In iantaylor-NOAA/Lingcod_2021: Estimate the Status of Lingcod off the US West Coast in 2021

# read ss_summary.sso files for each area
vals.n <- file.path("..", "models",
                    info_basemodels[["North"]],
                    "ss_summary.sso") %>%
  r4ss::SS_read_summary()
vals.s <- file.path("..", "models",
                    info_basemodels[["South"]],
                    "ss_summary.sso") %>%
  r4ss::SS_read_summary()

# get M estimates for each area/sex
M.f.n <- vals.n[["parameters"]]["NatM_uniform_Fem_GP_1", "Value"] %>% as.numeric %>% round(3)
M.m.n <- vals.n[["parameters"]]["NatM_uniform_Mal_GP_1", "Value"] %>% as.numeric %>% round(3)
M.f.s <- vals.s[["parameters"]]["NatM_uniform_Fem_GP_1", "Value"] %>% as.numeric %>% round(3)
M.m.s <- vals.s[["parameters"]]["NatM_uniform_Mal_GP_1", "Value"] %>% as.numeric %>% round(3)

# unfished spawning and summary biomass 
smry.n <- vals.n[["derived_quants"]]["SmryBio_unfished","Value"] %>%
  as.numeric %>%
  round() %>% 
  format(., big.mark = ',')
smry.s <- vals.s[["derived_quants"]]["SmryBio_unfished","Value"] %>%
  as.numeric %>%
  round() %>% 
  format(., big.mark = ',')
SSB.n <- vals.n[["derived_quants"]]["SSB_unfished","Value"] %>%
  as.numeric %>%
  round() %>%
  format(., big.mark = ',')
SSB.s <- vals.s[["derived_quants"]]["SSB_unfished","Value"] %>%
  as.numeric %>%
  round() %>%
  format(., big.mark = ',')

# # catchability when calculated as a float is not 
# # available in ss_summary.sso
# Q.n <- mod.n$cpue$Eff_Q[mod.n$cpue$Fleet == 7][1]

The north and south models represent genetically distinct sub-populations of r spp and may differ in numerous ways. However, there are enough similarities in management, fisheries, and biology that some similarity across these stocks and the models used to represent them is to be expected. A fundamental challenge in fisheries stock assessment is understanding spatial variability among stocks and finding appropriate ways to share information across stocks [@punt101093/icesjms/fsr039]. The following section is intended to provide information regarding the evaluation of the plausibility of the estimates for the two areas.

Estimates of growth in the two areas match prior expectations for males with faster growth in the north relative to the south (Figure \@ref(fig:compare-north-vs-south-growth)), but females are estimated to growth to a slightly larger size in the south. The estimated variability in growth is smaller in the north compared to the south, which may reflect differences in biology or a greater spatial heterogeneity in growth in the south. Estimated growth in both areas use a reference age of 14 for mean length at age, <!-- manual update: Linf not available in SS_summary.sso r model$Growth_Parameters$Linf %>% round(1) %>% paste(collapse = " and ")

mod.2021.n.023.001$Growth_Parameters$Linf %>% round(1) [1] 118.7 77.5 mod.2021.s.018.001$Growth_Parameters$Linf %>% round(1) [1] 122.6 65.2 --> but the corresponding $L_\infty$ values are 118.7 and 77.5 for females and males respectively in the north and 122.6 and 65.2 in the south. The estimated length at age 14 in the north is more precise than in the south (Figure \@ref(fig:compare-north-vs-south-pars)), reflecting the larger volume of conditional age-at-length data include in the north model. Thus, the estimate of larger $L_\infty$ in the south is unlikely to be statistically significant.

Estimates of key productivity parameters (i.e., $M$ and $h$) differ significantly among the two areas, indicating that the southern stock is less productive than the northern stock (Figure \@ref(fig:compare-north-vs-south-pars)). Additionally, the north model estimates almost equal $M$ for females and males (r M.f.n and r M.m.n respectively), whereas the south model has a lower estimate of female $M$ than male $M$ (r M.f.s and r M.m.s). The $M$ estimates are uncertain in both models, although more so in the south than the north.

Estimates of unfished spawning biomass in the two areas are higher in the south than the north (r SSB.n mt and r SSB.s mt for north and south), but this comparison is misleading due to the differences in $M$ between areas resulting in a smaller fraction of recruits reaching spawning ages in the north than the south. The estimates of unfished age-3+ biomass are similar: r smry.n mt and r smry.s mt for the north and south (Figure \@ref(fig:compare-north-vs-south-quants)). The differences in estimated \glspl{msy} are larger than those for biomass because the lower estimates of $M$ and $h$ in the south equate to lower productivity relative to stock size.

There are no precise estimates for the amount of r spp habitat in either area, but a rough approximation can be found by calculating the spatial extent of the \gls{s-wcgbt} survey area between the 55 m inner limit and 300 m, a depth which represents a decline in frequency of r spp in that survey. By this measure, the ratio of north to south areas is about 2.3:1. Thus, the biomass estimates (Figure \ref{fig:sens-timeseries-north-vs-south}) are more closer to each other than would be expected had the densities been equal in the two areas. However, one must account for catchability and because the \gls{s-wcgbt} does not provide an absolute estimate of abundance with a non-trivial amount of habitat and biomass inside the 55 m isobath. The estimated catchability of the \gls{s-wcgbt} is similar among areas, 0.81 in the north and 0.95 in the south.

The differences in scale (Table \ref{tab:table-compare-north-vs-south}) among the two areas are less plausible when matching values are used for the productivity parameters (fixing female $M$ = 0.3 and $h$ = 0.7). In those sensititivity analyses, the estimated spawning biomass in the south model is greater than that of the north for almost all years from the 1940s onward and never falls below $B_{40\%}$. The catchability of the \gls{s-wcgbt} in those scenarios is likewise implausibly different: 2.05 in the north and 0.32 in the south Thus, the different parameter estimates (Table \ref{tab:table-compare-north-vs-south}) for the north and south play an important role in providing values for quantities of interest that are balanced among the two model, and likely provide better advice for managing the r spp lingcod stocks throughout the U.S. west coast.

iantaylor-NOAA/Lingcod_2021 documentation built on Oct. 30, 2024, 6:42 p.m.