SSB with external wtatage: clarify inclusion of age 0 fish

[iantaylor-NOAA]

Figure out mismatch in SSB calculations for model shared by Iago Mosqueira in this VLab forums post.

[iantaylor-NOAA]

I replicated Iago's calculation for the Vendace model he shared (product of numbers at age in beginning of the year and wtatage input for fleet = -2 doesn't equal SSB in derived quantities) and also confirmed that there's no mismatch for the Pacific Hake. I will dig deeper tomorrow.

[Rick-Methot-NOAA]

We should test this after fixing wt-at-age updating per #138

[iantaylor-NOAA]

Thanks for the reminder to revisit this, @Rick-Methot-NOAA.

I just confirmed the same small mismatch using 3.30.18.
SSB_2019 reported in Report.sso is 8128
That same value calculated as the product of the beginning-of-year numbers at age from Report.sso and fecundity at age from wtatage.sso is 8216. Difference is only 1% but seems too large for rounding error. Difference is not present in hake model.

I'm re-assigning to you and will email you the associated files.

[Rick-Methot-NOAA]

This mismatch occurs because the external calculation erroneously uses the age 0 fish.
In this vendance example, the age 0 fish have tiny, but non-zero fecundity.
In the internal calc of SSB at beginning of the year, the age 0 fish do not yet exist, so are not included in the SSB.
In this annual model configuration, recruitment of age 0 fish then occurs immediately after the SSB is calculated.
These age 0 fish are in the N-at-age table output for the beginning of the year.
So, the external calculation is different and incorrect due to inclusion of the age 0 fish in the SSB.