Plot: Beverton-Holt stock-recruitment

[grinnellm]

Here's what I have so far, plotting MPDs for AM2 only, spawning biomass vs recruitment. Still needs the lines.

[grinnellm]

On that note, are the Bev-Holt parameters saved somewhere?

[Shawkshaw]

These should all be in the iscam.rep file so kappa beta ro

[jaclyncleary]

The function I used in my old R code:

plot.curve <- function(sbo, clr) { st=seq(0, max(sbt, sbo), length=100) #correct, sbo if(rectype==1) {

Beverton-Holt

            rrt=kappa*ro*st/(sbo+(kappa-1)*st)*exp(-0.5*tau^2)  
        }
        if(rectype==2)
        {
            #Ricker
            rrt=kappa*ro*st*exp(-log(kappa)*st/sbo)/sbo *exp(-0.5*tau^2) 
        }
        lines(st, rrt, col=clr)
        ro=ro*exp(-0.5*tau^2)
        points(sbo, ro, pch="O", col=clr, cex=1.25)
        points(sbo, ro, pch="+", col=clr, cex=1.25)
    }
    plot.curve(sbo, clr=4);     
    print("blue curve and blue circle+= sbo per SSB")

[grinnellm]

Hmm, I must be missing something, sorry. Can you spell it out for me? The BH equation above: rrt=kapparost/(sbo+(kappa-1)st)exp(-0.5tau^2) looks like it's missing some punctuation? Can you write it with so, kappa, beta, and ro?

[grinnellm]

Nope, I think I have it.

[grinnellm]

[jaclyncleary]

great. we'll make an assessment biologist out of you yet :)

[jaclyncleary]

Matt- Just double checking with you on eqns, that you plotted: xx = sbt[1:(length(yr)-min(age))] yy = rt

[grinnellm]

You mean that I omitted the first two years of Recruits?

[jaclyncleary]

that you omit the first two years of sbt. the rt vector is already 2 years shorter than sbt. basically we don't have rt values to match with sbt_1951 and sbt_1952 because we would have had to observe them in 1959 and 1950.

[grinnellm]

You got it - I omitted the first two years of rt and sbt, so I use years 1953 to 2017. I just want to confirm my equation is correct (assessment biologist in training). I extract the following variables from the iscam.rep file:

• so (not used -- is that correct?)
• kappa
• beta
• ro
• sbo

And then I calculate Recruitment as

• Recruitment = kappa ro Abundance / (sbo + (kappa - 1) Abundance) exp(-0.5 * beta^2)

where Abundance is sbt from the iscam.rep file. Is that correct?

[jaclyncleary]

I think we're saying the same thing. For the points: plot the vector of rt values (vector length is 65 representing 1953-2017) on the y-axis against sbt [1953-2017] from iscam.rep file, removing the first two values of the sbt vector.

Then for the BH curve, use the equation as you've written but use tau in the last term. Ie, exp(-0.5 tau^2) yes abundance == sbt from iscam.rep, and tau is also in the iscam rep file.

Can you also please add a symbol to show sbo vs. ro (both from iscam.rep)?

In looking at my old code, I see the following equation used in the plotting of ro: ro=roexp(-0.5tau^2)

@Shawkshaw - do you know why/ what this adjustment to ro represents?

Add to caption: symbol x corresponds to the MPD estimate of unfished spawning biomass (SB0) and unfished age-2 recruitment R0

[grinnellm]

[grinnellm]

Getting closer:) Triangles represent MPD of SB_0 vs R_0. Is that the bias correction for the log-transformed data?

[jaclyncleary]

perhaps eh? In the old figs, the "triangles represent MPD of SB_0 vs R_0" fall directly on the line.

[grinnellm]

Yes, I thought it would be on the line too -- might be bug somewhere? This is the current equation:

• Recruitment = kappa ro Abundance / (sbo + (kappa-1) Abundance) exp(-0.5 * tau^2)

[jaclyncleary]

the equation is correct. let's see if @Shawkshaw has something to add :)

[jaclyncleary]

@Shawkshaw - clarification: the ro=ro*exp(-0.5tau^2) changes the triangle in the figs so that it's on the line, and I'm not sure why (i.e., what this equation represents, except that Steve did it...)

[Shawkshaw]

Jaclyn, I can't seem to find any reference to this particular equations but if you look at this parameterization of the B-H model Rt=(soBt-k/(1+betaBt-k))exp(residuals-0.5tau^2) and the parameterization of the equation we are using Rt = k ro Bt / (sbo + (k-1) Bt) exp(-0.5 * tau^2) he set the equation up for estimating unfished recruits (ro) by setting everything but the process error (tau) at 0 ...

[grinnellm]

Can we close this? The MPD points are not on the lines in the current version -- is that how you want it @jaclyncleary ? It's easy to apply the correction (above) to put them on the lines if you prefer.

[jaclyncleary]

let's leave them as-is. I don't actually know whether they are supposed to be on the line or not...