Haddock 4X5Y: 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 model were the most recent Canadian DFO stock assessment:
DFO. 2017. Assessment of 4X5Y Haddock in 2016. DFO Can. Sci. Advis. Sec. Sci. Advis. Rep. 2017/006
the ‘Data inputs and Exploratory modelling’ document:
and the ‘Modelling and reference points’ document:
Robustness tests
Robustness operating models have yet to be specified for Haddock 4X5Y. These should be subject to consideration by stakeholders, however working from the stock assessments a number of central uncertainties have already been identified:
Robustness OM 1: Growth
From assessment:
“Differences in the growth between the Bay of Fundy and the Scotian Shelf regions have been documented for this resource, and a recent analysis confirmed it is still appropriate to use separate age length keys (Stone and Hansen 2015). However, the defined survey strata used to evaluate growth differences between the Bay of Fundy and the Scotian Shelf are different from the statistical areas used to match length-weight and age length key relationships with catch data. The impact of this mismatch should be evaluated. Given that the location of future harvesting cannot be predicted, this growth mismatch could have effects on the accuracy of projections”
Robustness OM 2: Natural mortality rate
From assessment:
“The high M used in the assessment model could be aliasing fish moving to adjacent areas or deeper waters where the fishery or survey cannot catch them. Noteworthy is that the adjacent Haddock stock on Eastern Georges Bank also shows high total mortality (Z) on older (Age 8+) fish (Stone and Hansen 2015). Research on a possible mechanism for high M on older ages would aid in the understanding of the population dynamics of 4X5Y Haddock”
Robustness OM 3: Strength of 2013 age class
From assessment:
“The 2013 year class appears to be much stronger than anything previously witnessed, but there is uncertainty around this estimate given the retrospective, the small number of observations in both the survey and fishery, and the apparent mismatch between survey abundance estimates and the VPA in recent years. The Coefficient of Variation (CV) is high for the VPA estimate of the 2013 year class (0.4 at Age 3 in 2016)”
The default assumption here was to ignore the last two (very strong) recruitment estimates, but these could be assumed to be correct for specifying a new robustness operating model (a more optimistic future projection over the short term).
Robustness OM 4: Recruitment compensation
The assessed stock-recruitment relationship shows very high recruitment compensation and an attempt to approximate this with a Beverton-Holt model led to steepness estimates hitting an upper bound of 0.99. A possibel robustness scenario could include lower levels of recruitment compensation, which is a principal determinant of stock resilience.
Robustness OM 5: Stock-recruitment relationshp
VPA stock-recruit data may imply a non-asyptotic stock-recruitment relationship (e.g. Ricker model)
Improvements (operating model specification given more time)
Decadal growth parameters were assumed but these were the average of Bay of Fundy and Scotian Shelf parameters for each decade (Growth worksheet of the Haddock_4X5Y_DFO.xlsx workbook).
Projections used the most recent growth curve (2005-2013)
The length-weight a and b parameters were taken from an outdated 1998 report and need updating.
The current depletion estimate (see below) is based on unfished biomass given an R0 estimate from a post-hoc fit to the VPA stock-recruit data. This should be revised and updated.
The estimate of unfished spawning biomass also puts initial stock depletion at around 0.44. This requires manual adjustment of magnitude of N in the first year to create a depleted stock in 1985 (simulated as the first 1:maxage recruitment deviations). This is not ideal and should be based on the VPA estimates of recruitment (or N) for the initial year (1985).
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Melanogrammus
Common Name: Haddock
Management Agency: DFO
Region: Atlantic 4X5Y
Latitude: 42.8
Longitude: -66
OM Parameters
OM Name: Name of the operating model: Haddock_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
DFO. 2017. Assessment of 4X5Y Haddock in 2016. DFO Can. Sci. Advis. Sec. Sci. Advis. Rep. 2017/006
Custom Parameters
Growth is specified by decade as above using the Karray[nsim,nyears+proyears] (von B K) and Linfarray[nsim, nyears+proyears] slots of custom parameters.
Age-specific time varying M was specified to be fixed at 0.2 for all ages and years, except 0.3, 0.6, and 0.9, for ages 10-11+ for the three time blocks (2000-2004, 2005-2009, and 2010-2015; respectively). This was specified in the M_ageArray[nsim, maxage, nyears+proyears] custom parameter slot.
Year specific selectivity was taken from the VPA assessment. Ages greater than 11 were assumed to be selected as the age 11+ age VPA age group. Projection years assumed the mean of the last 4 years of selectivity (2012-2015, normalized to max 1). This was specified in the V[nsim,maxage, nyears+proyears] custom parameter slot.
Recruitment deviations were taken from the estimates of the VPA stock assessment and were specified in the Perr[nsim,nyears+proyears+maxage-1] custom parameters slot.
Changes in growth to smaller faster growing individuals counter reductions in the length at maturity leading to a relative stable ogive of maturity at age. This was specified in the Mat_age[nsim, maxage, nyears+proyears] custom parameter slot.
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
The VPA includes a plus group at age 11. Here maximum age is set to 20 here to ensure calculations include the majority (more than 99.9 per cent) of older individuals.
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified Value(s): 30000
This is crudely calculated my MLE estimation in the worksheet ‘SR’ of the Haddock_4X5Y_DFO.xlsx workbook (~20.564M). Note that the correct R0 is only required 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.
To aid in computational efficiency and to keep the spawning biomass / numbers in a recognisable level I specified R0 at 30,000,000 which led to similar stock trajectory and magnitude as the 2016 assessment.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified Value(s): 0.2, 0.2
Using custom parameters, time-varying natural mortality rate by age is specified such that it is fixed at 0.2 for all ages and years, except 0.3, 0.6, and 0.9, for ages 10-11+ for the three time blocks (2000-2004, 2005-2009, and 2010-2015; respectively)
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
Natural mortality rate by cpars.
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, 1
Supporting documentation does not mention time-varing M. Here we assume it varies by a small arbitrary degree between 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): 0.95, 0.99
The stock recruitment-relationship indicates very strong recruitment compensation (an MLE estimate near 1 according to the naive post-hoc analyis of the SR worksheet if the Haddock_4X5Y_DFO.xlsx workbook), however this may be complicated by recent increases in natural mortality rate. I consider this as an upper bound (it is already very high and arbitrarily consider a lower bound of 0.95.
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 may not be appropriate given the Stock-Recruitment estimates of the VPA (above).
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: 0.03, 9.14
Calculated from the recruitment deviations of the VPA (an MLE estimate)(the SR worksheet if the Haddock_4X5Y_DFO.xlsx workbook). The MLE estimate of 0.696 was bracketted arbitrarily =/- 0.1.
The last two recruitment deviations (2014 and 2015) were ignored as there are insufficient repeat observations of these cohort (autocorrelated log-normal random deviations were sampled for these).
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): 0.49, 0.49
Calculated from the recruitment deviations of the VPA (an MLE estimate)(the SR worksheet if the Cod_5ZJM_DFO.xlsx workbook). Moderately weak positive lag-1 autocorrelation.
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): 52, 64
Time varying by decade (custom parameters see above). Future growth assumed to be the same as most recent.
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.28, 0.32
Time varying by decade (custom parameters see above). Future growth assumed to be the same as most recent.
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified Value(s): -0.64, -0.52
Time varying by decade (custom parameters see above). Future growth assumed to be the same as most recent.
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): 0.05, 0.07
Variability in length at age appears to be quite low. Here I ‘eye-ball’ the coefficient of variation but it could be improved by calculating from raw data.
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
Here we stick with the time varying growth in decadal blocks and do not superimpose any further interannual variability in growth.
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
Here we stick with the time varying growth in decadal blocks and do not superimpose any further interannual variability in growth.
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): 30, 40
The growth changes over time:
Coupled with the maturity at age changes over time:
Work together to keep maturity at age reasonably constant with an inflection point (age at 50% maturity) of age 2.5 reaching an asyptote (100% maturity) around 3.75.
Since this more parsimonious than trying to model changes in maturity at length we override the Mat_age custom parameter slot and assume an identical maturity at age ogive for all years including projections.
L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 8, 12
I arbitrarily set this to 8 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 in cpars: 0.09, 0.29
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). DLMtool is conditioned on SSB now relative to SSB0 inferred from initial year parameters (ie M=0.2 for all ages).
Given an M of 0.2 for all ages and years the estimate of unfished spawning biomass is 125,680 tonnes.
According to this, the stock is at a depletion level of around 17% (2015 SSB of 21,400 / 125,680). Given the considerable uncertainty over unfished recruitment arising from the post-hoc analysis of VPA estimates of Stock-Recruitment I assume this could be half or double the 17% point estimate and specify this as log-normal a prior in custompars truncated at 8.5 and 34% depletion.
This may or may not be supported by the relatively short time series of biomass estimates arising from the VPA:
The estimate of unfished spawning biomass also puts initial stock depletion at around 0.44. This requires manual adjustment of magnitude of N in the first year to create a depleted stock (simulated as the first 1:maxage recruitment deviations). This is not ideal and should be based on the VPA estimates of recruitment (or N) for the initial year.
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
Outdated from a 1998 study (to be revised)
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 3.09
Outdated from a 1998 study (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): 31
1985-2015, a total of 31 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
Not relevant to a fully mixed stock (as here)
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 |
|---|---|---|
| 1985 | 1.3800 | 1.3800 |
| 1986 | 0.8730 | 0.8730 |
| 1987 | 0.7670 | 0.7670 |
| 1988 | 1.1700 | 1.1700 |
| 1989 | 1.0200 | 1.0200 |
| 1990 | 0.6750 | 0.6750 |
| 1991 | 1.0600 | 1.0600 |
| 1992 | 1.4100 | 1.4100 |
| 1993 | 0.8650 | 0.8650 |
| 1994 | 0.3520 | 0.3520 |
| 1995 | 0.7870 | 0.7870 |
| 1996 | 0.5250 | 0.5250 |
| 1997 | 0.2980 | 0.2980 |
| 1998 | 0.6140 | 0.6140 |
| 1999 | 0.3380 | 0.3380 |
| 2000 | 0.2960 | 0.2960 |
| 2001 | 0.2770 | 0.2770 |
| 2002 | 0.2730 | 0.2730 |
| 2003 | 0.1750 | 0.1750 |
| 2004 | 0.2090 | 0.2090 |
| 2005 | 0.1180 | 0.1180 |
| 2006 | 0.0998 | 0.0998 |
| 2007 | 0.1690 | 0.1690 |
| 2008 | 0.1390 | 0.1390 |
| 2009 | 0.1630 | 0.1630 |
| 2010 | 0.2590 | 0.2590 |
| 2011 | 0.2270 | 0.2270 |
| 2012 | 0.3430 | 0.3430 |
| 2013 | 0.2630 | 0.2630 |
| 2014 | 0.1820 | 0.1820 |
| 2015 | 0.1170 | 0.1170 |
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 VPA 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
