Redbanded Rockfish for the Pacific Coast of Canada: a DFO Case Study Operating model
Technical report for Fisheries and Oceans Canada
Quang Huynh, University of British Columbia [email protected]
February 2019
Introduction
This operating model was specified based on data and life history parameters from a stock assessment document:
No assessment fit was found to be acceptable for providing catch advice. Therefore, only input parameters, priors, and data were used as the basis for creating the operating model. Assessment output was not used. From the data, stochastic SRA was used to explore potential historical scenarios to generate historical parameters for this operating model.
Pacific Marine Fisheries Commission (PMFC) major areas (outlined in dark blue) compared with Groundfish Management Unit areas for RBR (shaded). The operating model is based on PMFC areas 3CD and 5ABCDE combined (termed “coastwide” in the assessment).
Redbanded rockfish specimen (image from Edwards et al. 2017).
Stochastic SRA (Walters et al. 2003) was used to provide probability distributions of historical effort, depletion, and productivity parameters (e.g., steepness) to inform those parameters of the operating model. Life history inputs include natural mortality, growth, and maturity.
The model used the reconstructed catch going back to 1940, as well as sporadic age composition and mean length observations from the commercial hook-and-line fleet (Edwards et al. 2017).
Overall, the stochastic SRA suggested that the current stock is lightly depleted. This is supported by the high frequency of age samples in the plus-group.
Reconstructed catch (landings and discards) of redbanded rockfish specimen (Figure A.1 in Edwards et al. 2017).
Length frequencies (blue bubbles) and mean lengths (green dots connected by red lines) (cm) from commercial trawl samples (Figure D.1 in Edwards et al. 2017).
Female age frequencies (black dots) from the commercial hook and line fishery. Red lines are predictions from the assessment model which was not considered for management use (Figure E.3 in Edwards et al. 2017).
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Sebastes babcocki
Common Name: Redbanded Rockfish
Management Agency: DFO
Region: British Columbia, Canada
Latitude: 48.1, 48.5, 54.6, 54.5
Longitude: -127, -125, -131, -135
OM Parameters
OM Name: Name of the operating model: Stock:Redbanded Rockfish Fleet: Obs model:Generic_Obs Imp model:Perfect_Imp
nsim: The number of simulations: 192
proyears: The number of projected years: 50
interval: The assessment interval - how often would you like to update the management system? 3
pstar: The percentile of the sample of the management recommendation for each method: 0.5
maxF: Maximum instantaneous fishing mortality rate that may be simulated for any given age class: 3
reps: Number of samples of the management recommendation for each method. Note that when this is set to 1, the mean value of the data inputs is used. 1
Source: A reference to a website or article from which parameters were taken to define the operating model
Data from 2014 Stock Assessment document
Stock Parameters
Mortality and age: maxage, R0, M, M2, Mexp, Msd
maxage: The maximum age of individuals that is simulated (there is no plus group ). Single value. Positive integer
Specified Value(s): 100
The oldest observed fish in the DFO database is about 100 years.
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified in cpars: 1179.69, 11936.51
A large range of values from the stochastic SRA. There is high uncertainty in the absolute population size. The assessment was not considered robust enough to provide absolute biomass estimates.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified in cpars: 0.06, 0.06
The assessment used M = 0.06 (age-invariant) as the most plausible value.
M2: (Optional) Natural mortality rate at age. Vector of length maxage . Positive real number
Slot not used.
Mexp: Exponent of the Lorenzen function assuming an inverse relationship between M and weight. Uniform distribution lower and upper bounds. Real numbers <= 0.
Specified Value(s): 0, 0
We assumed age-invariant M.
Msd: Inter-annual variability in natural mortality rate expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
We assumed time-invariant M.
Natural Mortality Parameters
Sampled Parameters
Histograms of 48 simulations of M, Mexp, and Msd parameters, with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
The average natural mortality rate by year for adult fish for 3 simulations. The vertical dashed line indicates the end of the historical period:
M-at-Age
Natural mortality-at-age for 3 simulations in the first historical year, the last historical year (i.e., current year), and the last projected year:
M-at-Length
Natural mortality-at-length for 3 simulations in the first historical year, the last historical year (i.e., current year), and the last projected year:
Recruitment: h, SRrel, Perr, AC
h: Steepness of the stock recruit relationship. Uniform distribution lower and upper bounds. Values from 1/5 to 1
Specified Value(s): 0.55, 0.85
A range of steepness values was used. The assessment had a prior of steepness with mean of 0.674 and standard deviation of 0.168.
SRrel: Type of stock-recruit relationship. Single value, switch (1) Beverton-Holt (2) Ricker. Integer
Specified Value(s): 1
A value of 1 represents the Beverton-Holt stock recruitment curve which is commonly used for BC groundfish.
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: 0.14, 4.99
A prior mean of 0.4 for the standard deviation of the recruitment was used in the assessment.
AC: Autocorrelation in recruitment deviations rec(t)=ACrec(t-1)+(1-AC)sigma(t). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: -0.13, 0.17
Some autocorrelation is used to generate recruitment in the operating model.
Recruitment Parameters
Sampled Parameters
Histograms of 48 simulations of steepness (h), recruitment process error (Perr) and auto-correlation (AC) for the Beverton-Holt stock-recruitment relationship, with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Non-stationarity in stock productivity: Period, Amplitude
Period: (Optional) Period for cyclical recruitment pattern in years. Uniform distribution lower and upper bounds. Non-negative real numbers
Slot not used.
Amplitude: (Optional) Amplitude in deviation from long-term average recruitment during recruitment cycle (eg a range from 0 to 1 means recruitment decreases or increases by up to 100% each cycle). Uniform distribution lower and upper bounds. 0 < Amplitude < 1
Slot not used.
Growth: Linf, K, t0, LenCV, Ksd, Linfsd
Linf: Maximum length. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 52.7, 52.7
Growth estimates were obtained from length-age samples in the DFO groundfish database for the assessment. This is the reported value in the assessment document (Table D.4 of Edwards et al., 2017).
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 0.08, 0.08
This is the reported value in the assessment document (Table D.4 of Edwards et al., 2017).
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified in cpars: -2.22, -2.22
This is the reported value in the assessment document (Table D.4 of Edwards et al., 2017).
LenCV: Coefficient of variation of length-at-age (assumed constant for all age classes). Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1, 0.1
This parameter was not reported in the assessment document. In its absence, this is assumed to be 10% in the operating model which appears to be reasonable based on the following figure.
Age-length relationship of redbanded rockfish and estimated growth parameters by sex (Figure D.4 in Edwards et al. 2017).
Ksd: Inter-annual variability in growth parameter k expressed as coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No variability in growth is assumed here.
Linfsd: Inter-annual variability in maximum length expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No variability in growth is assumed here.
Growth Parameters
Sampled Parameters
Histograms of 48 simulations of von Bertalanffy growth parameters Linf, K, and t0, and inter-annual variability in Linf and K (Linfsd and Ksd), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
The Linf and K parameters in each year for 3 simulations. The vertical dashed line indicates the end of the historical period:
Growth Curves
Sampled length-at-age curves for 3 simulations in the first historical year, the last historical year, and the last projection year. 
Maturity: L50, L50_95
L50: Length at 50 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 42.25, 42.25
The assessment documented reported 50% maturity at approximately age 18. This is the mean length corresponding to age-18.
L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 5.37, 5.37
Based on the maturity ogive presented in the assessment, 95% maturity occurs by approximately age-27. This is the difference in mean length between age-18 and age-27.
Maturity Parameters
Sampled Parameters
Histograms of 48 simulations of L50 (length at 50% maturity), L95 (length at 95% maturity), and corresponding derived age at maturity parameters (A50 and A95), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Maturity at Age and Length
Maturity-at-age and -length for 3 simulations in the first historical year, the last historical year (i.e., current year), and the last projected year:
Stock depletion and Discard Mortality: D, Fdisc
D: Current level of stock depletion SSB(current)/SSB(unfished). Uniform distribution lower and upper bounds. Fraction
Specified in cpars: 0.65, 0.95
Overall, the stochastic SRA suggested that the current stock is lightly depleted. This is supported by the high frequency of age samples in the plus-group.
Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.9, 1
Very high discard mortality rate is assumed due to life history of rockfish.
Depletion and Discard Mortality
Sampled Parameters
Histograms of 48 simulations of depletion (spawning biomass in the last historical year over average unfished spawning biomass; D) and the fraction of discarded fish that are killed by fishing mortality (Fdisc), with vertical colored lines indicating 3 randomly drawn values.
Length-weight conversion parameters: a, b
a: Length-weight parameter alpha. Single value. Positive real number
Specified Value(s): 0
This is the reported value in the assessment document (Table D.3 of Edwards et al., 2017).
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 3.18
This is the reported value in the assessment document (Table D.3 of Edwards et al., 2017).
Spatial distribution and movement: Size_area_1, Frac_area_1, Prob_staying
Size_area_1: The size of area 1 relative to area 2. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5, 0.5
No justification provided.
Frac_area_1: The fraction of the unfished biomass in stock 1. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5, 0.5
A fully mixed stock is simulated.
Prob_staying: The probability of inviduals in area 1 remaining in area 1 over the course of one year. Uniform distribution lower and upper bounds. Positive fraction.
Specified Value(s): 0.5, 0.5
A fully mixed stock is simulated.
Spatial & Movement
Sampled Parameters
Histograms of 48 simulations of size of area 1 (Size_area_1), fraction of unfished biomass in area 1 (Frac_area_1), and the probability of staying in area 1 in a year (Frac_area_1), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Fleet Parameters
Historical years of fishing, spatial targeting: nyears, Spat_targ
nyears: The number of years for the historical spool-up simulation. Single value. Positive integer
Specified Value(s): 75
The historical catch data goes back to 1940 and ends in 2014 for a total of 75 years.
Spat_targ: Distribution of fishing in relation to spatial biomass: fishing distribution is proportional to B^Spat_targ. Uniform distribution lower and upper bounds. Real numbers
Specified Value(s): 1, 1.2
We model some spatial targetting by the fishery.
Trend in historical fishing effort (exploitation rate), interannual variability in fishing effort: EffYears, EffLower, EffUpper, Esd
EffYears: Years representing join-points (vertices) of time-varying effort. Vector. Non-negative real numbers
The historical catch years.
EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
The 95% credibility interval of F in the stochastic SRA was used to bound historical effort in the operating model.
EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
The 95% credibility interval of F in the stochastic SRA was used to bound historical effort in the operating model.
| EffYears | EffLower | EffUpper |
|---|---|---|
| 1940 | 0.00253 | 0.00917 |
| 1941 | 0.01060 | 0.06240 |
| 1942 | 0.01710 | 0.07160 |
| 1943 | 0.05630 | 0.18300 |
| 1944 | 0.06000 | 0.23600 |
| 1945 | 0.07760 | 0.28100 |
| 1946 | 0.09940 | 0.33000 |
| 1947 | 0.01900 | 0.07260 |
| 1948 | 0.03020 | 0.11200 |
| 1949 | 0.04390 | 0.12300 |
| 1950 | 0.01800 | 0.06890 |
| 1951 | 0.08150 | 0.30500 |
| 1952 | 0.05520 | 0.19400 |
| 1953 | 0.03110 | 0.14800 |
| 1954 | 0.03500 | 0.12600 |
| 1955 | 0.02340 | 0.09460 |
| 1956 | 0.02280 | 0.11200 |
| 1957 | 0.04210 | 0.12700 |
| 1958 | 0.02810 | 0.08200 |
| 1959 | 0.02790 | 0.09920 |
| 1960 | 0.04600 | 0.18400 |
| 1961 | 0.04740 | 0.18900 |
| 1962 | 0.06820 | 0.27600 |
| 1963 | 0.05380 | 0.29500 |
| 1964 | 0.03270 | 0.12900 |
| 1965 | 0.02930 | 0.12400 |
| 1966 | 0.02920 | 0.15000 |
| 1967 | 0.04450 | 0.16800 |
| 1968 | 0.02730 | 0.11100 |
| 1969 | 0.05800 | 0.33300 |
| 1970 | 0.09380 | 0.35500 |
| 1971 | 0.07600 | 0.25500 |
| 1972 | 0.11500 | 0.42000 |
| 1973 | 0.07520 | 0.26700 |
| 1974 | 0.06660 | 0.43000 |
| 1975 | 0.13300 | 0.42300 |
| 1976 | 0.09030 | 0.33900 |
| 1977 | 0.15500 | 0.59300 |
| 1978 | 0.15800 | 0.60700 |
| 1979 | 0.23300 | 0.75200 |
| 1980 | 0.18100 | 0.66700 |
| 1981 | 0.15200 | 0.47300 |
| 1982 | 0.10600 | 0.42400 |
| 1983 | 0.13100 | 0.48000 |
| 1984 | 0.19800 | 0.68400 |
| 1985 | 0.34500 | 1.20000 |
| 1986 | 0.64600 | 2.43000 |
| 1987 | 0.85300 | 3.82000 |
| 1988 | 0.95600 | 3.40000 |
| 1989 | 1.01000 | 4.79000 |
| 1990 | 1.50000 | 5.07000 |
| 1991 | 1.89000 | 6.50000 |
| 1992 | 1.38000 | 4.90000 |
| 1993 | 1.22000 | 5.49000 |
| 1994 | 1.91000 | 6.36000 |
| 1995 | 1.12000 | 4.12000 |
| 1996 | 0.98900 | 3.38000 |
| 1997 | 0.66800 | 2.30000 |
| 1998 | 0.44500 | 1.85000 |
| 1999 | 1.23000 | 4.88000 |
| 2000 | 2.25000 | 7.49000 |
| 2001 | 1.55000 | 5.18000 |
| 2002 | 1.52000 | 6.42000 |
| 2003 | 1.98000 | 5.47000 |
| 2004 | 1.88000 | 6.20000 |
| 2005 | 2.00000 | 6.43000 |
| 2006 | 1.47000 | 4.83000 |
| 2007 | 0.94000 | 3.46000 |
| 2008 | 1.09000 | 3.65000 |
| 2009 | 0.95300 | 3.52000 |
| 2010 | 0.52500 | 3.81000 |
| 2011 | 0.64000 | 2.70000 |
| 2012 | 0.55000 | 3.26000 |
| 2013 | 0.68700 | 2.36000 |
| 2014 | 0.65800 | 2.62000 |
Esd: Additional inter-annual variability in fishing mortality rate. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.1, 0.1
A generic value of 0.1 was used.
Historical Effort
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in historical fishing mortality (Esd), with vertical colored lines indicating 3 randomly drawn values used in the time-series plot:
Time-Series
Time-series plot showing 3 trends in historical fishing mortality (OM@EffUpper and OM@EffLower or OM@cpars$Find):
Annual increase in catchability, interannual variability in catchability: qinc, qcv
qinc: Average percentage change in fishing efficiency (applicable only to forward projection and input controls). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Trend in fishing efficiency (projections). No future changes in efficiency is modelled.
qcv: Inter-annual variability in fishing efficiency (applicable only to forward projection and input controls). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.1, 0.1
Some background interannual variability in catchability is modeled (10%).
Future Catchability
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in fishing efficiency (qcv) and average annual change in fishing efficiency (qinc), with vertical colored lines indicating 3 randomly drawn values used in the time-series plot:
Time-Series
Time-series plot showing 3 trends in future fishing efficiency (catchability): 
Fishery gear length selectivity: L5, LFS, Vmaxlen, isRel
L5: Shortest length corresponding to 5 percent vulnerability. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 29.43, 34.4
Based on age distributions of samples from the commercial fishery, the smallest animals caught are about 5-10 years old. This length range includes those ages.
LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 50.41, 52.63
Based on age distributions of samples from the commercial fishery, the most abundant animals caught are about 15-20 years old. We assume the modal ages are the youngest fully-selected ages. This length range includes those ages.
Vmaxlen: The vulnerability of fish at Stock@Linf . Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 1, 1
We follow the assumption of assessment model that selectivity is flat-topped.
isRel: Selectivity parameters in units of size-of-maturity (or absolute eg cm). Single value. Boolean.
Specified Value(s): FALSE
Selectivity is in terms of absolute length, not relative to length at maturity.
Fishery length retention: LR5, LFR, Rmaxlen, DR
LR5: Shortest length corresponding ot 5 percent retention. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Retention follows selectivity.
LFR: Shortest length that is fully retained. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Retention follows selectivity.
Rmaxlen: The retention of fish at Stock@Linf . Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 1, 1
Retention follows selectivity.
DR: Discard rate - the fraction of caught fish that are discarded. Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 0, 0
With 100% monitoring of the BC groundfish fishery, all discards are assumed to be accounted for.
Time-varying selectivity: SelYears, AbsSelYears, L5Lower, L5Upper, LFSLower, LFSUpper, VmaxLower, VmaxUpper
SelYears: (Optional) Years representing join-points (vertices) at which historical selectivity pattern changes. Vector. Positive real numbers
Slot not used.
AbsSelYears: (Optional) Calendar years corresponding with SelYears (eg 1951, rather than 1), used for plotting only. Vector (of same length as SelYears). Positive real numbers
Slot not used.
L5Lower: (Optional) Lower bound of L5 (use ChooseSelect function to set these). Vector. Non-negative real numbers
Slot not used.
L5Upper: (Optional) Upper bound of L5 (use ChooseSelect function to set these). Vector. Non-negative real numbers
Slot not used.
LFSLower: (Optional) Lower bound of LFS (use ChooseSelect function to set these). Vector. Non-negative real numbers
Slot not used.
LFSUpper: (Optional) Upper bound of LFS (use ChooseSelect function to set these). Vector. Non-negative real numbers
Slot not used.
VmaxLower: (Optional) Lower bound of Vmaxlen (use ChooseSelect function to set these). Vector. Fraction
Slot not used.
VmaxUpper: (Optional) Upper bound of Vmaxlen (use ChooseSelect function to set these). Vector. Fraction
Slot not used.
Current Year: CurrentYr
CurrentYr: The current calendar year (final year) of the historical simulations (eg 2011). Single value. Positive integer.
Specified Value(s): 2014
The terminal year of the assessment was used.
Existing Spatial Closures: MPA
MPA: (Optional) Matrix specifying spatial closures for historical years.
Slot not used.
Obs Parameters
The observation model parameters are taken from the Generic_Obs object subject to a few additional changes which are documented here.
Catch statistics: Cobs, Cbiascv, CAA_nsamp, CAA_ESS, CAL_nsamp, CAL_ESS
Cobs: Log-normal catch observation error expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.1, 0.3
As Generic_Obs.
Cbiascv: Log-normal coefficient of variation controlling the sampling of bias in catch observations for each simulation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.1
As Generic_Obs.
CAA_nsamp: Number of catch-at-age observation per time step. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 100, 400
As Generic_Obs. Age composition data do not seem to be collected regularly. Thus, this operating model can be used to evaluate the value of collecting annual age comps. The number of observed age comps in the commercial fleet was not reported, although the surveys typically collect 100-400 annual age samples.
CAA_ESS: Effective sample size (independent age draws) of the multinomial catch-at-age observation error model. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 25, 50
As Generic_Obs. Age composition data do not seem to be collected regularly. Available data from the commercial fleet come from very few sampling trips, although age comps from surveys come from more frequent sampling tows of around 25-50 (e.g., Table D.9 and D.10 of Edwards et al. 2017). We use the sampling tow numbers as the effective sample size here. This operating model can be used to evaluate the value of collecting annual age comps.
CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 100, 1500
Randomly-collected annual length samples range from several hundred to almost 1,500 (Figures D.1 and D.2 of Edwards et al. 2017).
CAL_ESS: Effective sample size (independent length draws) of the multinomial catch-at-length observation error model. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 25, 50
As Generic_Obs. The effective sample size is usually smaller than the nominal sample size.
Index imprecision, bias and hyperstability: Iobs, Ibiascv, Btobs, Btbiascv, beta
Iobs: Observation error in the relative abundance indices expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 0.52, 0.56
The survey CVs were estimated to be rather large for some surveys. Thus, the range is set from 0.2 - 0.6 in the operating model.
Ibiascv: Not Used. Log-normal coefficient of variation controlling error in observations of relative abundance index. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Btobs: Log-normal coefficient of variation controlling error in observations of current stock biomass among years. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2, 0.5
As Generic_Obs.
Btbiascv: Uniform-log bounds for sampling persistent bias in current stock biomass. Uniform-log distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.33, 3
As Generic_Obs.
beta: A parameter controlling hyperstability/hyperdepletion where values below 1 lead to hyperstability (an index that decreases slower than true abundance) and values above 1 lead to hyperdepletion (an index that decreases more rapidly than true abundance). Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.67, 1.5
Since the survey is carried out according to a systematic design, we assume that it varies roughly proportionally to real abundance and specify a beta parameter between 2/3 and 3/2.
Bias in maturity, natural mortality rate and growth parameters: LenMbiascv, Mbiascv, Kbiascv,t0biascv, Linfbiascv
LenMbiascv: Log-normal coefficient of variation for sampling persistent bias in length at 50 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
As Generic_Obs.
Mbiascv: Log-normal coefficient of variation for sampling persistent bias in observed natural mortality rate. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Kbiascv: Log-normal coefficient of variation for sampling persistent bias in observed growth parameter K. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
As Generic_Obs.
t0biascv: Log-normal coefficient of variation for sampling persistent bias in observed t0. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
As Generic_Obs.
Linfbiascv: Log-normal coefficient of variation for sampling persistent bias in observed maximum length. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05
As Generic_Obs.
Bias in length at first capture, length at full selection: LFCbiascv, LFSbiascv
LFCbiascv: Log-normal coefficient of variation for sampling persistent bias in observed length at first capture. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05
As Generic_Obs.
LFSbiascv: Log-normal coefficient of variation for sampling persistent bias in length-at-full selection. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05
As Generic_Obs.
Bias in fishery reference points, unfished biomass, FMSY, FMSY/M ratio, biomass at MSY relative to unfished: FMSYbiascv, FMSY_Mbiascv, BMSY_B0biascv
FMSYbiascv: Not used. Log-normal coefficient of variation for sampling persistent bias in FMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
FMSY_Mbiascv: Log-normal coefficient of variation for sampling persistent bias in FMSY/M. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
BMSY_B0biascv: Log-normal coefficient of variation for sampling persistent bias in BMSY relative to unfished. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Management targets in terms of the index (i.e., model free), the total annual catches and absolute biomass levels: Irefbiascv, Crefbiascv, Brefbiascv
Irefbiascv: Log-normal coefficient of variation for sampling persistent bias in relative abundance index at BMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Crefbiascv: Log-normal coefficient of variation for sampling persistent bias in MSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Brefbiascv: Log-normal coefficient of variation for sampling persistent bias in BMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5
As Generic_Obs.
Depletion bias and imprecision: Dbiascv, Dobs
Dbiascv: Log-normal coefficient of variation for sampling persistent bias in stock depletion. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5
As Generic_Obs.
Dobs: Log-normal coefficient of variation controlling error in observations of stock depletion among years. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05, 0.1
As Generic_Obs.
Recruitment compensation and trend: hbiascv, Recbiascv
hbiascv: Log-normal coefficient of variation for sampling persistent bias in steepness. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Recbiascv: Log-normal coefficient of variation for sampling persistent bias in recent recruitment strength. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1, 0.3
As Generic_Obs.
Obs Plots
Observation Parameters
Catch Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in catch observations (Csd) and persistent bias in observed catch (Cbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Depletion Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in depletion observations (Dobs) and persistent bias in observed depletion (Dbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Abundance Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in abundance observations (Btobs) and persistent bias in observed abundance (Btbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Index Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in index observations (Iobs) and hyper-stability/depletion in observed index (beta), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Time-series plot of 3 samples of index observation error:
Plot showing an example true abundance index (blue) with 3 samples of index observation error and the hyper-stability/depletion parameter (beta):
Recruitment Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in index observations (Recsd) , with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Composition Observations
Sampled Parameters
Histograms of 48 simulations of catch-at-age effective sample size (CAA_ESS) and sample size (CAA_nsamp) and catch-at-length effective (CAL_ESS) and actual sample size (CAL_nsamp) with vertical colored lines indicating 3 randomly drawn values:
Parameter Observations
Sampled Parameters
Histograms of 48 simulations of bias in observed natural mortality (Mbias), von Bertalanffy growth function parameters (Linfbias, Kbias, and t0bias), length-at-maturity (lenMbias), and bias in observed length at first capture (LFCbias) and first length at full capture (LFSbias) with vertical colored lines indicating 3 randomly drawn values:
Reference Point Observations
Sampled Parameters
Histograms of 48 simulations of bias in observed FMSY/M (FMSY_Mbias), BMSY/B0 (BMSY_B0bias), reference index (Irefbias), reference abundance (Brefbias) and reference catch (Crefbias), with vertical colored lines indicating 3 randomly drawn values:
Imp Parameters
Output Control Implementation Error: TACFrac, TACSD
TACFrac: Mean fraction of TAC taken. Uniform distribution lower and upper bounds. Positive real number.
Specified Value(s): 0.9, 1.05
We assume, on average, high deviation (including underages and overages) between the TAC and achieved catch across simulations.
TACSD: Log-normal coefficient of variation in the fraction of Total Allowable Catch (TAC) taken. Uniform distribution lower and upper bounds. Non-negative real numbers.
Specified Value(s): 0, 0.05
We also some interannual variability between the TAC and achieved catch.
Effort Control Implementation Error: TAEFrac, TAESD
TAEFrac: Mean fraction of TAE taken. Uniform distribution lower and upper bounds. Positive real number.
Specified Value(s): 0.9, 1.05
We have little information to inform this parameter, and set the implementation error in effort equal to the TAC implementation error.
TAESD: Log-normal coefficient of variation in the fraction of Total Allowable Effort (TAE) taken. Uniform distribution lower and upper bounds. Non-negative real numbers.
Specified Value(s): 0, 0.05
We have little information to inform this parameter, and set the implementation error in effort equal to the TAC implementation error.
Size Limit Control Implementation Error: SizeLimFrac, SizeLimSD
SizeLimFrac: The real minimum size that is retained expressed as a fraction of the size. Uniform distribution lower and upper bounds. Positive real number.
Specified Value(s): 1, 1
We assume that a size limit would be well-implemented.
SizeLimSD: Log-normal coefficient of variation controlling mismatch between a minimum size limit and the real minimum size retained. Uniform distribution lower and upper bounds. Non-negative real numbers.
Specified Value(s): 0, 0
We assume that the implementation of the size limit is relatively consistent between years.
Imp Plots
Implementation Parameters
TAC Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in TAC implementation error (TACSD) and persistent bias in TAC implementation (TACFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
TAE Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in TAE implementation error (TAESD) and persistent bias in TAC implementation (TAEFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Size Limit Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in size limit implementation error (SizeLimSD) and persistent bias in size limit implementation (SizeLimFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Historical Simulation Plots
Historical Time-Series
Spawning Biomass
Depletion
Absolute
Vulnerable Biomass
Depletion
Absolute
Total Biomass
Depletion
Absolute
Recruitment
Relative
Absolute
Catch
Relative
Absolute
Historical Fishing Mortality
Historical Time-Series
References
Walters, C.J., Martell, S.J.D., Korman, J. 2006. A stochastic approach to stock reduction analysis. Can. J. Fish. Aqua. Sci. 63:212-213.