Simplified). We’d like to get area-specific likelihood profiles of final depletion.
Below is our area-specific relative biomass trends in each area. The values are similar at around 0.23.

The Bratio estimate for areas combined in the final year in the model (from report.sso DERIVED_QUANTITIES report:6), is:
Label Value StdDev
Bratio_2024 0.233001 0.0169819
I’ve tried to setup the process for deriving a likelihood profile for Area 1 using the depletion fleet approach as outlined in the Stock Synthesis manual.

#_fleetinfo
#_type surveytiming area units need_catch_mult fleetname
……
3 1 1 1 0 Depletion_Survey #_17

#_CPUE_data
#_year month index obs se_log
……..
1965 1 17 1 1e-04 #_39
2024 1 17 0.19648 1e-04 #_40

Above the 0.19648 value is the lowest final depletion value I profile over, which corresponds to the lower 95% confidence limit for the estimate of final depletion. I run 11 models with increasingly higher values for the 2024 final depletion estimate to get the profile.
This is my output, something is clearly wrong. We’d really appreciate your insights, and if what we are requesting is possible. If needed I can share you some input files directly.

The SS3 manual comment we were referring to is in section '7.10.0.1 Units'.

Cheers
Brett

[iantaylor-NOAA]

Hi Brett,
Thanks for sharing this case. Are you able to share the ReK2_250604_Simplified model input files? If you don't want them public, you could email nmfs.stock.synthesis@noaa.gov.

I've never actually run a profile with a depletion fleet, but I see it as a useful tool. However, I think you will need to account for the depletion index in the likelihood calculations to get the profile to make matches your expectation. That is, the blue line for index data includes a likelihood element which will increase as the 2024 fraction unfished diverges from 0.19648. If you were to subtract the contribution of fleet 17 from the index and total likelihoods, perhaps the minimum would occur at the point estimate of 0.233001?

[BMC1986]

Hi Ian,
Thanks for your suggestion about the subtracting the contribution of fleet 17.
I sort of understand the point about the depletion index affecting the likelihood calculations and will investigate how to account for it in the profile. The approach works fine for our single area models. I was thinking it had something to do with the depletion fleet only being pre-specified in one area.
Thanks again
Brett

[Rick-Methot-NOAA]

The depletion fleet is defined to use spawning biomass (SSB), so by definition it is summed over all the areas. If you want to profile on spawning biomass in just one area, then you could create a survey that occurs in that single area and give that survey a selectivity that matched the maturity ogive.

[iantaylor-NOAA]

I was confused when I suggested that the depletion index contributes to the likelihood. If things are working correctly, the index should be fit perfectly at each point in the profile, and have no contribution. That makes me think that either the profile is not converging or indeed something else is wrong. The likelihood for the model with depletion specified at the MLE estimate of Bratio_2024 should match the likelihood of the MLE with no depletion fleet and increase as a result of any changes from that value.

I'm also curious if fixing the RecrDist_GP_1_area_2_month_1 parameter and its annual deviations changes the results at all.

I'll try to explore more on this tomorrow.