Grey Seal 5ZJM (Eastern Georges Bank): a DFO Case Study Operating model
Technical report for Fisheries and Oceans Canada
Tom Carruthers, University of British Columbia [email protected]
Introduction
The primary documents for specifing this operating were three recent population assessments:
Unlike other MSEtool operating models, this operating model is configured to be numbers only (removals in numbers not weight) and therefore makes the length and weight of all individuals equal to 1. This means growth parameters and weight-length parameters are not required, and maturity is specified by age in the custom parameters slot (cpars)
Survival rate is a core uncertainty in these models. However if the pregnancy rate can be assumed to be correct, to obtain the 1:3 ratio of recruits per adult (see figure below), the higher ranges of adult natural mortality rate must be assumed (ie ~ 6 percent of Hammill et al 2017)(see worksheet SSB0). To make this possible I’ve included senescence of older (age 26+) individuals and assigned an M of 0.9 for ages 27 to 36.
Robustness tests
Robustness OM 1: high carrying capacity
Robustness OM 2: low carrying capacity
Robustness OM 3: higher recruitment compensation
Robustness OM 4: Natural mortality rate M of age 0 pups is lower and commensurate with older estimates of 76% survival
Improvements (operating model specification given more time)
Currently I’m assuming the natural mortality rate of the Hammill et al. (2017) assessment rather than the values estimated from the 2017 assessment which are in the range of 0.032-0.039. The latter infers 1% survival to ages 110 and 90 respectively and a recruits: spawner ratio ~ 6-9 which seems far too high given paired observations of numbers and recruitment provided to me. Additionally I am assuming mortality rates of pups follow recent survival estimates of 33%.
Explicit carrying capacity numbers were provided in the 2014 assessment of Hammill et al. (2014). These however are not much higher than current estimates: i.e. current (2016) populations size estimates for Sable Island are 313 thousand. Hammill et al. (2017) estimate a carrying capacity of 540 thousand with a very large standard error of 190 thousand. The +/- 1 StErr used here leads to a range of 350-730 thousand individuals (current stock depletion of between 33 and 78 percent. Only depletion in the range of 0.3-0.6 could be reconciled with the other model inputs.
The population numbers: recruitment figures show a ~ 3:1 linear relationship without evidence of recruitment compensation. If (as it appears) current population assessments do not include other information on habitat limitations or similar, it it likely the the case that carrying capacity estimates originate from model priors (since the data can be expected to be uninformative). Carrying capacity will strongly determine future population depletion reference points with respect to particular removal strategies and is therefore arguably the most important source of uncertainty for the Grey Seal component of a multi-species MSE.
Another large and related uncertainty is the degree of recruitment compensation. Here I assume a range of 0.35 - 0.4 for steepness just to get close to model predictions of recovery over the years from 1978 - 2016. However even this relatively narrow range will strongly determine the impact of future removals (MPs).
Any MSE of Grey Seals will require new performance metrics that reflect management objectives. For example by evaluating the probability of population declining to a particular fraction of the maximum observed population size.
NOTE: because this is a numbers model, any management procedures relating to the use of length data may lead to errors since length data are not generated in a credible way (all individuals are length 1 and weight 1).
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Halichoerus grypus
Common Name: Grey Seal
Management Agency: DFO
Region: Sable Island
Latitude: -59.9
Longitude: 39.9
OM Parameters
OM Name: Name of the operating model: Grey_Seal_5ZJM_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
Custom Parameters
Because this is a numbers model, maturity (pregnancy rate) is specified by age rather than length (the default for MSEtool). To get around this, any length slots such as L50 (length at 50% maturity) are ignored and instead a matrix of maturity at age Mat_age[simulation, age, year] is added to cpars that matches the pregnancy rate at age.
Removals of seals are all assumed to be young of the year, which required a custom vulnerability (V) matrix in cpars.
The population is believed to be recovering from low levels. To generate an increasing population, process error terms for the initial cohorts are set to low levels using the Perr slot of custom parameters.
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): 36
Ten years plust the age at senescence of around 26 (Hammill pers. comm.)
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified Value(s): 3e+05
(Thousands) This is tweaked by hand to create the range in current stock numbers of 300-450 thousand.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified Value(s): 1.08, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.06, 0.09, 0.14, 0.2, 0.3, 0.46, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9
Age dependent M was modelled. Similar to the assessment of Hammill et al. 2017 this is assumed to be around 6% with a juvenile survival of 33% (following the most recent estimates)
M2: (Optional) Natural mortality rate at age. Vector of length maxage . Positive real number
Specified Value(s): 1.09, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.07, 0.11, 0.16, 0.24, 0.35, 0.53, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91, 0.91
Age dependent.
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
Age specific mortality is modelled using M and M2 above. I did not use the Lorenzen parameterization.
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): 0.05, 0.15
We assume moderate variability in natural mortality rate among years.
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): 0.35, 0.4
The population recruitment-relationship indicates very weak recruitment compensation (i.e. steepness < 0.3). However I had to assume some recruitment compensation to simulate recoveries from 10 - 350 tonnes over the course of 1978 to 2016.
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 - asymptotic recruitment with female numbers.
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: 0.04, 1.06
Very low interannual variability in recruitment - simulated in cpars (ignore values cited above).
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, 0
No autocorrelation in recruitment strength
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): 1, 1
Numbers model (same weight per individual) Linf=1
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 1000, 1000
Numbers model (same weight per individual) K
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified Value(s): 0, 0
Numbers model (same weight per individual) t0 negative
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, 0
Numbers model: no lengths so this is zero.
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
Numbers model (same weight per individual), no growth model
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
Numbers model (same weight per individual), no growth model
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): 0.01, 0.01
The cpars attribute Mat_age is used to specify maturity at age because growth (length) is not applicable in this numbers model.
L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.01, 0.01
The cpars attribute Mat_age is used to specify maturity at age because growth (length) is not applicable in this numbers model.
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): 0.3, 0.6
Recent assessments (Hammill et al. 2017) put current (2013) numbers at 273,135 which given the K estimates used in the R0 estimation leads to a range in current population depletion of 0.35 - 0.78. However in this analysis could not reconcile stock recovery trends with depletion outside of the range of 0.3 to 0.6.
Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No discarding and if there were this can be set at zero.
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): 1
Numbers model. W=L
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 1
Numbers model. W=L
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 population 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 population 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): 39
1969-2013, a total of 45 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
Mixed population so this is not influential.
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
1960-2013
EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Calculated from known removals divided by numbers estimates (see sheet ‘F D’ in Grey_Seal_5ZJM_DFO.xlsx workbook)
EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Calculated from known removals divided by numbers estimates (see sheet ‘F D’ in Grey_Seal_5ZJM_DFO.xlsx workbook)
| EffYears | EffLower | EffUpper |
|---|---|---|
| 1978 | 0.00e+00 | 0.00e+00 |
| 1979 | 0.00e+00 | 0.00e+00 |
| 1980 | 1.96e-03 | 1.96e-03 |
| 1981 | 0.00e+00 | 0.00e+00 |
| 1982 | 4.90e-03 | 4.90e-03 |
| 1983 | 4.13e-04 | 4.13e-04 |
| 1984 | 0.00e+00 | 0.00e+00 |
| 1985 | 0.00e+00 | 0.00e+00 |
| 1986 | 0.00e+00 | 0.00e+00 |
| 1987 | 6.08e-04 | 6.08e-04 |
| 1988 | 5.70e-03 | 5.70e-03 |
| 1989 | 2.13e-03 | 2.13e-03 |
| 1990 | 0.00e+00 | 0.00e+00 |
| 1991 | 5.22e-05 | 5.22e-05 |
| 1992 | 0.00e+00 | 0.00e+00 |
| 1993 | 0.00e+00 | 0.00e+00 |
| 1994 | 0.00e+00 | 0.00e+00 |
| 1995 | 1.35e-04 | 1.35e-04 |
| 1996 | 3.53e-05 | 3.53e-05 |
| 1997 | 0.00e+00 | 0.00e+00 |
| 1998 | 6.71e-03 | 6.71e-03 |
| 1999 | 6.49e-03 | 6.49e-03 |
| 2000 | 6.30e-03 | 6.30e-03 |
| 2001 | 6.17e-03 | 6.17e-03 |
| 2002 | 6.28e-03 | 6.28e-03 |
| 2003 | 7.17e-03 | 7.17e-03 |
| 2004 | 6.92e-03 | 6.92e-03 |
| 2005 | 8.06e-03 | 8.06e-03 |
| 2006 | 7.36e-03 | 7.36e-03 |
| 2007 | 6.28e-03 | 6.28e-03 |
| 2008 | 1.02e-02 | 1.02e-02 |
| 2009 | 3.37e-03 | 3.37e-03 |
| 2010 | 3.04e-03 | 3.04e-03 |
| 2011 | 8.90e-03 | 8.90e-03 |
| 2012 | 5.60e-03 | 5.60e-03 |
| 2013 | 5.60e-03 | 5.60e-03 |
| 2014 | 5.60e-03 | 5.60e-03 |
| 2015 | 5.60e-03 | 5.60e-03 |
| 2016 | 5.60e-03 | 5.60e-03 |
Esd: Additional inter-annual variability in fishing mortality rate. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Historical mortality from extractions has already been specified so this is set to zero.
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
Effort controls are not an option this can be set to zero.
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, 0
Again, effort controls are not an option.
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): 0.01, 0.01
Specified in custom parameters: age zero vulnerability is 1, all other ages vulnerability is 0.
LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.02, 0.02
Specified in custom parameters: age zero vulnerability is 1, all other ages vulnerability is 0.
Vmaxlen: The vulnerability of fish at Stock@Linf . Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 0, 0
Specified in custom parameters: age zero vulnerability is 1, all other ages vulnerability is 0.
isRel: Selectivity parameters in units of size-of-maturity (or absolute eg cm). Single value. Boolean.
Specified Value(s): FALSE
Vulnerability at age is specified in custom parameters.
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 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): 2016
Last assessment year.
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): 0.01, 0.02
Extractions are known very precisely
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): 0.01
Extractions are known with high accuracy
CAA_nsamp: Number of catch-at-age observation per time step. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 40, 60
Assuming annual estimates from tagging are around 50 seals per year.
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): 40, 60
No pseudo replication
CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 100, 200
Frequency of size observations is assumed to the same as age observations.
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
No pseudo replication
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): 0.05, 0.1
Relative abundance can be observed precisely
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): 0.05, 0.1
Absolute abundance can be observed precisely
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): 0.02, 0.05
Absolute abundance can be observed accurately
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): 1, 1
Hyperstability not an issue.
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
Not applicable to seal management.
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): 0.1
Not applicable to seal management.
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
Not applicable to seal management.
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
Not applicable to seal management.
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): 0.1
Not applicable to seal management.
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): 0.1
Not applicable to seal management.
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): 0.1
Not applicable to seal management.
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
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): 0.1
Not applicable to seal management.
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): 0.1
Uncertain.
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
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
Uncertain.
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
Uncertain.
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): 0.2, 0.4
Uncertain.
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
Not applicable to seal management.
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, 0.1
Not applicable to seal management.
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
Recommendations for removals are taken exactly
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): 0.01, 0.02
Recommendations for removals are taken exactly
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
Not applicable to seal management.
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): 0.01, 0.02
Not applicable to seal management.
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
Not applicable to seal management.
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): 0.01, 0.02
Not applicable to seal management.
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
