Skip to contents

Case Study: Alaska Sablefish (Single Region)

e_single_region_sablefish_case_study.Rmd

Overview

This case study sets up the 2024 federal Alaska sablefish stock assessment in SPoRC and compares it against the operational ADMB model (tem.tpl). Unlike the eastern Bering Sea pollock case study, which is an exact bridge, this one is a close bridge: the population dynamics and most likelihood components correspond one to one, but a handful of conventions in tem.tpl have no counterpart in SPoRC and are deliberately not reproduced. Those are enumerated in Where the two models differ, and they are the reason the two trajectories are close rather than identical.

The 2024 assessment treats sablefish on an Alaska-wide scale, from the Bering Sea to the Eastern Gulf of Alaska, as a panmictic single-region model:

Dimension Value
Regions 1 (panmictic, Bering Sea through Eastern Gulf of Alaska)
Years 1960–2024
Ages 2–31 (30 age classes, plus group at 31)
Sexes 2 (female, male)
Fishery fleets 2 (fixed gear, trawl)
Survey fleets 3 (domestic longline, domestic trawl, cooperative Japanese longline)

Because the model is single region and single population, the pp, rr and τ\tau subscripts of the model equations all collapse to one and are dropped from the notation below. The sex subscript ss is retained, since sablefish is sex structured.

Everything the case study needs ships with the package in sgl_rg_sable_data.

library(SPoRC)
library(here)
library(RTMB)
library(ggplot2)
data("sgl_rg_sable_data")

dat <- sgl_rg_sable_data
n_yrs <- length(dat$years)
n_ages <- length(dat$ages)

Model dimensions

Setup_Mod_Dim builds the input list that every subsequent helper updates: a data list, a parameter list, and a mapping list. Note that years and ages are passed as indices rather than calendar values here, which is why the year vector runs 1:65 rather than 1960:2024.

input_list <- Setup_Mod_Dim(
  years = 1:length(dat$years),      # 1960-2024
  ages = 1:length(dat$ages),        # ages 2-31
  lens = seq(41, 99, 2),            # length bins
  n_regions = 1,
  n_sexes = dat$n_sexes,            # 1 = female, 2 = male
  n_fish_fleets = dat$n_fish_fleets, # 1 = fixed gear, 2 = trawl
  n_srv_fleets = dat$n_srv_fleets,
  n_pop = dat$n_pop,
  verbose = FALSE
)

Recruitment

Sablefish assumes no stock recruit relationship. Recruitment arises about a mean parameter μRec\mu^{\text{Rec}} with lognormal annual deviations, split evenly between the sexes:

Ny,a=1,s=μRecexp⁡(ϵyRec−σRec,y22by)ψs,ψs=0.5N_{y,a=1,s} = \mu^{\text{Rec}}\exp\left(\epsilon^{\text{Rec}}_{y} - \dfrac{\sigma^{2}_{\text{Rec},y}}{2}b_{y}\right)\psi_{s},\qquad \psi_{s} = 0.5

Two features of this expression have most of the setup. The first is σRec,y\sigma_{\text{Rec},y}, which is not constant: the assessment uses an early period value fixed at 0.40.4 and a late period value that switches on in 1976,

σRec,y={0.4,y<1976σReclate,y≥1976\sigma_{\text{Rec},y} = \begin{cases} 0.4, & y < 1976\\ \sigma^{\text{late}}_{\text{Rec}}, & y \geq 1976\end{cases}

which is sigmaR_switch together with sigmaR_spec = "fix_early_est_late". The late value is estimated here to follow the assessment, though in practice it is weakly informed and fixing it is the more defensible choice.

The second is byb_{y}, the Methot and Taylor (2011) bias correction ramp. It rises from zero over an early window, sits at its maximum through the data-rich period, and descends again as recent cohorts become poorly observed:

by={0,y<ystartbmaxy−ystartyfull−ystart,ystart≤y<yfullbmax,yfull≤y<ylastbmax(1−y−ylastyend−ylast),y≥ylastb_{y} = \begin{cases} 0, & y < y^{\text{start}}\\ b^{\max}\dfrac{y - y^{\text{start}}}{y^{\text{full}} - y^{\text{start}}}, & y^{\text{start}} \leq y < y^{\text{full}}\\ b^{\max}, & y^{\text{full}} \leq y < y^{\text{last}}\\ b^{\max}\left(1 - \dfrac{y - y^{\text{last}}}{y^{\text{end}} - y^{\text{last}}}\right), & y \geq y^{\text{last}} \end{cases}

The four breakpoints are supplied through bias_year. These are indexed in deviation-index space, not calendar years. Passing calendar years leaves every range empty and silently gives by=0b_{y} = 0 throughout, which removes the bias correction without any warning.

Initial age structure is a geometric series (init_age_strc = 1) depleted by a historical fishing mortality:

Na,s′=μRecexp⁡(−(a−1)Za,s′+ϵaInit−σRec22b)ψs,Za,s′=Ma,s+FInitSela,s,f=1FshN^{'}_{a,s} = \mu^{\text{Rec}}\exp\left(-(a-1)Z^{'}_{a,s} + \epsilon^{\text{Init}}_{a} - \dfrac{\sigma_{\text{Rec}}^{2}}{2}b\right)\psi_{s},\qquad Z^{'}_{a,s} = M_{a,s} + F^{\text{Init}}\,\text{Sel}^{\text{Fsh}}_{a,s,f=1}

with the plus group accumulated as a closed geometric sum. The 2024 assessment builds its historical rate as hist_hal_prop * exp(log_avg_F_fish1), a fixed proportion of the fixed-gear mean fishing mortality, which is exactly init_F_form = "prop" with init_F_spec = "fix":

FInit=logit−1(θInit)exp⁡(μf=1Fsh),logit−1(θInit)=0.1F^{\text{Init}} = \text{logit}^{-1}\left(\theta^{\text{Init}}\right)\exp\left(\mu^{\text{Fsh}}_{f=1}\right),\qquad \text{logit}^{-1}\left(\theta^{\text{Init}}\right) = 0.1

The "prop" form matters: because FInitF^{\text{Init}} moves with μFsh\mu^{\text{Fsh}}, a single parameter both depletes the initial age structure and scales the F series. This is the assessment’s own construction, so it is reproduced here, but "abs" is the better choice when a model’s historical F is conceptually independent of the mean F of the modeled period.

input_list <- Setup_Mod_Rec(
  input_list = input_list,
  rec_model = "mean_rec",
  do_rec_bias_ramp = 1,
  # bias_year is in DEV-INDEX space, not calendar years. The four breakpoints
  # are the start of the ascending limb, the start of full correction, the start
  # of the descending limb, and the last estimated deviation.
  bias_year = c(length(1960:1979),
                length(1960:1989),
                (length(1960:2023) - 5),
                length(1960:2024) - 2) + 1,
  sigmaR_switch = as.integer(length(1960:1975)),
  ln_sigmaR = array(log(c(0.4, 1.2)), dim = c(2, input_list$data$n_pop, input_list$data$n_regions)),
  sigmaR_spec = "fix_early_est_late",
  dont_est_recdev_last = 1,
  init_age_strc = 1,
  # hist_hal_F is a fixed proportion of the fixed-gear mean F in tem.tpl
  init_F_form = "prop",
  init_F_spec = "fix",
  init_F_par = array(stats::qlogis(0.1), dim = c(input_list$data$n_regions,
                                                 input_list$data$n_seas,
                                                 input_list$data$n_fish_fleets))
)

Biological dynamics

Natural mortality is sex specific and fixed. The 2024 assessment estimates it under a lognormal prior, with males with an offset δM\delta^{M} from the female value, but that offset has no direct counterpart in SPoRC, so both values are fixed at the assessment’s estimates instead:

Ms={0.1134156,s=female0.1052175,s=maleM_{s} = \begin{cases} 0.1134156, & s = \text{female}\\ 0.1052175, & s = \text{male}\end{cases}

Spawning biomass is female only, evaluated at the spawning point within the year:

SSBy=∑aNy,a,s=1exp⁡(−tspawnZy,a,s=1)Wy,a,s=1Maty,a\text{SSB}_{y} = \sum_{a} N_{y,a,s=1}\exp\left(-t^{\text{spawn}}Z_{y,a,s=1}\right)W_{y,a,s=1}\,\text{Mat}_{y,a}

Composition data are fit as both ages and lengths, so a size-age transition matrix converts numbers at age to numbers at length, and an ageing error matrix smears the expected age compositions before they reach the likelihood.

fixed_natmort <- array(0, dim = c(input_list$data$n_pop,
                                  input_list$data$n_regions,
                                  n_yrs, n_ages, input_list$data$n_sexes))
fixed_natmort[,,,,1] <- 0.1134156 # female M
fixed_natmort[,,,,2] <- 0.1052175 # male M

input_list <- Setup_Mod_Biologicals(
  input_list = input_list,
  WAA = dat$WAA,
  MatAA = dat$MatAA,
  AgeingError = as.matrix(dat$age_error),
  SizeAgeTrans = dat$SizeAgeTrans,
  Use_M_prior = 0,
  fit_lengths = 1,
  M_spec = "fix",
  Fixed_natmort = fixed_natmort
)

Movement and tagging

The model is panmictic, so movement is an identity matrix and no tagging data are used. Both still have to be declared.

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 = rep(0, input_list$data$n_fish_fleets)
)

Catch and fishing mortality

Fishing mortality is a mean rate with annual deviations, and catch is fit lognormally:

log⁡Fy,f=μfFsh+ϵy,fF,ℓF=λF∑y∑f(ϵy,fF)22σF2\log F_{y,f} = \mu^{\text{Fsh}}_{f} + \epsilon^{F}_{y,f},\qquad \ell^{F} = \lambda^{F}\sum_{y}\sum_{f}\dfrac{\left(\epsilon^{F}_{y,f}\right)^{2}}{2\sigma_{F}^{2}}

The 2024 assessment writes both its catch and its F penalty as unweighted sums of squares, wt_ssqcatch * norm2(log(obs) - log(pred)) and wt_fmort_reg * norm2(log_F_devs). Setting σ=1/2\sigma = 1/\sqrt{2} makes 1/(2σ2)=11/(2\sigma^{2}) = 1, so SPoRC’s Gaussian form collapses to exactly that sum of squares and the assessment’s weights are reused unchanged as Wt_Catch = 50 and Wt_F = 0.1.

input_list <- Setup_Mod_Catch_and_F(
  input_list = input_list,
  ObsCatch = dat$ObsCatch,
  UseCatch = dat$UseCatch,
  Use_F_pen = 1,
  sigmaC_spec = 'fix',
  sigmaF_spec = "fix",
  # sigma = 1/sqrt(2) makes 1/(2 sigma^2) = 1, so the Gaussian reduces to the
  # assessment's unweighted norm2 and its lambdas transfer directly.
  ln_sigmaC = array(log(sqrt(1/2)), dim = c(input_list$data$n_regions, n_yrs,
                                            input_list$data$n_seas,
                                            input_list$data$n_fish_fleets)),
  ln_sigmaF = array(log(sqrt(1/2)), dim = c(input_list$data$n_regions,
                                            input_list$data$n_seas,
                                            input_list$data$n_fish_fleets))
)

Fishery index and compositions

Indices are fit lognormally. The 2024 assessment divides by the coefficient of variation rather than the standard error,

ℓIdx=λIdx∑y(logIyobs−logIypred)22CVy2,CVy=SEyIyobs\ell^{\text{Idx}} = \lambda^{\text{Idx}}\sum_{y}\dfrac{\left(\log I^{\text{obs}}_{y} - \log I^{\text{pred}}_{y}\right)^{2}}{2\,\text{CV}_{y}^{2}},\qquad \text{CV}_{y} = \dfrac{\text{SE}_{y}}{I^{\text{obs}}_{y}}

which is why the standard errors are passed as ObsFishIdx_SE / ObsFishIdx. Passing the raw standard errors instead would weight the index by a factor of IobsI^{\text{obs}} too many and effectively remove it from the fit.

Compositions are multinomial. Sablefish is sex structured but its age compositions are not sex specific, so fishery ages are aggregated across sexes (agg), meaning the expected proportions are summed over sexes before being compared to the observations. Length compositions are sex specific and are fit as spltRspltS, which normalizes each sex to sum to one separately, so no implicit sex ratio is inferred from them.

Only the fixed-gear fleet has an index and age compositions; both fleets have length compositions.

input_list <- Setup_Mod_FishIdx_and_Comps(
  input_list = input_list,
  ObsFishIdx = dat$ObsFishIdx,
  # tem.tpl divides by the CV, not the SE
  ObsFishIdx_SE = dat$ObsFishIdx_SE / dat$ObsFishIdx,
  UseFishIdx = dat$UseFishIdx,
  ObsFishAgeComps = dat$ObsFishAgeComps,
  UseFishAgeComps = dat$UseFishAgeComps,
  ISS_FishAgeComps = dat$ISS_FishAgeComps,
  ObsFishLenComps = dat$ObsFishLenComps,
  UseFishLenComps = dat$UseFishLenComps,
  ISS_FishLenComps = dat$ISS_FishLenComps,
  fish_idx_type = c("biom", "none"),
  FishAgeComps_LikeType = c("Multinomial", "none"),
  FishLenComps_LikeType = c("Multinomial", "Multinomial"),
  # ages aggregate over sexes; lengths are split by sex
  FishAgeComps_Type = c("agg_Year_1-terminal_Fleet_1",
                        "none_Year_1-terminal_Fleet_2"),
  FishLenComps_Type = c("spltRspltS_Year_1-terminal_Fleet_1",
                        "spltRspltS_Year_1-terminal_Fleet_2")
)

Survey indices and compositions

The three survey fleets are the domestic longline survey (abundance), the domestic trawl survey (biomass), and the cooperative Japanese longline survey (abundance). Age compositions are available for the two longline surveys and aggregate over sexes; length compositions are available for all three and split by sex. Surveys are timed halfway through the year, matching tem.tpl’s use of mid-year survival SmidS^{\text{mid}} in its predicted indices:

Iy,fpred=qf∑a∑sNy,a,sexp⁡(−0.5Zy,a,s)Sela,s,fSrvWy,a,sI^{\text{pred}}_{y,f} = q_{f}\sum_{a}\sum_{s} N_{y,a,s}\exp\left(-0.5\,Z_{y,a,s}\right)\text{Sel}^{\text{Srv}}_{a,s,f}\,W_{y,a,s}

input_list <- Setup_Mod_SrvIdx_and_Comps(
  input_list = input_list,
  ObsSrvIdx = dat$ObsSrvIdx,
  ObsSrvIdx_SE = dat$ObsSrvIdx_SE / dat$ObsSrvIdx,
  UseSrvIdx = dat$UseSrvIdx,
  ObsSrvAgeComps = dat$ObsSrvAgeComps,
  ISS_SrvAgeComps = dat$ISS_SrvAgeComps,
  UseSrvAgeComps = dat$UseSrvAgeComps,
  ObsSrvLenComps = dat$ObsSrvLenComps,
  UseSrvLenComps = dat$UseSrvLenComps,
  ISS_SrvLenComps = dat$ISS_SrvLenComps,
  srv_idx_type = c("abd", "biom", "abd"),
  SrvAgeComps_LikeType = c("Multinomial", "none", "Multinomial"),
  SrvLenComps_LikeType = c("Multinomial", "Multinomial", "Multinomial"),
  SrvAgeComps_Type = c("agg_Year_1-terminal_Fleet_1",
                       "none_Year_1-terminal_Fleet_2",
                       "agg_Year_1-terminal_Fleet_3"),
  SrvLenComps_Type = c("spltRspltS_Year_1-terminal_Fleet_1",
                       "spltRspltS_Year_1-terminal_Fleet_2",
                       "spltRspltS_Year_1-terminal_Fleet_3")
)

Fishery selectivity and catchability

The fixed-gear fleet is logistic, parameterized by the age at 50% selection and a slope:

Sela,s,f=1Fsh=11+exp⁡[−ks(a−as50)]\text{Sel}^{\text{Fsh}}_{a,s,f=1} = \dfrac{1}{1 + \exp\left[-k_{s}\left(a - a^{50}_{s}\right)\right]}

and has three time blocks, 1960–1994, 1995–2015, and 2016–2024, reflecting the shift from the pre-IFQ fishery through the IFQ era. Catchability is blocked on the same boundaries.

The trawl fleet is dome shaped, using the reparameterized gamma form in which amaxa^{\max} is the age at maximum selection and γ\gamma controls the steepness of the descending limb:

p=12[(amax)2+4γ2−amax],Sela,s,f=2Fsh=(aamax)amax/pexp⁡(amax−ap)p = \tfrac{1}{2}\left[\sqrt{\left(a^{\max}\right)^{2} + 4\gamma^{2}} - a^{\max}\right],\qquad \text{Sel}^{\text{Fsh}}_{a,s,f=2} = \left(\dfrac{a}{a^{\max}}\right)^{a^{\max}/p}\exp\left(\dfrac{a^{\max} - a}{p}\right)

Parameter sharing across sexes and blocks stabilizes the fit and cannot be expressed through the _spec arguments, so the map is set by hand afterwards. The first fixed-gear block shares its slope between sexes; the trawl fleet shares parameters across all blocks.

input_list <- Setup_Mod_Fishsel_and_Q(
  input_list = input_list,
  cont_tv_fish_sel = c("none_Fleet_1", "none_Fleet_2"),
  fish_sel_blocks = c("Block_1_Year_1-35_Fleet_1",
                      "Block_2_Year_36-56_Fleet_1",
                      "Block_3_Year_57-terminal_Fleet_1",
                      "none_Fleet_2"),
  fish_sel_model = c("logist1_Fleet_1", "gamma_Fleet_2"),
  fish_q_blocks = c("Block_1_Year_1-35_Fleet_1",
                    "Block_2_Year_36-56_Fleet_1",
                    "Block_3_Year_57-terminal_Fleet_1",
                    "none_Fleet_2"),
  fish_fixed_sel_pars_spec = c("est_all", "est_all"),
  fish_q_spec = c("est_all", "fix")
)

# share the slope across sexes in the early fixed-gear block
input_list$map$fish_fixed_sel_pars <- factor(c(1:7, 2, 8:11, rep(12:13, 3), rep(c(14, 13), 3)))

Survey selectivity and catchability

The domestic longline survey is logistic with two time blocks, split at 2016. The trawl survey uses a power function, a single-parameter descending form,

Sela,s,f=2Srv=1aϕs\text{Sel}^{\text{Srv}}_{a,s,f=2} = \dfrac{1}{a^{\phi_{s}}}

and the cooperative Japanese longline survey is logistic with its parameters fixed at the assessment’s values, since it ended in 1994 and is only weakly informed by the remaining data. Its slope parameters are shared with the domestic longline survey.

input_list <- Setup_Mod_Srvsel_and_Q(
  input_list = input_list,
  cont_tv_srv_sel = c("none_Fleet_1", "none_Fleet_2", "none_Fleet_3"),
  srv_sel_blocks = c("Block_1_Year_1-56_Fleet_1",
                     "Block_2_Year_57-terminal_Fleet_1",
                     "none_Fleet_2",
                     "none_Fleet_3"),
  srv_sel_model = c("logist1_Fleet_1", "exponential_Fleet_2", "logist1_Fleet_3"),
  srv_q_blocks = c("none_Fleet_1", "none_Fleet_2", "none_Fleet_3"),
  srv_fixed_sel_pars_spec = c("est_all", "est_all", "est_all"),
  srv_q_spec = c("est_all", "est_all", "est_all"),
  # tem.tpl predicts survey indices from mid-year survival
  t_srv = array(0.5, dim = c(input_list$data$n_regions,
                             input_list$data$n_seas,
                             input_list$data$n_srv_fleets))
)

# Longline survey slopes (indices 2 and 5) are shared across time blocks and
# with the cooperative Japanese survey, which estimates nothing of its own. The
# trawl survey's power function has a single parameter per sex (indices 7, 8).
input_list$map$srv_fixed_sel_pars <-
  factor(c(1:3, 2, 4:6, 5, rep(7, 4),
           rep(8, 4), rep(c(NA, 2), 2), rep(c(NA, 5), 2)))

# Cooperative Japanese survey logistic parameters, kept at the 2024 values
input_list$par$srv_fixed_sel_pars[1,,,1,3] <- c(0.980660760456, 0.9295241)
input_list$par$srv_fixed_sel_pars[1,,,2,3] <- c(1.22224502478, 0.8821623)

Weighting

Data sources have a λ\lambda weight that multiplies the whole component likelihood, on top of the observed standard errors and input sample sizes already supplied. For compositions these come from Francis reweighting; the values below are the 2024 assessment’s converged weights.

dim_comps <- function(n_fleets) {
  array(NA, dim = c(input_list$data$n_regions, n_yrs, input_list$data$n_seas,
                    input_list$data$n_sexes, n_fleets))
}

Wt_FishAgeComps <- dim_comps(input_list$data$n_fish_fleets)
Wt_FishAgeComps[1,,,1,1] <- 0.826107286513784   # fixed gear ages

Wt_FishLenComps <- dim_comps(input_list$data$n_fish_fleets)
Wt_FishLenComps[1,,,1,1] <- 4.1837057381917     # fixed gear lengths, female
Wt_FishLenComps[1,,,2,1] <- 4.26969350917589    # fixed gear lengths, male
Wt_FishLenComps[1,,,1,2] <- 0.316485920691651   # trawl lengths, female
Wt_FishLenComps[1,,,2,2] <- 0.229396580680981   # trawl lengths, male

Wt_SrvAgeComps <- dim_comps(input_list$data$n_srv_fleets)
Wt_SrvAgeComps[1,,,1,1] <- 3.79224544725927     # domestic longline ages
Wt_SrvAgeComps[1,,,1,3] <- 1.31681114024037     # cooperative Japanese ages

Wt_SrvLenComps <- dim_comps(input_list$data$n_srv_fleets)
Wt_SrvLenComps[1,,,1,1] <- 1.43792019016567     # domestic longline, female
Wt_SrvLenComps[1,,,2,1] <- 1.07053763450712     # domestic longline, male
Wt_SrvLenComps[1,,,1,2] <- 0.670883273592302    # domestic trawl, female
Wt_SrvLenComps[1,,,2,2] <- 0.465207132450763    # domestic trawl, male
Wt_SrvLenComps[1,,,1,3] <- 1.27772810174693     # cooperative Japanese, female
Wt_SrvLenComps[1,,,2,3] <- 0.857519546948587    # cooperative Japanese, male

input_list <- Setup_Mod_Weighting(
  input_list = input_list,
  Wt_Catch = 50,
  Wt_FishIdx = 0.448,
  Wt_SrvIdx = 0.448,
  Wt_Rec = 1.5,
  Wt_F = 0.1,
  Wt_Tagging = 0,
  Wt_FishAgeComps = Wt_FishAgeComps,
  Wt_FishLenComps = Wt_FishLenComps,
  Wt_SrvAgeComps = Wt_SrvAgeComps,
  Wt_SrvLenComps = Wt_SrvLenComps
)

Fitting

fit_model extracts the three lists and calls MakeADFun internally. The newton_loops argument takes additional Newton steps using the Hessian and gradient after the main optimizer converges, which serves as a convergence check as well as a refinement.

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

sabie_rtmb_model <- fit_model(data, parameters, mapping,
                              random = NULL, newton_loops = 3, silent = TRUE)

sabie_rtmb_model$sd_rep <- RTMB::sdreport(sabie_rtmb_model)

Comparison against the 2024 assessment

Because this is a single-population, single-region model, SSB and Rec are dimensioned npop×nr×nyn_{\text{pop}} \times n_{r} \times n_{y} and coerce to a vector directly.

ts_df <- rbind(
  data.frame(Par = "Spawning Biomass", Year = 1960:2024,
             RTMB = as.vector(sabie_rtmb_model$rep$SSB),
             ADMB = dat$admb_spbiom),
  data.frame(Par = "Recruitment", Year = 1960:2024,
             RTMB = as.vector(sabie_rtmb_model$rep$Rec),
             ADMB = dat$admb_recr)
)

ts_df$pct_diff <- 100 * (ts_df$RTMB - ts_df$ADMB) / ts_df$ADMB
Quantity Median difference Maximum difference
Spawning biomass 0.280.28 % 2.42.4 %
Recruitment 0.310.31 % 10.410.4 %

The joint negative log likelihood converges to 4411.994411.99 with a maximum absolute gradient of 6×10−126\times10^{-12}. The largest recruitment differences sit in individual strong year classes, where a small shift in a deviation moves that single year without moving the trajectory; spawning biomass, which integrates over ages, stays within 2.42.4 percent everywhere.

Where the two models differ

The 2024 assessment estimates a single log⁡M\log M under a lognormal prior and adds a male offset δM\delta^{M}, optionally with annual and age deviations. SPoRC parameterizes sex-specific natural mortality directly rather than as an offset, so an exact match to the prior structure is not available. Both values are therefore fixed at the assessment’s estimates, which removes MM from the comparison entirely rather than leaving it as an uncontrolled difference.

References

Francis, R.I.C.C. 2011. Data weighting in statistical fisheries stock assessment models. Canadian Journal of Fisheries and Aquatic Sciences 68: 1124–1138.

Methot, R.D., and Taylor, I.G. 2011. Adjusting for bias due to variability of estimated recruitments in fishery assessment models. Canadian Journal of Fisheries and Aquatic Sciences 68: 1744–1760.