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Case Study: Bering Sea and Aleutian Islands Northern Rock Sole

ac_bsai_northern_rock_sole_case_study.Rmd

Overview

This case study reproduces the 2024 Bering Sea and Aleutian Islands northern rock sole assessment, Model 24.2, in SPoRC. The assessment runs on the flatfish model fm.tpl.

The model is single region, single season, two sex, with one fishery fleet and one survey:

Source Years Observations Likelihood
Catch 1975–2024 50 Lognormal, weight 300
Bottom trawl survey biomass 1982–2024 42 Lognormal
Fishery age compositions 1979–2023 42 Multinomial, joint across sexes
Survey age compositions 1979–2023 44 Multinomial, joint across sexes

Ages run a=1a = 1 to a+=20a_{+} = 20, the plus group, and years y1=1975y_{1} = 1975 to yend=2024y_{\text{end}} = 2024. Both surveys’ 2020 year is absent, so the index and the compositions each skip it.

Two sexes is what makes this assessment different from the other single region case studies here, and it shows up in four places.

Natural mortality is sex specific and estimated, Mf=0.192M_{f} = 0.192 and Mm=0.226M_{m} = 0.226, with a lognormal prior on the female’s only.

Initial numbers at age are free and estimated separately for each sex. The assessment writes

Ny1,a,s=12exp⁡(log⁡Ninit¯+ϵa,sinit)a=2,…,a+N_{y_{1},a,s} = \tfrac{1}{2}\exp\left(\overline{\log N^{\text{init}}} + \epsilon^{\text{init}}_{a,s}\right) \qquad a = 2, \ldots, a_{+}

so one level log⁡Ninit¯\overline{\log N^{\text{init}}} is shared and each sex has its own deviations ϵa,sinit\epsilon^{\text{init}}_{a,s}. Those deviations are penalized about zero, and separately the two sexes are compared to each other by ∑a(ϵa,minit−ϵa,finit)2\sum_{a}(\epsilon^{\text{init}}_{a,m} - \epsilon^{\text{init}}_{a,f})^{2}. The penalty is a statement about how far apart the sexes’ initial age structures may sit, which is not the same statement as how variable each one is: initial numbers at age hold the exploitation the stock had already seen before y1y_{1} as well as year-class strength, and with sex specific selectivity and mortality the two sexes need not have departed from equilibrium by the same amount.

Fishery selectivity is logistic in both parameters of both sexes, varying annually, with the male curve scaled by a constant:

Sely,a,fFsh=11+exp⁡[−kfeδy,fk(a−af50eδy,f50)]Sely,a,mFsh=eγ1+exp⁡[−kmeδy,mk(a−am50eδy,m50)]\text{Sel}^{\text{Fsh}}_{y,a,f} = \frac{1}{1 + \exp\left[-k_{f}e^{\delta^{k}_{y,f}}\left(a - a^{50}_{f}e^{\delta^{50}_{y,f}}\right)\right]} \qquad \text{Sel}^{\text{Fsh}}_{y,a,m} = \frac{e^{\gamma}}{1 + \exp\left[-k_{m}e^{\delta^{k}_{y,m}}\left(a - a^{50}_{m}e^{\delta^{50}_{y,m}}\right)\right]}

with γ\gamma (male_sel_offset) estimated at −0.110-0.110, so the male curve tops out at eγ=0.895e^{\gamma} = 0.895 rather than one. Survey selectivity is time invariant and its male parameters are multiplicative offsets on the female’s, km=kfeδkk_{m} = k_{f}e^{\delta_{k}} and am50=af50eδ50a^{50}_{m} = a^{50}_{f}e^{\delta_{50}}.

Both curves stop at age 17. The assessment’s nselages evaluates the logistic through age 17 and holds ages 18 to 20 at the age-17 value. That is not cosmetic here: in years where the estimated slope is shallow the curve has not saturated by 17, and evaluating it smoothly instead moves total biomass by about two percent.

Recruitment is a mean with annual deviations and a Ricker curve is fitted as a penalty on the residual over 1978 to 2018, never generating recruitment.

library(SPoRC)
data(sgl_rg_bsai_nrs_data)
dat <- sgl_rg_bsai_nrs_data
yrs <- dat$years
n_yrs <- length(yrs)
n_ages <- length(dat$ages)
n_sexes <- dat$n_sexes
n_srv <- dat$n_srv_fleets
mle <- dat$mle
i_srv <- match(dat$yrs_srv, yrs)

Model dimensions

Single region, single season and single population, so those subscripts collapse to one and are dropped throughout. The sex subscript does not.

The survey enters as two fleets. The assessment reads its index in July and its compositions on January 1, off one selectivity curve. Two fleets sharing a curve is how that is written: fleet 1 holds the index at tsrv=(7−1)/12t^{\text{srv}} = (7 - 1)/12, fleet 2 holds the compositions at tsrv=0t^{\text{srv}} = 0 (inconsistent in the flatfish model).

input_list <- Setup_Mod_Dim(
  years = yrs,
  ages = dat$ages,
  lens = NA,
  n_regions = dat$n_regions,
  n_sexes = dat$n_sexes,
  n_fish_fleets = dat$n_fish_fleets,
  n_srv_fleets = dat$n_srv_fleets,
  n_seas = dat$n_seas,
  n_pop = dat$n_pop,
  natal_region = dat$natal_region,
  verbose = FALSE
)

Recruitment and the initial age structure

Recruitment is a mean with deviations, and the Ricker appears in the objective only through the residual χy=log⁡Ry−log⁡R̂y\chi_{y} = \log R_{y} - \log \widehat{R}_{y}. That is rec_model = "mean_rec" with sr_penalty = "ricker".

The assessment parameterizes its curve as R=ASe−BSR = A S e^{-BS}. SPoRC writes the Ricker in depletion form, R=R0(S/S0)exp⁡(α(1−S/S0))R = R_{0}(S/S_{0})\exp\left(\alpha\left(1 - S/S_{0}\right)\right) with α=log⁡(4h/(1−h))\alpha = \log(4h/(1-h)), and the two are the same curve at α=log⁡(Aϕ0)\alpha = \log(A\phi_{0}) and R0=α/(Bϕ0)R_{0} = \alpha/(B\phi_{0}), where ϕ0\phi_{0} is unfished female spawning biomass per recruit at the reference year. Both are estimated here, so the conversion supplies starting values rather than fixed ones.

Initial numbers at age are free (init_age_strc = 4), estimated per sex (InitDevs_sex_spec = "est_all"), sharing one level (InitDevs_pen_center = "own_mean"), and compared to each other (Use_init_sex_pen = 1).

inv_steepness <- function(s) qlogis((s - 0.2) / 0.8)

# The Ricker conversion, evaluated at the assessment's own M and terminal
# biologicals
Nspr <- numeric(n_ages)
Nspr[1] <- 0.5
for(a in 2:n_ages) Nspr[a] <- Nspr[a-1] * exp(-mle$M_f)
Nspr[n_ages] <- Nspr[n_ages] / (1 - exp(-mle$M_f))
phi0 <- sum(Nspr * exp(-dat$t_spawn * mle$M_f) * dat$WAA[1,1,n_yrs,1,,1] * dat$MatAA[1,1,n_yrs,1,,1])
a_sr <- log(exp(mle$R_logalpha) * phi0)
h_sr <- exp(a_sr) / (4 + exp(a_sr))
sr_R0 <- a_sr / (exp(mle$R_logbeta) * phi0)

input_list <- Setup_Mod_Rec(
  input_list = input_list,
  rec_model = "mean_rec",
  rec_lag = 1,
  SR_ref_yr = n_yrs,
  sr_penalty = "ricker",
  sr_pen_sigma = dat$sr_pen_sigma,
  sr_pen_yrs = dat$sr_pen_yrs,
  sr_R0_spec = "est",
  steepness_h = array(inv_steepness(h_sr), dim = c(1, 1)),
  h_spec = "est_shared_pop_r",
  ln_sr_R0 = array(log(sr_R0), dim = 1),
  do_rec_bias_ramp = 1,
  bias_year = rep(n_yrs + 1, 4),
  sigmaR_switch = 1,
  sigmaR_spec = "fix",
  ln_sigmaR = array(log(dat$sigmaR), dim = c(2, 1, 1)),
  RecDevs_pen_center = "fixed",
  dont_est_recdev_last = 0,
  init_age_strc = 4,
  equil_init_age_strc = 2,
  InitDevs_spec = NULL,
  InitDevs_sex_spec = "est_all",
  InitDevs_pen_center = "own_mean",
  Use_init_sex_pen = 1,
  init_sex_pen_sigma = dat$sigmaR,
  ln_global_R0 = mle$mean_log_rec,
  t_spawn = dat$t_spawn,
  use_rinit = 0
)

init_age_strc = 4 projects no equilibrium at all: the deviations are the initial numbers themselves rather than multipliers on an equilibrium, which is what the assessment estimates. Under that option the deviations are log abundances, so the penalty on them is a prior on log abundance directly.

InitDevs_sex_spec = "est_all" gives each sex its own curve. Pairing it with InitDevs_pen_center = "own_mean" pools the center over every penalized cell across both sexes, so the sexes share one estimated level. That is stationary at the same point as the assessment, whose shared log⁡Ninit¯\overline{\log N^{\text{init}}} forces the pooled deviations to sum to zero at its own estimate.

Use_init_sex_pen adds the likelihood penalty between the sexes. A sum of squares with weight one corresponds to σ=1/2\sigma = 1/\sqrt{2}, which is dat$sigmaR here.

The recruitment deviation penalty is a sum of squares about zero. Turning the bias ramp on with every break past the last year is what centers it there; do_rec_bias_ramp = 0 would instead hold the ramp at one and center the penalty on −σR2/2-\sigma_{R}^{2}/2.

Biological dynamics

Weight at age and maturity are year specific empirical inputs, and spawning biomass is female only, so the male slice of maturity is never read. Natural mortality is estimated by sex, with a lognormal prior on the female’s.

input_list <- Setup_Mod_Biologicals(
  input_list = input_list,
  WAA = dat$WAA,
  WAA_fish = dat$WAA_fish,
  WAA_srv = dat$WAA_srv,
  MatAA = dat$MatAA,
  AgeingError = dat$AgeingError,
  fit_lengths = 0,
  M_spec = "est_ln_M",
  M_popblk_spec = list(1),
  M_regionblk_spec = list(1),
  M_yearblk_spec = list(1:n_yrs),
  M_ageblk_spec = list(1:n_ages),
  M_sexblk_spec = list(1, 2),
  Use_M_prior = 1,
  M_prior = data.frame(popblk = 1, regionblk = 1, yearblk = 1, ageblk = 1, sexblk = 1,
                       mu = dat$m_prior$mu, sd = dat$m_prior$sd),
  addtocomp = 1e-3,
  comp_const_obs = 1,
  addtosrvidx = 0,
  addtofishidx = 0
)

M_sexblk_spec = list(1, 2) is what makes mortality sex specific: one block per sex, so two parameters. Every other block specification is a single group.

comp_const_obs = 1 puts the 0.001 constant on both sides of the multinomial likelihood (i.e., on the observed and predicted compositions).

Movement and tagging

Neither is used.

input_list <- Setup_Mod_Movement(input_list = input_list, use_fixed_movement = 1,
                                 Fixed_Movement = NA, do_recruits_move = 0)

input_list <- Setup_Mod_Tagging(input_list = input_list, use_conv_fish_tagging = 0)

Catch and fishing mortality

The assessment weights its catch likelihood by 300, which is a lognormal at σ=1/600\sigma = 1/\sqrt{600}.

input_list <- Setup_Mod_Catch_and_F(
  input_list = input_list,
  ObsCatch = dat$ObsCatch,
  UseCatch = dat$UseCatch,
  Use_F_pen = 0,
  ln_F_mean_spec = "fix",
  sigmaC_spec = "fix",
  ln_sigmaC = array(log(dat$sigmaC), dim = c(1, n_yrs, 1, 1))
)

The assessment has two weak penalties on fishing mortality, one pulling annual FF toward 0.2 and one forcing the mean deviation to zero. ln_F_mean_spec = "fix" does the same thing by fixing the mean, so the deviations have all of log⁡F\log F. Hoervrt, yhr first has no counterpart in SPoRC is left out.

Fishery compositions

Compositions are joint across sexes, females then males, so each year’s observation holds the sex ratio as well as the age structure.

input_list <- Setup_Mod_FishIdx_and_Comps(
  input_list = input_list,
  ObsFishIdx = array(NA, dim = c(1, n_yrs, 1, 1)),
  ObsFishIdx_SE = array(NA, dim = c(1, n_yrs, 1, 1)),
  UseFishIdx = array(0, dim = c(1, n_yrs, 1, 1)),
  ObsFishAgeComps = dat$ObsFishAgeComps,
  UseFishAgeComps = dat$UseFishAgeComps,
  ISS_FishAgeComps = dat$ISS_FishAgeComps,
  ObsFishLenComps = array(NA, dim = c(1, n_yrs, 1, length(input_list$data$lens), n_sexes, 1)),
  UseFishLenComps = array(0, dim = c(1, n_yrs, 1, 1)),
  ISS_FishLenComps = array(0, dim = c(1, n_yrs, 1, n_sexes, 1)),
  fish_idx_type = "none",
  FishIdx_LikeType = "lognormal",
  FishAgeComps_LikeType = "Multinomial",
  FishLenComps_LikeType = "none",
  FishAgeComps_Type = "spltRjntS_Year_1-terminal_Fleet_1",
  FishLenComps_Type = "none_Year_1-terminal_Fleet_1"
)

spltRjntS is the joint form: one multinomial over both sexes at once, which holds the sex ratio. The input sample size goes in the first sex’s slot, since the joint composition is one observation rather than two. There is no fishery index, so fish_idx_type = "none" with the use flags off; FishIdx_LikeType still has to name a family, and it is never evaluated.

Survey index and compositions

The index is on fleet 1 and the compositions on fleet 2.

input_list <- Setup_Mod_SrvIdx_and_Comps(
  input_list = input_list,
  ObsSrvIdx = dat$ObsSrvIdx,
  ObsSrvIdx_SE = dat$ObsSrvIdx_SE,
  UseSrvIdx = dat$UseSrvIdx,
  ObsSrvAgeComps = dat$ObsSrvAgeComps,
  UseSrvAgeComps = dat$UseSrvAgeComps,
  ISS_SrvAgeComps = dat$ISS_SrvAgeComps,
  ObsSrvLenComps = array(NA, dim = c(1, n_yrs, 1, length(input_list$data$lens), n_sexes, n_srv)),
  UseSrvLenComps = array(0, dim = c(1, n_yrs, 1, n_srv)),
  ISS_SrvLenComps = array(0, dim = c(1, n_yrs, 1, n_sexes, n_srv)),
  srv_idx_type = c("biom", "none"),
  SrvIdx_LikeType = rep("lognormal", n_srv),
  SrvAgeComps_LikeType = c("none", "Multinomial"),
  SrvLenComps_LikeType = rep("none", n_srv),
  SrvAgeComps_Type = c("none_Year_1-terminal_Fleet_1", "spltRjntS_Year_1-terminal_Fleet_2"),
  SrvLenComps_Type = paste0("none_Year_1-terminal_Fleet_", 1:n_srv),
  t_srv = array(dat$t_srv, dim = c(1, 1, n_srv))
)

The observed index standard errors go in on the log scale, converted from the assessment’s coefficients of variation by σ=log⁡(CV2+1)\sigma = \sqrt{\log(\text{CV}^{2} + 1)}.

Fishery selectivity and catchability 

input_list <- Setup_Mod_Fishsel_and_Q(
  input_list = input_list,
  fish_sel_model = paste0("logist1_Fleet_1_NSelBins_", dat$nselages),
  cont_tv_fish_sel = "iid_Fleet_1",
  fish_sel_blocks = "none_Fleet_1",
  fish_q_blocks = "none_Fleet_1",
  fish_fixed_sel_pars_spec = "est_all",
  fish_sel_devs_spec = "est_all",
  fish_sel_sex_offset = "scale",
  fishsel_pe_pars_spec = "fix",
  fish_q_spec = "fix"
)

Three things are named here.

_NSelBins_17 is the plateau. Bins beyond 17 are kept at bin 17’s value rather than evaluated through the logistic, which is the assessment’s nselages.

fish_sel_sex_offset = "scale" multiplies the male curve by an estimated constant eγe^{\gamma}. Each sex keeps its own a50a^{50} and kk; only the scale links them. The scaled curve is allowed above one, though here it sits below.

fishsel_pe_pars_spec = "fix" holds the deviation penalties at the assessment’s own standard deviations, 0.35 on a50a^{50} and 0.2 on the slope, for both sexes. The deviations are independent across years, which is cont_tv_fish_sel = "iid".

Survey selectivity and catchability 

input_list <- Setup_Mod_Srvsel_and_Q(
  input_list = input_list,
  srv_sel_model = paste0("logist1_Fleet_", 1:n_srv, "_NSelBins_", dat$nselages),
  cont_tv_srv_sel = paste0("none_Fleet_", 1:n_srv),
  srv_sel_blocks = paste0("none_Fleet_", 1:n_srv),
  srv_q_blocks = paste0("none_Fleet_", 1:n_srv),
  srv_fixed_sel_pars_spec = c("est_all", "est_shared_f_1"),
  srv_sel_sex_offset = rep("par", n_srv),
  srv_q_spec = c("est_all", "fix"),
  Use_srv_q_prior = 1,
  srv_q_prior = data.frame(region = 1, fleet = 1, block = 1,
                           mu = dat$q_prior$mu, sd = dat$q_prior$sd),
  t_srv = array(dat$t_srv, dim = c(1, 1, n_srv))
)

est_shared_f_1 on fleet 2 is what makes the composition fleet read the index fleet’s curve, so the two survey fleets are one gear seen at two times. Fleet 2’s catchability is fixed, since it has no index to scale. This is needed given the inconsistency with the survey timing with respect to when it observes the index and composition information (should be identical between the two data sources, but is not).

srv_sel_sex_offset = "par" is the other offset form: the male parameter slots hold offsets on the female’s rather than parameters of their own, so am50=af50eδ50a^{50}_{m} = a^{50}_{f}e^{\delta_{50}} and km=kfeδkk_{m} = k_{f}e^{\delta_{k}}, which is how the assessment writes them.

The catchability prior needs care. The assessment penalizes log⁡q\log q against log⁡1.5\log 1.5 at σ=0.2\sigma = 0.2, but it writes the penalty over a vector of qq with one element per survey year, so the same prior is accidentally counted 42 times. One parameter at σ=0.2/42\sigma = 0.2/\sqrt{42} holds the same information, which is what dat$q_prior$sd holds.

Weighting 

input_list <- Setup_Mod_Weighting(
  input_list = input_list,
  Wt_Catch = 1, Wt_FishIdx = 0, Wt_SrvIdx = 1,
  Wt_Rec = 1, Wt_Init_Rec = 1, Wt_F = 1, Wt_Tagging = 0,
  Wt_FishAgeComps = array(1, dim = c(1, n_yrs, 1, n_sexes, 1)),
  Wt_FishLenComps = array(1, dim = c(1, n_yrs, 1, n_sexes, 1)),
  Wt_SrvAgeComps = array(1, dim = c(1, n_yrs, 1, n_sexes, n_srv)),
  Wt_SrvLenComps = array(1, dim = c(1, n_yrs, 1, n_sexes, n_srv))
)

data <- input_list$data
parameters <- input_list$par
mapping <- input_list$map

Every weight is one. The assessment’s own weights are kept as standard deviations where they belong instead: the catch weight of 300 became σC\sigma_{C}, and the composition weights of one are the input sample sizes.

Starting at the assessment’s estimate

Every parameter is set to the assessment’s maximum likelihood estimate, and the objective is evaluated there before anything is optimized.

parameters$ln_F_mean[1,1,1] <- mle$log_avg_fmort
parameters$ln_F_devs[1,,1,1] <- mle$fmort_dev
parameters$ln_RecDevs[1,1,] <- mle$rec_dev

# free numbers at age absorb the assessment's shared mean_log_init
parameters$ln_InitDevs[1,1,,1] <- mle$mean_log_init + mle$init_dev_f
parameters$ln_InitDevs[1,1,,2] <- mle$mean_log_init + mle$init_dev_m

parameters$ln_M[1] <- log(mle$M_f)
parameters$ln_M[2] <- log(mle$M_m)
parameters$ln_srv_q[1,1,1] <- mle$ln_q

parameters$fish_fixed_sel_pars[1,1,1,1,1] <- log(mle$sel50_fsh_f)
parameters$fish_fixed_sel_pars[1,2,1,1,1] <- log(mle$sel_slope_fsh_f)
parameters$fish_fixed_sel_pars[1,1,1,2,1] <- log(mle$sel50_fsh_m)
parameters$fish_fixed_sel_pars[1,2,1,2,1] <- log(mle$sel_slope_fsh_m)
parameters$ln_fishsel_devs[1,,1,1,1] <- mle$sel50_devs_f
parameters$ln_fishsel_devs[1,,2,1,1] <- mle$slope_devs_f
parameters$ln_fishsel_devs[1,,1,2,1] <- mle$sel50_devs_m
parameters$ln_fishsel_devs[1,,2,2,1] <- mle$slope_devs_m
parameters$ln_fishsel_sex_scale[1,1,2,1] <- mle$male_sel_offset
parameters$fishsel_pe_pars[1,1,,1] <- log(dat$a50_sigma)
parameters$fishsel_pe_pars[1,2,,1] <- log(dat$slp_sigma)

# The two survey fleets share these through the map, and a collapsed parameter
# starts at the mean of its cells, so both fleets hold the value.
for(sf in 1:n_srv) {
  parameters$srv_fixed_sel_pars[1,1,1,1,sf] <- log(mle$sel50_srv)
  parameters$srv_fixed_sel_pars[1,2,1,1,sf] <- log(mle$sel_slope_srv)
  parameters$srv_fixed_sel_pars[1,1,1,2,sf] <- mle$sel50_srv_m
  parameters$srv_fixed_sel_pars[1,2,1,2,sf] <- mle$sel_slope_srv_m
} # end sf loop

seed <- fit_model(data, parameters, mapping, do_optim = FALSE, silent = TRUE)

The following provides a comparison of the difference prior to optimization:

spawning biomass                 0.0044 %
recruitment                      0.0035 %
total biomass (January 1)        0.0037 %
predicted catch                  0.0004 %
fishery selectivity, both sexes  6.1e-16
survey selectivity, both sexes   4.4e-16

Those are the assessment’s own reported values, which print six significant digits, so the comparison is at the precision the files were written.

SPoRC writes each likelihood component as a proper density while the assessment drops normalizing constants, so the comparison subtracts exactly the constants the assessment omits:

Component SPoRC less constants Assessment Difference
Survey index 39.5985376517 39.598500 3.8×10−53.8\times10^{-5}
Catch 0.6064001814 0.606399 1.2×10−61.2\times10^{-6}
Fishery age compositions 1311.1426871787 1311.140000 2.7×10−32.7\times10^{-3}
Survey age compositions 105.4014222156 105.401000 4.2×10−44.2\times10^{-4}
Recruitment deviations 34.9402161182 34.940200 1.6×10−51.6\times10^{-5}
Initial age deviations 69.6462663837 69.646300 3.4×10−53.4\times10^{-5}
Initial age sex penalty 3.8347157423 3.834720 4.3×10−64.3\times10^{-6}
Stock-recruit penalty 45.8810127892 45.881000 1.3×10−51.3\times10^{-5}
Selectivity deviations 89.0529773910 89.052900 7.7×10−57.7\times10^{-5}
Catchability prior 3.7852767335 3.785280 3.3×10−63.3\times10^{-6}
Natural mortality prior 0.7504986404 0.750499 3.6×10−73.6\times10^{-7}

Every difference is at the assessment’s own print precision. The largest, the fishery compositions, is 2.7 thousandths on a component of 1311.

Fitting and comparison 

est <- fit_model(data, parameters, mapping, do_optim = TRUE, newton_loops = 3, silent = TRUE)
est$sdrep <- RTMB::sdreport(est, hessian.fixed = est$he(est$optim$par))

353 parameters against the assessment’s 405, the difference being the projection block the assessment estimates alongside the model. The objective falls from 1518.549 at the assessment’s estimate to 1518.543, and the gradient reaches 1.7×10−111.7\times10^{-11}.

Median Maximum
Spawning biomass 0.02 % 0.13 %
Recruitment 0.03 % 0.05 %
Quantity SPoRC Assessment
MM female 0.19163 0.19165
MM male 0.22569 0.22571
Survey catchability 1.6332 1.6329
Male fishery selectivity scale 0.89532 0.89542

Why the two differ

One penalty is left. The assessment adds 0.01∑y(Fy−0.2)20.01\sum_{y}(F_{y} - 0.2)^{2}, pulling every year’s fishing mortality toward 0.2. Its weight of 0.01 is σ≈7\sigma \approx 7 on the FF scale, which is a numerical stabilizer left over from the early estimation phases rather than a statement about fishing mortality, so SPoRC does not have it.

Adding it back closes the rest of the gap. With it the assessment’s estimate is stationary in SPoRC’s objective to better than the assessment’s own convergence level, the optimizer moves the objective by 4×10−114\times10^{-11}, and every quantity above matches to the digits the assessment reports. Without it, spawning biomass sits 0.02 percent from the assessment at the median and 0.13 percent in 1975.

Two constants remain and neither matters: the assessment adds 10−610^{-6} inside its catch logarithms and 10−310^{-3} to its Ricker prediction, worth 10−710^{-7} and 4×10−64\times10^{-6} objective units.