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

Biological data {#sec-biological-data}

Natural mortality

Natural mortality was modeled as a single value for each sex applied across all ages within that sex with a Hamel-Then prior applied as in the previous assessments. However, whereas the 2017 assessment used a maximum age of 21 for in calculating the prior for both females and males, here the maximum age has been updated to match the 99.9 percentile of the approximately 9,000 ages for males and 30,000 ages for females in the \gls{pacfin} database to develop separate priors for males and females. Those percentiles are 18 years for females and 13 years for males. The number of ages available in the south model were too few to explore a separate maximum age calculation for that area.

The mean of the lognormal Hamel-Then prior is 5.4 divided by the maximum age, so the resulting prior means were r round(5.4/18, 3) for females and r round(5.4/13, 3) for males. The oldest aged r spp in the commercial fishery was 35 for females and 16 for males. No fish older than age 17 were seen in any of the surveys and the oldest fish landed by the recreational fleet was 23.

This represents a significant increase from the 0.257 mean used in the previous assessments for both sexes.

The log-scale standard error of the Hamel-Then prior is 0.438, so the the central 95\% of the resulting prior for female $M$ covered the range r round(qlnorm(p = 0.025, log(5.4/18), 0.438), 3) to r round(qlnorm(p = 0.975, log(5.4/18), 0.438), 3). The central 95\% of the resulting prior for male $M$ covered the range r round(qlnorm(p = 0.025, log(5.4/13), 0.438), 3) to r round(qlnorm(p = 0.975, log(5.4/13), 0.438), 3).

These values were at the upper end of the range of values estimated in previous studies. Jagielo [-@jagielo1994assessment] estimated $M$ for male and female r spp using three empirical models based on life-history parameters [@hoenig_empirical_1983; @alverson1975; @pauly1980]. Estimates of $M$ for male r spp ranged from 0.23 to 0.39, while estimates for female r spp ranged from 0.16 to 0.19. The averages of the estimates were 0.18 for females and 0.32 for males. Starr et al. [-@starr2005] estimated natural mortality rates from a short term tag-recapture study and came up with ranges of 0.24 to 0.34 for females and 0.13 to 0.23 for males. However, these estimates do not take into account variation in $M$ across the year (or between years), especially for males during nest-guarding.

Maturation and fecundity {#sec-biological-data-maturation-and-fecundity}

A new estimate of functional maturity-at-age (Figure \@ref(fig:bio6-maturity)) based on histological analysis of ovaries was developed for these models (pers. comm., M. Head, \gls{nwfsc}; Figure \@ref(fig:age-mat-forassessment)). The previous assessment [@haltuch2019lingcod] used length-based maturity but noted that differences in maturity at length between north and south areas appeared attributable to regional differences in growth. The estimated age at 50\% maturity was 3.23 for the north based on 327 samples for which both ovaries and age estimates were available and 2.74 years for the south based on 322 samples.

Sex ratio

The observed sex ratio by length confirmed that males grow to a smaller size than females and suggested that there are slightly more females in the population or that females are better sampled than males (Figure \@ref(fig:biology-sexratio-lengthfractionfemale)). The impact of nest guarding may be limiting the availability of males, but there is limited data to investigate this. A cursory look at length by latitude and sex using data from the \gls{s-wcgbt} suggested that males and females are equally dispersed coastwide (Figure \@ref(fig:biology-sexratio-lengthbylatitude)), and thus, a sex ratio of 50:50 was assumed for this assessment.

Length-Weight relationship {#sec-biological-data-Length-Weight-relationship}

The weight-length relationship for r spp was estimated outside of the assessment model by fitting biological data to the standard power function, $W = aL^b$. $W$ is weight in kilograms and $L$ is fork length in centimeters.

Spatial differences were investigated by comparing the residuals across latitude, region, and depth for a model that included the standard power relationship fit to all coastwide samples. Comparisons were made using Tukey's honestly significant difference test for pairwise multiple comparisons [@tukey1949]. Residuals of the fit between length and weight showed significant differences among latitude (p-value < 0.001, as a continuous variable) and among regions north and south of \CapeM (p-value < 0.001, as factors). The relationship between length and weight changed with depth (p-value = 0.02, as a continuous variable) but not when applying similar depth categories (55 - 183, 183 - 400, and >400 m) as was used to expand composition data (p-value = 0.16) or more refined depth categories (55 - 85, 85 - 110, 110 - 140, 140 - 183, and >183 m; p-value = 0.20).

The parameters of the weight-length relationship were re-estimated using data from the \gls{s-wcgbt}. Data included lengths and weights collected between 2003 and 2019 for r ifelse(params$area == "North", "7,869", "5,547") fish. Of these samples, r ifelse(params$area == "North", "4,978", "3,052") were female and r ifelse(params$area == "North", "2,805", "1,787") were male. These data resulted in the following estimates of the weight-length relationiship, r sprintf("$W=%1.9f * L^{%1.4f}$", ifelse(params$area == "North", lw.WCGBTS$North_NWFSC.Combo_F[1], lw.WCGBTS$South_NWFSC.Combo_F[1]), ifelse(params$area == "North", lw.WCGBTS$North_NWFSC.Combo_F[2], lw.WCGBTS$South_NWFSC.Combo_F[2])) for females and r sprintf("$W=%1.9f * L^{%1.4f}$", ifelse(params$area == "North", lw.WCGBTS$North_NWFSC.Combo_M[1], lw.WCGBTS$South_NWFSC.Combo_M[1]), ifelse(params$area == "North", lw.WCGBTS$North_NWFSC.Combo_M[2], lw.WCGBTS$South_NWFSC.Combo_M[2])) for males (Figure \ref{fig:len-weight}). These relationships are very similar to those used for the previous assessment [@haltuch2019lingcod]. Additionally, Hart [-@hart1967] reported the relationship between $W$ and $L$ as $log(W) = 3.6558 * log(L) - 9.4845$. Jagielo [-@jagielo1994assessment] reported $W = 0.000001760 * L^{3.3978}$ for females and $W = 0.000003953 * L^{3.2149}$ for males when fitting to mean weight-at-length as measured from data collected by the West Coast survey.

Growth (length-at-age)

A model based change-point analysis [@kapur2020] was used to identify a biologically relevant stock boundary using size-at-age data from the \gls{s-wcgbt} and r get_fleet("Lam", col="label_long") [@lam2021geographic]. A generalized additive model was fit to observed r spp lengths of a single age as the response variable. Predictor variables included a smoother for latitude. Each age-sex combination was analyzed separately. The first derivative was taken from the fitted spline to detect the latitude at which differences in size-at-age were most pronounced (i.e., the maximum absolute value) and statistically significant (i.e., where the confidence interval does not include 0). The resulting latitude was rounded to the nearest integer as there were no detectable differences when half-degrees were used. 77.8\% of significant age-sex combinations detected a break between latitudes $38^\circ 00^\prime$ and $40^\circ 00^\prime$ N (Figure \@ref(fig:Lam-kapurage7latitude)). This range is in agreement with the genetic break point identified for r spp by Longo et al. [-@longo2020strong].

r Spp display sexually dimorphic growth. Females grow faster and reach larger sizes than males. @jagielo1994assessment estimated growth using a fixed length at age 1 of 30 cm that resulted in estimates of $L_{\infty}$ for males of 93.21 cm and females of 131.05 cm and $k$ of 0.1694 for males and 0.1137 for females. He also found that the average length for age-0 fish, i.e., \gls{yoy}, r spp was 11.99 cm and for age-2 fish was 48.1 cm for Washington samples. Additionally, growth trajectories diverge considerably by sex after the age of three because female r spp tend to grow faster and live longer than male r spp. Male r spp mature at age three.

Estimates of growth parameters were investigated and starting values for model inputs were updated using the \gls{s-wcgbt} data. Spatial differences were investigated by fitting an overall von Bertalanffy relationship between age and length across all coastwide samples and then comparing the residuals across latitude and depth using Tukey's honestly significant difference test for pairwise multiple comparisons. Residuals of the fit between age and length showed significant differences among latitude (p-value < 0.001, as a continuous variable) and among regions north and south of \CapeM (p-value < 0.001, as factors). r Spp grow faster and attained a larger size north of \CapeM. The relationship between age and length changed with depth (p-value = 0.02, as a continuous variable), and unlike with the length-weight relationship, age and length fits varied by depth bins (p-value < 0.001). When applying similar depth categories (55 - 183, 183 - 400, and >400 m), as was used to expand composition data, patterns were not statistically distinguishable between shallow (55 - 183 m) and deep (>400 m) depths (p-value = 0.62) and mid (183-400 m) and deep depths (p-value = 0.24). When using more refined depth categories (55 - 85, 85 - 110, 110 - 140, 140 - 183, and >183 m), patterns were nearly not statistically distinguishable between shallow (<85 m) and mid-shallow (85-110 m) depths (p-value = 0.043) and were not statistically distinguishable between mid-deep (140-183 m) and deep (>183 m) depths (p-value = 0.84).

Externally estimated von Bertalanffy growth parameters for r spp using \Gls{s-wcgbt} data were as follows: r sprintf("$k = %.3f$ and $L_{\\infty} = %.3f$", ifelse(params$area == "North", la.WCGBTS$North_NWFSC.Combo_F[2], la.WCGBTS$South_NWFSC.Combo_F[2]), ifelse(params$area == "North", la.WCGBTS$North_NWFSC.Combo_F[1], la.WCGBTS$South_NWFSC.Combo_F[1])) for females and r sprintf("$k = %.3f$ and $L_{\\infty} = %.3f$", ifelse(params$area == "North", la.WCGBTS$North_NWFSC.Combo_M[2], la.WCGBTS$South_NWFSC.Combo_M[2]), ifelse(params$area == "North", la.WCGBTS$North_NWFSC.Combo_M[1], la.WCGBTS$South_NWFSC.Combo_M[1])) for males. These estimates were used as initial values within the base model for estimating growth. Samples used to generate these estimates include r ifelse(params$area == "North", "5,145", "3,910") age and length samples, of which r ifelse(params$area == "North", "3,290", "2,178") are female and r ifelse(params$area == "North", "1,795", "1,228") are male.

Ageing precision and bias

r Spp are aged using dorsal fin rays, which has been found to have the highest accuracy, readability, and minimal between-reader bias when compared to other ageing structures [e.g., @chiltonAgeDeterm; @cass1983first; @claiborne2016]. However, recent studies suggest that surface reads from otoliths may be comparable in terms of accuracy and readability. For this assessment, r spp samples from fishery-dependent and -independent sources were aged using the fin-ray method.

During the process of reading ages, the first and second annuli can be re-absorbed as the fish ages, obscuring early annulus rings and leading under-ageing. However, error can be minimized using known mean annular radii measurements for the first, second, and third annuli, as established by Beamish and Chilton [-@beamish1977age] and later validated by McFarlane and King [-@mcfarlane2001validity].

For this assessment, between-reader ageing error was determined using the nwfscAgeingError package [@nwfscAgeingError2008], which is publicly available at https://github.com/pfmc-assessments/nwfscAgeingError. This package implements the Punt et al. [-@punt2008quantifying] model. It calculates the likelihood of model parameters given an observed data set that includes age reads provided by multiple readers for a set of ageing structures. For each reader, two sets of parameters are estimated that define the standard deviation and bias of the reads provided by that reader. The set of parameters that best describes the standard deviation and bias between age readers is determined with a step-wise model-selection function and compared using \gls{aic}.

Initial explorations for seven different combinations of age readers showed little bias among readers. Therefore, all 2,441 double reads were pooled into a single analysis to estimate variability in age estimation (Figure \@ref(fig:ageing-double-reads)). The best fit model, as chosen by both \gls{aic} and \gls{bic}, used "Curvilinear CV" (a 3-parameter Hollings-form relationship of CV with true age). The standard deviation in estimated age was 0.24 years at age one, 0.56 years at age five, 1.1 years at age ten, and 1.65 years at age fifteen (Figure \@ref(fig:numbers10-ageerror-matrix-1)).

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