clean up SPR-related definitions

[iantaylor-NOAA]

Notes in README related to SPR=100% should be Fishing Intensity = 100%, which corresponds to an SPR-target of 40%. Also, the Glossary definitions of B_spr=40% don't look right.

[iantaylor-NOAA]

Also previous commit was related to this issue: 8f2a943

[andrew-edwards]

See discussion from issue #158 . I just came across Ian's comment in the Exec Summary to remind us to look at that issue. The comment worked!

[andrew-edwards]

The comment in the text (and issue #158) suggests changing the definition of 'fishing intensity'. Interestingly, compare this year's Table d and Figure f with 2016 assessment version (and text at start of 'Exploitation Status' - the years with median fishing intensity > management target switch from being 2008 and 2010 last year, to just 1999 this year. Text is currently correct.

[iantaylor-NOAA]

I don't know if I resisted the language change before, but I think it would be fine to define (1-SPR)/(1-SPR_40%) as "Relative Fishing Intensity" and re-define "Fishing Intensity" as 1-SPR. Comparing Table d and Figure f across 2016 document and our new draft, they appear very similar, with 1999, 2008, and 2010 all close to the 100% line in both figures, but the relative positions shifted.

Looking at Table 11 in both docs, indicates that our new draft base model has the estimated spawning biomass for 1999, slightly increased, from 785 to 790, but the change in fishing intensity (status-quo definition) is a bit bigger than that, from 96.9% to 101.1%. That leads me to believe that the change in fishing intensity is influenced by changes in the estimated selectivity for that year. From Figure 26, it looks like our new estimate for 1999 selectivity is slightly dome-shaped with a peak at age 4, perhaps resulting in a higher estimated fraction of those newly-mature fish being exploited and a resultant decrease in their spawning potential.

[andrew-edwards]

I'll keep checking the Exec Summary (numbers etc. are correct and wording makes sense) but keeping the existing terminology from last year (else I'll get in a mess). Then we can go through in one go and change terminology and Glossary etc.

[aaronmberger-nwfsc]

agree with use of relative fishing intensity (1-SPR)/(1-SPR_40%) vs fishing intensity 1-SPR. Ian, this is something we should discuss in general with our assessment folks and maybe switch to in general (not just hake)

[iantaylor-NOAA]

Just committed cleanup of glossary as a894ace. It would probably be good to have everyone read the revised glossary text to see if it all makes sense now before closing this issue. I'm also working on a figure to better illustrate what SPR means.

[cgrandin]

That makes sense to me and it was a good idea to remove the old definitions. I went through the whole glossary and fixed a few errors, see commit 0d752d413fd39a8049319b3dae106af5318fe0ae.

[iantaylor-NOAA]

Thank you. Sorry for all the errors. I clearly didn't read through the edited version a final time. On question: is "DFO" really the acronym used for Fisheries and Oceans Canada, such that you don't need to separately define "FOC"? Also, would it makes sense to have a separate entry for "Fisheries and Oceans Canada" which DFO could just point to?

[cgrandin]

Yes. Apparently FOC sounds like another word which we are not supposed to say. I'll add an entry for Fisheries and Oceans Canada. I think it is referred to as that in the document several times.

[iantaylor-NOAA]

:+1: As far as I can tell, my agency hasn't yet figured out whether it's called "NMFS" or "NOAA Fisheries"

[iantaylor-NOAA]

I revised the existing figure in the appendix and added a new one in commit 373624e which is an attempt to illustrate how SPR is calculated. Feel free to edit or suggest changes. If this figure seems OK, we can close this issue.

[andrew-edwards]

Hopefully people agree with the equations I've added to the Glossary. I think it would be helpful to have them put together in a logical order somewhere - I may do it (Saturday or Sunday) at the end of the Glossary and then move after if appropriate. I'm finally seeing how it all fits together.....

[iantaylor-NOAA]

I just looked over each change you made to the glossary and I agree with everything. Thank you for making this glossary better. The additional equations are useful. Sorry we took so long to get to this point, but it will be useful for the future. I don't know that grouping them in one place is necessary but you're welcome to move stuff around as you wish.

One minor distinction that I'm not sure we need to make is that the the relationship between SPR and F depends on things like natural mortality and selectivity, so that you could have the same SPR associated with fishing hard on the oldest ages, or less hard on a larger set of ages, as long as the spawning potential got equally impacted. But I think writing SPR(F) as in equation A.5 is good for getting the point across that SPR is dependent on fishing effort.

[andrew-edwards]

Thanks. Good point. One thing - exploitation fraction is in terms of 3+ (in glossary and in document), which kind of seems a bit strange given so many age-2's were caught this year. So maybe should highlight that in the text somewhere (something like 'Note that exploitation fraction has traditionally been calculated in terms of fish age-3 and older, though in 2016 a large proportion of fish caught were age-2'. I'm done shortly, so haven't got time now to put that somewhere, just noting it here...

[andrew-edwards]

Andy to check SPR_40% type things in figures and captions and text.

[andrew-edwards]

SPR_40% might be used a bit so should maybe go back on. Even though it is just 0.4!

[andrew-edwards]

I'm done for today - may do a bit tomorrow night and Sunday. Ian's Figure A.2 really helps, and I can see how to clarify the spawning output definition. Cheers...

[andrew-edwards]

So, Figure A.2 and current SPR defn on p132 of Glossary suggests that 'Spawning output per recruit' is 'total female spawning biomass per recruit'. Bottom panel of Fig A.2 gives female spawning biomass per recruit for each age class, sum them up to get the total. Do that for fishing (dark grey) and no fishing (light grey), divide one by the other (as per SPR definition in equation A.5 and legend in figure) to give SPR.

Spawning output per recruit then equals total female spawning biomass per recruit. I think it would be clearer to define SPR in terms of 'total female spawning biomass per recruit', exactly as Ian has in Figure A.2. The current defn of spawning output is

"Spawning output: The total production of eggs (or possibly viable egg equivalents if egg quality is taken into account) given the number of females-at-age (and maturity- and fecundity-at-age)."

But, searching hake-assessment.tex, this is only used in: -- maturity section: "The resulting product of maturity and weight results in a relative spawning output of 0.10 at age 2, 0.25 at age 3, 0.40 at age 4, and 0.52 at age 5." [Defn may be correct wrt this sentence] -- Figure 37 (and it's y-axis) say 'spawning output', but tracking down the code Fig 37 is built with:

if (2 %in% subplots) {
    if (any(uncertainty)) {
        if (verbose) 
            cat("subplot 2: spawning biomass with uncertainty intervals\n")
        if (plot) 
            plotSpawnBio(show_uncertainty = TRUE)

which plots the spawning biomass. So this should be changed to spawning biomass.

So.... am I okay to change the occurrences of 'spawning output' in the glossary to 'total female spawning biomass', except for the actual definition of spawning output which seems to be related to the text in the maturity section? This would be much clearer to me (and Chris!), and be consistent with Ian's Figure A.2. I want to refer to Fig A.2 in the SPR definition, but it's confusing with the 'spawning output' definition not making much sense to me. And, this is consistent with the Agreement that talks about the 'biomass, on a per recruit basis'.

[andrew-edwards]

Meant to add that a quick Google search finds previous use of 'spawning output per recruit' to be 'per-capita spawning biomass'.

https://books.google.ca/books?id=kNc3AQAAMAAJ&pg=PA221&lpg=PA221&dq=spawning+output+fisheries&source=bl&ots=V2JXd5BcE-&sig=tuL-sXbJ8puAmI0OMu1bj0NWxg8&hl=en&sa=X&ved=0ahUKEwjEovL4q-jRAhVB7IMKHYOSC6AQ6AEIKzAC#v=onepage&q=spawning%20output%20fisheries&f=false

[iantaylor-NOAA]

Sorry for not chiming in on the spawning biomass vs. spawning output discussion before. Here's my current thinking on the subject.

I think we should replace "spawning output" everywhere it occurs with "spawning biomass" either in a "per recruit" context or not. "Spawning output" is a useful term, but I don't think we need it here.

"Spawning output" is best used for assessments where the spawning contribution is not proportional to mature female biomass. For instance, in the Yelloweye Rockfish assessment for the U.S. west coast, we used a relationships from E.J.Dick's thesis which estimated that a 10kg yelloweye produced about 4 times as many eggs as a 5kg fish. We therefore measured all things related to spawning, such as the B0 and B40% reference points, SPR, etc. in terms of numbers of eggs. Thus, "biomass" wasn't representative so we used "spawning output". I didn't make any of that up, I was just following in the footsteps of those who had done other assessments where eggs weren't proportional to biomass.

For hake, there are two issues at work that relate to the choice of language.

First, the first row of the wtatage function that we're using represents the combination of maturity and fecundity, and the fecundity is assumed to be proportional to biomass, but those values were calculated in 2011 using a growth curve and weight-length relationship that doesn't exactly match our current vector of weight at age. However, that's a pretty trivial detail and the INTENT was to have spawning contributions proportional to biomass, so I don't think that there's any need to use "spawning output".

Second, the SSplotComparisons function that we use for some of the time series plots has been configured to look for whether fecundity is assumed proportional to mature female biomass and label the y-axis as either "spawning biomass" or "spawning output". However, for models that use the empirical wtatage input rather than a parametric fecundity function, the function can't tell whether things are proportional or it defaults to "spawning output". However, this can be over-ridden and I will attempt to do so now.

I will also go ahead and change "spawning output" throughout the glossary to "spawning biomass".

[cgrandin]

Thanks for the explanation Ian. I was going to offer to change all the plots which have "spawning output" to "spawning biomass" but I see you have started that. I can do it in the morning if you have other stuff to do.

[iantaylor-NOAA]

Figures worked out with previous commit. I've just completed the conversion of a last few instances of "spawning output" to "spawning biomass". Thanks Aaron for all your work today. I haven't done much and this is it for me until the morning.

[aaronmberger-nwfsc]

Yep, I'm just building and sending off to Owen, then calling it an evening.

[iantaylor-NOAA]

I think this issue can be put to bed as well.