Cod 4X5Y: a DFO Case Study Operating model
Technical report for Fisheries and Oceans Canada
Tom Carruthers, University of British Columbia [email protected]
Introduction
This operating model was specified using a stock assessment document:
and an stock status update report:
Robustness tests
Probably the most important area for robustness testing is past, current and future natural mortality rate scenarios.
Robustness OM_R1 (in folder /robustness) sees future M constant at 0.2
Robustness OM_R2 sees future M reduce from 0.6 to 0.2 (historical levels) over a 50 year period
Improvements (operating model specification given more time)
Uncertainty in recruitment compensation could be characterized by bootstrapping the Stock-Recruitment VPA predictions for multiple VPA runs including uncertainty in M, growth etc.
Similarly, uncertainty in age selectivity and trend in F could be specified using multiple VPAs using bootstrapping or alternative scenarios for M etc.
MLE estimates of recruitment variation (slot Perr) and autocorrelaton (AC) were used but these should include some degree of uncertainty.
In the absence of assessment documentation regarding the length-weight relationship, archaic FishBase values were used which is not ideal.
The variability in catchability should be characterized by (F assessed)/(observed E). Without effort data I just guessed this at 10%, but this should be updated.
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Gadus morhua
Common Name: Atlantic cod
Management Agency: DFO
Region: Atlantic 4X5Y
Latitude: 42
Longitude: -65
OM Parameters
OM Name: Name of the operating model: Cod_4X5Y_DFO
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? 4
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: 2
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
Clark D.S. Emberly J. 2008. Assessment of Cod in Division 4X in 2008. Canadian Science Advisory Secretariate. Research Document 2009/018
Custom Parameters
The OM is specified according to two assessments documents. The first, which details a VPA from 1980-2008 provides estimates of age-selectivity. The latter assessment provides F trend from 1970-2015. Matries for age selectivity and F trend are specified in the custom parameter OM slot under the names, V and Find, respectively. You can view the R script Build.r to see how these were derived. In this first preliminary OM there isn’t a theoretically rigorous way to incorporate uncertainty in selectivity and F trend so the same selectivity and Ftrend are assumed among all simulations (the magnitude of F is optimized for each simulation to match an uncertain, simulation-specific estimate of current stock depletion).
There is reason to believe that natural mortality rate may have rapidly increased in recent years. A custom parameter attribute is included to model these probable shifts in M. The 2008 assessment assumes that M was 0.2 across all ages for years prior to 1996 after which it was assumed to be 0.76 from 1996 to 2008. This is used as the base assumption here but alternative future scenarios for M are the focus of in robustness operating models. Time varying M was specified using the cpars attribute M_array, a matrix of dimensions nsim x maxage x (nyears + proyears).
Landings from 1960-2015
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): 20
Following catch-at-age data this is a maximum of ~13 years but it is set at 20 here to ensure calculations include all older individuals.
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified Value(s): 1000
This is crudely calculated my MLE estimation in the worksheet ‘SR’ of the Cod_4X5Y_DFO.xlsx workbook. Note that the correct R0 is only require in MSE if absolute quantities of TAC advice are to be used. Ie if you want to know how well a particular TAC (e.g. 10000 tonnes) may work in the future, as opposed to a scale-less MP which generally provide advice scaled to the catches of any stock.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified Value(s): 0.2, 0.2
The assessment considers a mean historical level of 0.2 that may have increased rapidly to 0.76 after 1995. At the level of 0.76, only very low stock levels (less than 1% depletion) were able to be simulated. In this application we assume 0.2 until 1995 after which a value of 0.6 is assumed. This is specified as a custom M array in cpars.
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): 0.1, 0.15
Cod may be exhibiting relatively high levels of interannual variability in natural mortality rate. Here we assume a CV of 10 to 15% following Figure 39.
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): 0.45, 0.8
The stock recruitment-relationship indicates weak recruitment compensation, however this may be complicated by recent increases in natural mortality rate. The MLE estimate of steepness from the 2008 VPA estimates of age 1 numbers and age 4+ biomass is 0.34 (worksheet ‘SR’ of the Cod_4X5Y_DFO.xlsx workbook). We arbitrarily assume some uncertainty in this value of between 0.3 to 0.4. See ‘Improvements’ above for a note on better ways to characterize uncertainty in steepness.
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 appears consistent with the Stock-Recruitment estimates of the VPA.
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: 0.15, 7.04
Calculated from the recruitment deviations of the VPA (an MLE estimate)
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 Value(s): -0.1, -0.1
Calculated from the recruitment deviations of the VPA (an MLE estimate)
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 Value(s): 108.3, 115.2
The Western 4X growth curve has a maximum length of around 115cm (see ‘Growth’ worksheet of the Cod_4X5Y_DFO.xlsx workbook). In the West this is shorter at around 108cm. Here we assume these are upper and lower bounds.
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2, 0.24
The Western 4X growth curve has a higher growth rate of 0.237 compared with the East with a K value of 0.204. These are considered upper and lower bounds for maximum somatic growth rate this operating model.
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified Value(s): 0, 0
Estimated to be the maximum value of zero in the Growth worksheet.
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
In the absence of length at age data I assume this to be 10%.
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 Value(s): 39.51, 48.29
Although the Assessment does not provide a schedule of maturity at length or age, a number of other ancillary documents cite an average age at 50% maturity of 2.5 years. I arbitrarily assume some uncertainty in this value of between 2.25 and 2.75 and use the East and West growth curves to predict length at 50% maturity from these (green text in sheet ‘Growth’ of the Cod_4X5Y_DFO.xlsx workbook)
L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 2.6, 3.4
I arbitrarily set this to 7.5 cm following a typical maturity schedule (10 - 15 per cent of age at maturity)
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 Value(s): 0.01, 0.05
The VPA assessment does not quantify unfished spawning biomass. Given R0, M and the maturity schedule this can be calculated easily (although it clearly depends heavily on M).
Given an M of 0.2 the estimate of unfished spawning biomass is 403,730tonnes.
Given an M of 0.76 the estimate of unfished spawning biomass is 20,160tonnes
The question then is what is the spawning biomass today. Here I use the 2008-2015 biomass indices and the 2008 VPA age 3+ biomass estimate to extrapolate VPA 3+ biomass (Spawning biomass given our maturity schedule) in 2005. The 2008 - 2015 decline is around 40% according to the index:
2017 Biomass index
Implying that the 16,000 tonnes (age 3+) assessed in 2008 is now around 9,600 tonnes.
2008 Assessment biomass
Given the unfished spawning estimates above this makes current stock depletion either 2.3 percent (9,600 / 403.730) or 47.6 percent (9,600 / 20,160).
These depletion estimates should be paired to the assumption over future M in this and future robustness operating models (47.6 percent depletion for M = 0.76 and 2.3 percent depletion for M = 0.2).
Given the relatively high variability in M, I assume these depletion estimates are higly uncertaint in both cases between 0.35 - 0.6 in the former and 0.01 - 0.05 for the latter.
Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 1, 1
Discard mortality rate is assumed to be 100%.
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
From FishBase (to be revised) (kgs)
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 3.08
From FishBase (to be revised)
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): 46
1970-2015, a total of 46 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
Spatial targetting. We’re going to stick to the default level of 1 (effort distributed in proportion to density)
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
Specified by Find in custom parameters
EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Specified by Find in custom parameters
EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Specified by Find in custom parameters
| EffYears | EffLower | EffUpper |
|---|---|---|
| 1970 | 0.422 | 0.422 |
| 1971 | 1.000 | 1.000 |
| 1972 | 0.704 | 0.704 |
| 1973 | 1.180 | 1.180 |
| 1974 | 0.745 | 0.745 |
| 1975 | 0.605 | 0.605 |
| 1976 | 0.596 | 0.596 |
| 1977 | 0.721 | 0.721 |
| 1978 | 1.090 | 1.090 |
| 1979 | 0.903 | 0.903 |
| 1980 | 1.240 | 1.240 |
| 1981 | 1.090 | 1.090 |
| 1982 | 1.210 | 1.210 |
| 1983 | 1.330 | 1.330 |
| 1984 | 0.994 | 0.994 |
| 1985 | 0.663 | 0.663 |
| 1986 | 1.100 | 1.100 |
| 1987 | 1.200 | 1.200 |
| 1988 | 0.422 | 0.422 |
| 1989 | 0.928 | 0.928 |
| 1990 | 0.737 | 0.737 |
| 1991 | 1.320 | 1.320 |
| 1992 | 1.420 | 1.420 |
| 1993 | 1.570 | 1.570 |
| 1994 | 0.704 | 0.704 |
| 1995 | 0.489 | 0.489 |
| 1996 | 0.191 | 0.191 |
| 1997 | 0.563 | 0.563 |
| 1998 | 0.373 | 0.373 |
| 1999 | 0.588 | 0.588 |
| 2000 | 0.447 | 0.447 |
| 2001 | 0.447 | 0.447 |
| 2002 | 0.273 | 0.273 |
| 2003 | 0.497 | 0.497 |
| 2004 | 0.596 | 0.596 |
| 2005 | 0.414 | 0.414 |
| 2006 | 0.621 | 0.621 |
| 2007 | 0.530 | 0.530 |
| 2008 | 1.250 | 1.250 |
| 2009 | 0.207 | 0.207 |
| 2010 | 1.000 | 1.000 |
| 2011 | 0.389 | 0.389 |
| 2012 | 0.406 | 0.406 |
| 2013 | 0.555 | 0.555 |
| 2014 | 0.422 | 0.422 |
| 2015 | 0.207 | 0.207 |
Esd: Additional inter-annual variability in fishing mortality rate. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Specified by Find in custom parameters
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): -0.1, 0.1
Trend in fishing efficiency (projections). In the future, is a unit of effort going to lead to higher fishing mortality (positive qinc) or lower fishing mortality (negative qinc). Since there isn’t a compelling reason to expect fishing to become more or less efficient, we set the % annual increase to be very close to zero, -0.1 to 0.1.
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
This should be calculated from assessment fishing mortality rate divided by observed fishing effort ie sd(F(y)/E(y)). In the absence of effort data (E) I’m guessing this is moderate at 10% interannual variability.
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 Value(s): 1, 1
From the VPA
LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 1, 1
From the VPA
Vmaxlen: The vulnerability of fish at Stock@Linf . Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 1, 1
From the VPA
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
No general discarding rate.
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): 2015
The last year of F estimates from the update assessment
Existing Spatial Closures: MPA
MPA: (Optional) Matrix specifying spatial closures for historical years.
Slot not used.
Obs Parameters
The observation model parameter are taken from the Generic_Obs model subject to a few addtional 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): 0.05, 0.1
Catches are observed more precisely than the Precise_Unbiased object with a CV of between 5 and 10 per cent.
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): 0.02
Mean bias (under / over reporting) in catches is assumed to be small with a CV of 0.025 - 95% of simulations are between 95% and 105% of true simulated catches.
CAA_nsamp: Number of catch-at-age observation per time step. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 100, 200
As Precise_Unbiased
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 Precise_Unbiased
CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 100, 200
As Precise_Unbiased
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 Precise_Unbiased
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 Value(s): 0.1, 0.15
Relative abundance indices are assumed to be observed somewhat more precisely than the Precise_Unbiased model with a CV of between 10 and 15 per cent.
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
This parameter is not used in this version of DLMtool.
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 Precise_Unbiased
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): 0.5, 2
The bias in the absolute abundance index is assumed to be reasonably high and could be 1/2 to 2 times the true value.
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): 0.66, 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 Precise_Unbiased
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 Precise_Unbiased
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): 0.05
As Precise_Unbiased
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
Unbiased
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): 0.02
Twice as accurate as Generic_Obs with L-infinity values within plus or minus 5% of true value.
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 Precise_Unbiased
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): 0.4
Highly dependent on M for which future levels are highly uncertain.
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): 0.15
More stable and better known than FMSY.
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
Again, highly dependent on M which is very uncertain in the future.
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): 0.5
Uncertain due to uncertainty in BMSY/B0
Crefbiascv: Log-normal coefficient of variation for sampling persistent bias in MSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5
Less likely to be biased than FMSY as high estimated Ms lead to low estimated B0 (MSY is the proportional to the product more or less)
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
Arbitrarily we make this twice as potentially biased as Iref and Cref.
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
Could be very seriously biased given changing M scenarios
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
In a data-limited situation it is unlikely that radically new data would become available regarding depletion meaning that while estimates may be biased, they are likely to be relatively precise. We assign a level of imprecision consistent with observations of catch rate data among years at between 0.05- 0.1.
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): 0.1
Steepness appears consistently low according to S-R estimates from the 2008 VPA
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): 0.05, 0.1
As Precise_Unbiased
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): 1, 1.05
Here we assume that the actual catches can be up to 5% higher than the recommended TAC.
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): 0.02, 0.05
We assume that the bias in the actual catch is relatively consistent between years and set the range for this parameter to a low value.
Effort Control Implementation Error: TAEFrac, TAESD
TAEFrac: Mean fraction of TAE taken. Uniform distribution lower and upper bounds. Positive real number.
Specified Value(s): 1, 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): 0.02, 0.05
We assume that the bias in the effort is relatively consistent between years and set the range for this parameter to a low value.
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, 1.05
We assume that, on average, 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): 0.02, 0.05
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
