Rougheye Rockfish BC: a DFO Case Study Operating model
Technical report for Fisheries and Oceans Canada
Tom Carruthers, University of British Columbia [email protected]
November 2017
Introduction
This operating model was specified using a stock assessment document:
‘A review of rougheye rockfish Sebastes aleutianus along the Pacific coast of Canada: biology, distribution and abundance trends’. Research Document 2005/096. Haigh, R., Olsen, N., and Starr P.
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Sebastes aleutianus
Common Name: Rougheye Rockfish
Management Agency: DFO
Region: British Columbia
Latitude: 54.5, 53, 51.2, 48.2, 48.2, 50, 54.5
Longitude: -134, -133.5, -131, -125.8, -122, -122, 129
OM Parameters
OM Name: Name of the operating model: Rougheye_Rockfish_BC
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: 0.8
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
Haigh et al. 2005
Custom Parameters
A number of parameters are determined by Stochastic Stock Reduction analysis (a DLMtool function StochasticSRA (Walters et al 2006).
These parameters include the historical fishing mortality rate trajectory, age-selectivity and stock depletion.
The Stochastic SRA is fitted to historical catch data:
in addition to catch at age data:
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): 164
Here we assume a maximum age of 164 which roughly corresponds with the age at which survival is 1% given the lowest bound on natural mortality rate of 0.028, ie. -ln(0.01)/0.028 = 164.47.
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified in cpars: 548670.66, 17618925.5
Unless management options are specified in absolute numbers (e.g. tonnes) the MSE is scale-less (has no units) and this value is inconsequential. Here it is set to 1000 arbitrarily.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified in cpars: 0.03, 0.04
The assessment assumes a point value of M of 0.035 y-1 (page 12) for both male fish and females aged 0-13. This was bracketed by +/- 20% leading to a mean M in the range of 0.028 - 0.042. This is close to the range determined by McDermott (1994)(0.03-0.04) which is referenced in the Assessment in Section 3.4.2.
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): 0.05, 0.2
Given that M is very poorly quantified in most fishery settings, the annual variability in M is poorly known but likely to vary due to variability in predation pressure, food availability, disease and the density of the stock and related stocks that compete for prey or cannibalize recruits. To address the possibility of M changing among years in these simulations I set an arbitrary level of inter-annual variability with a lognormal CV of between 5% and 20% (i.e. 0.05 - 0.2), corresponding with 95% probability interval of +/-10% to +/- 40%. Note that due to the longevity of Rougheye Rockfish quite substantial inter-annual variability in M would be necessary to generate data inconsistent with the assumption of time-invariant M (noting the possible exception of a trend in M, below)
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 steepness of the stock-recruitment curve (unfished recruitment at 20% unfished spawning biomass). The most recent canary rock fish assessment specifies two possible values for steepness 0.55 and 0.70 which are assumed here in the absence of an assessment for rougheye. The range is however widened to reflect a higher degree of uncertainty over this value: 0.45 - 0.8.
SRrel: Type of stock-recruit relationship. Single value, switch (1) Beverton-Holt (2) Ricker. Integer
Specified Value(s): 1
A value of 1 represents the Beverton-Holt stock recruitment curve which is commonly assumed form of density dependence for rockfishes in BC.
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: 0.6, 1.73
Determined by Stochastic SRA.
AC: Autocorrelation in recruitment deviations rec(t)=ACrec(t-1)+(1-AC)sigma(t). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified in cpars: -0.15, 0.1
Determine by Stochastic SRA.
Recruitment Parameters
Sampled Parameters
Histograms of 48 simulations of steepness (h), recruitment process error (Perr) and auto-correlation (AC) for the Beverton-Holt stock-recruitment relationship, with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Non-stationarity in stock productivity: Period, Amplitude
Period: (Optional) Period for cyclical recruitment pattern in years. Uniform distribution lower and upper bounds. Non-negative real numbers
Slot not used.
Amplitude: (Optional) Amplitude in deviation from long-term average recruitment during recruitment cycle (eg a range from 0 to 1 means recruitment decreases or increases by up to 100% each cycle). Uniform distribution lower and upper bounds. 0 < Amplitude < 1
Slot not used.
Growth: Linf, K, t0, LenCV, Ksd, Linfsd
Linf: Maximum length. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 53.5, 56.11
Maximum length. The assessment report (Source) provides MLE estimates of the growth parameters in Section 3.4.1, page 11. The mean value for females is set to: 54.75cm. Arbitrarily, a small degree of uncertainty is used to bracket this value, +/- 2.5%.
From Haigh et al. 2005
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 0.08, 0.09
Maximum growth rate. The mean value for females is set to: 0.08548. Arbitrarily, a moderate degree of uncertainty is used to bracket this value, +/- 10%.
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified in cpars: -0.53, -0.53
Theoretical age at length zero. The value for females is taken exactly and no uncertainty is simulated.
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): 0.08, 0.12
This was taken from the assessment report, Figure 2.
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): 0.2, 0.3
Inter-annual variability in growth rate expressed as a log normal standard deviation. Studies of temporal variability in growth of rockfish are not common but older studies of rockfish growth have found moderate inter-annual variability in K values among years with a CV of around 25% (e.g. widow rockfish, Pearson and Hightower 1991).
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
the inter-annual variability in maximum length expressed as a log normal standard deviation. Taken from the same study above, this is relatively constant.
Growth Parameters
Sampled Parameters
Histograms of 48 simulations of von Bertalanffy growth parameters Linf, K, and t0, and inter-annual variability in Linf and K (Linfsd and Ksd), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
The Linf and K parameters in each year for 3 simulations. The vertical dashed line indicates the end of the historical period:
Growth Curves
Sampled length-at-age curves for 3 simulations in the first historical year, the last historical year, and the last projection year. 
Maturity: L50, L50_95
L50: Length at 50 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 39.76, 47.75
Although the Assessment does not provide a schedule of maturity at length or age, it does provide an estimate of the length at 50% maturity (L50) in Section 3.4.1. page 11. The assessment specifies 50% maturity at a length of 43.9cm. An arbitrary bracketing of +/- 10% puts this in the range of 39.51 - 48.29cm.
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
The length interval between the length at 50% maturity and 95% maturity. Based on the maturity ogives of the Canary Rockfish assessment (a parallel DLMtool operating model specification document), the increment to 95% maturity was 3-4 cm which based on the mean maturity at length of 51 cm corresponds to 6% and 8% of the mean length at maturity respectively. Borrowing from the Canary Rockfish OM specification (e.g. Robin Hood approach, Punt et al. 2011) this puts the L50_95 increment for Rougheye between 2.6 and 3.4 cm.
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: 0.16, 0.97
The biomass indices provided in the assessment document do not provide a reliable basis for inferring stock status. To do this I use a form of stock reduction analysis the DLMtool function StochasticSRA() which operates on the final operating model object to provide ranges on current stock depletion and to fill historical time-series of fishing effort. The analysis requires fleet dynamics information such as the size vulnerability schedule and changes in catchability.
Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.8, 1
Discard mortality rate was set to a conservative range of 80 per cent to 100 percent, consistent with the values published by the Pacific Management Council
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 the assessment document
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 2.9
From the assessment document
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): 0.1, 0.1
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): 0.1, 0.1
Fraction of unfished habitat in area 1 of 2.
It is unlikely that a substantial fraction of Rougheye rockfish inhabit the near shore protected areas. There is possibility for refuges (‘technical closed areas’) where rockfish are present but it is unprofitable or not feasible to fish. In this analysis I specify a small prospective (candidate - for testing of MPs that close areas) closed area that has moderate stock mixing.
Frac_area_1 is the default area for testing marine reserves or simulating habitat that is outside of the range of fishing. To simulate a mixed stock we simulate a stock in which 10% of individuals are in area 1 and 90% are in area 2, 0.1.
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): 0.85, 0.95
To simulate uncertain mixing among areas I assume that between 85 per cent and 95 per cent of individuals remain in the same area among years.
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
Determined by StochasticSRA (below 1971-2016, 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
This is the vertex (year) for a major change in effort (fishing mortality rate). In this case we use the estimates from the Calculated by Stochastic SRA for each historical year.
EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Calculated by Stochastic SRA
EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
Calculated by Stochastic SRA
| EffYears | EffLower | EffUpper |
|---|---|---|
| 1971 | 0.00000 | 0.0000 |
| 1972 | 0.00236 | 0.0167 |
| 1973 | 0.00221 | 0.0158 |
| 1974 | 0.00000 | 0.0000 |
| 1975 | 0.00000 | 0.0000 |
| 1976 | 0.00000 | 0.0000 |
| 1977 | 0.00348 | 0.0236 |
| 1978 | 0.02180 | 0.1380 |
| 1979 | 0.03940 | 0.2790 |
| 1980 | 0.06650 | 0.3980 |
| 1981 | 0.02310 | 0.1440 |
| 1982 | 0.04040 | 0.1960 |
| 1983 | 0.11000 | 0.6170 |
| 1984 | 0.07690 | 0.3890 |
| 1985 | 0.10800 | 0.6480 |
| 1986 | 0.18800 | 1.1000 |
| 1987 | 0.23700 | 1.1900 |
| 1988 | 0.14800 | 0.8370 |
| 1989 | 0.39900 | 1.8900 |
| 1990 | 0.36700 | 1.8800 |
| 1991 | 0.42000 | 2.5300 |
| 1992 | 0.38500 | 1.7000 |
| 1993 | 0.69700 | 2.8400 |
| 1994 | 0.87800 | 3.4100 |
| 1995 | 0.75000 | 2.8100 |
| 1996 | 1.04000 | 3.4900 |
| 1997 | 0.97300 | 3.0800 |
| 1998 | 0.75500 | 2.0000 |
| 1999 | 0.76600 | 2.2500 |
| 2000 | 0.91900 | 2.8800 |
| 2001 | 1.00000 | 2.6900 |
| 2002 | 0.83300 | 1.8000 |
| 2003 | 0.76400 | 2.2300 |
| 2004 | 0.73700 | 2.0200 |
| 2005 | 0.77300 | 2.0800 |
| 2006 | 0.61800 | 1.7000 |
| 2007 | 0.70100 | 1.8400 |
| 2008 | 0.76600 | 2.2400 |
| 2009 | 0.93600 | 3.0600 |
| 2010 | 1.18000 | 3.2000 |
| 2011 | 0.91500 | 3.2600 |
| 2012 | 0.97000 | 3.8600 |
| 2013 | 0.87100 | 3.2000 |
| 2014 | 1.12000 | 4.8300 |
| 2015 | 0.77900 | 6.2600 |
| 2016 | 0.84400 | 4.5200 |
Esd: Additional inter-annual variability in fishing mortality rate. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.1, 0.2
Interannual variability in fishing effort (expressed as a CV). This is really variability in addition to the underlying trend described by EffLower and EffUpper. It is used only to generate historical fishing patterns. In data-limited cases a very simple (general, mean) historical trajectory in effort may be established and it may be desirable to add additional interannual variability to reflect changes in fishing intensity among years. In this case we’re going to use the Stochastic SRA function in DLMtool to determine this according to annual catches so do not need to specify additional variability. It is set to 0.
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): 0.01, 0.03
Interannual variability in fishing efficiency. We borrow this range from the Canary Rockfish operating model for which an assessment is available and indices very little variability in fishing efficiency among years: 0.01 - 0.03.
Future Catchability
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in fishing efficiency (qcv) and average annual change in fishing efficiency (qinc), with vertical colored lines indicating 3 randomly drawn values used in the time-series plot:
Time-Series
Time-series plot showing 3 trends in future fishing efficiency (catchability): 
Fishery gear length selectivity: L5, LFS, Vmaxlen, isRel
L5: Shortest length corresponding to 5 percent vulnerability. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 26.77, 49.93
Calculated by Stochastic SRA
LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 53.49, 56.11
Calculated by Stochastic SRA
Vmaxlen: The vulnerability of fish at Stock@Linf . Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 1, 1
It is assumed that the vulnerability of the largest, oldest fish is 100% (flat-topped selectivity) and we specify a value of 1.
isRel: Selectivity parameters in units of size-of-maturity (or absolute eg cm). Single value. Boolean.
Specified Value(s): FALSE
In this case we are not specifying L5 and LFS as a fraction of length at maturity but rather in absolute units (cm) the same as those of the growth and maturity 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
The general discard rate. What fraction of fish across all size and age classes are discarded? There is general discarding across all size-classes in some fisheries. We assume that this is not the case in the rockfish fishery.
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
The current year (last historical year) can be used to make the plots more informative. As the stock assessment which was used to parameterize the OM uses data up to 2016, we set this parameter to 2016.
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): 0.1, 0.2
Catches are observed more precisely than the Generic_Obs object with a CV of between 10 and 20 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): 0.05
Mean bias (under / over reporting) in catches is assumed to be small with a CV of 0.05 95% of simulations are reported between 90% and 110% 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): 300, 600
Calculated from the worksheet ‘nCAA calc’ in Rougheye_Rockfish_BC.xlsx spreadsheet.
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): 300, 600
Effective sample size is identical to CAA_nsamp
CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 300, 600
Assumed to be the same as catch at age
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): 300, 600
Assumed to be the same as catch at age
Index imprecision, bias and hyperstability: Iobs, Ibiascv, Btobs, Btbiascv, beta
Iobs: Observation error in the relative abundance indices expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Positive real numbers
Specified in cpars: 0.84, 0.98
Relative abundance indices are assumed to be observed imprecisely CV of between 20 and 30 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 Generic_Obs.
Btbiascv: Uniform-log bounds for sampling persistent bias in current stock biomass. Uniform-log distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.33, 3
The bias in the absolute abundance index is assumed to be reasonably high and could be 1/3 to 3 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 Generic_Obs.
Mbiascv: Log-normal coefficient of variation for sampling persistent bias in observed natural mortality rate. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Generic_Obs.
Kbiascv: Log-normal coefficient of variation for sampling persistent bias in observed growth parameter K. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.02
Twice as accurate as Generic_Obs with K values within plus or minus 5% of true value.
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
We choose not to simulate bias in this growth parameter and assume in all cases it is correct.
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
Given the reasonably extensive length sampling data, it is straightforward to estimate Length at First Capture for rockfish from the length frequency data and this is likely to be reasonably well known without substantial bias.
LFSbiascv: Log-normal coefficient of variation for sampling persistent bias in length-at-full selection. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05
As Generic_Obs
Bias in fishery reference points, unfished biomass, FMSY, FMSY/M ratio, biomass at MSY relative to unfished: FMSYbiascv, FMSY_Mbiascv, BMSY_B0biascv
FMSYbiascv: Not used. Log-normal coefficient of variation for sampling persistent bias in FMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
Note that FMSY is not the same as the maximum sustainable rate of fishing, Fmax.
Assuming surplus production dynamics, FMSY is half of Fmax. Above FMSY and below Fmax are sustainable fishing rates that lead to lower biomass than BMSY and do not provide as much yield (on average, at equilibrium) as fishing at FMSY with biomass at BMSY It has been proposed by Gulland (1978) and Walters and Martell (2003) that FMSY may be summarized as a fraction of natural mortality rate M. Gulland suggested FMSY = M, Walters and Martell though FMSY=0.5 x M.
It is not clear how biased such an estimate could be but assuming that this uncertainty reflects the possible range of prescribed values (and brackets the true ratio) and this occurs on top of bias in estimates of natural mortality, the range of possible biases must be higher than that assigned to M (0.2). This is set at 0.3 to reflect the potential for inaccurate estimates of FMSY.
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
A number of MPs aim to fish at a fixed rate proportional to the estimate of M (e.g. Fratio). Other MPs use this ratio to undertake stock reduction analysis (e.g. DB-SRA). Given the references above we set this to be moderately inaccurate given a CV of 0.15.
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): 0.05
We have assigned a relatively precise CV for potential accuracy at 0.05.
Management targets in terms of the index (i.e., model free), the total annual catches and absolute biomass levels: Irefbiascv, Crefbiascv, Brefbiascv
Irefbiascv: Log-normal coefficient of variation for sampling persistent bias in relative abundance index at BMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
Here we assume that the index and MSY (a desirable catch level) can be known more accurately than a desirable absolute biomass level (e.g. BMSY) and assign these a range determined by a CV of 0.2.
Crefbiascv: Log-normal coefficient of variation for sampling persistent bias in MSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.2
As Irefbiascv.
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): 0.25
These are probably the most controversial observation model quantities, after all the most valuable output of a data-rich assessment is arguably the level of stock depletion (typically measured as spawning stock biomass today relative to unfished). If we could know this, for stocks with stationary productivity (where depletion is a very good predictor of stock productivity) we could achieve very good management performance with simple harvest control rules (in essence this is how the outputs of data-rich stock assessments are used).
Having said this, in most cases assessments are evaluated based on their fit to a fishery dependent (e.g. catch per unit effort) or fishery independent (e.g. trawl survey, acoustic survey) relative abundance index. It follows that often the depletion estimate arising from a stock assessment follows the raw data fairly well. Consequently, even anecdotal historical catch rate data may be used in a data-limited context to frame estimates of stock depletion. Similarly, if unfished densities of a species can be quantified (e.g. urchins per sq km of habitat), total estimates of habitat and current density surveys could be used to extrapolate a range of stock depletion.
Alternatively, length frequency data can provide an imprecise estimate of stock epletion when accompanied with estimates of natural mortality rate and growth (and some assumption about the pattern of recent fishing rates).
Here we assign an arbitrary value of 0.25 which is relatively imprecise and means that assume depletion could up to double or half of the true simulated value.
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): 0.2
The stock assessment provides very little support for particular values of recruitment compensation. In DLMtool this is parameterized as steepness (the fraction of unfished recruitment at 20% of unfished spawning biomass, a value ranging from 0.2-1). Here we assume that any MP could get this wrong by a large margin.
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, 0.2
As Generic_Obs
Obs Plots
Observation Parameters
Catch Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in catch observations (Csd) and persistent bias in observed catch (Cbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Depletion Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in depletion observations (Dobs) and persistent bias in observed depletion (Dbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Abundance Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in abundance observations (Btobs) and persistent bias in observed abundance (Btbias), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Index Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in index observations (Iobs) and hyper-stability/depletion in observed index (beta), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Time-series plot of 3 samples of index observation error:
Plot showing an example true abundance index (blue) with 3 samples of index observation error and the hyper-stability/depletion parameter (beta):
Recruitment Observations
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in index observations (Recsd) , with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Composition Observations
Sampled Parameters
Histograms of 48 simulations of catch-at-age effective sample size (CAA_ESS) and sample size (CAA_nsamp) and catch-at-length effective (CAL_ESS) and actual sample size (CAL_nsamp) with vertical colored lines indicating 3 randomly drawn values:
Parameter Observations
Sampled Parameters
Histograms of 48 simulations of bias in observed natural mortality (Mbias), von Bertalanffy growth function parameters (Linfbias, Kbias, and t0bias), length-at-maturity (lenMbias), and bias in observed length at first capture (LFCbias) and first length at full capture (LFSbias) with vertical colored lines indicating 3 randomly drawn values:
Reference Point Observations
Sampled Parameters
Histograms of 48 simulations of bias in observed FMSY/M (FMSY_Mbias), BMSY/B0 (BMSY_B0bias), reference index (Irefbias), reference abundance (Brefbias) and reference catch (Crefbias), with vertical colored lines indicating 3 randomly drawn values:
Imp Parameters
Output Control Implementation Error: TACFrac, TACSD
TACFrac: Mean fraction of TAC taken. Uniform distribution lower and upper bounds. Positive real number.
Specified Value(s): 1, 1.1
Here we assume that the actual catches can be up to 10% 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): 0.05, 0.1
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, 1.1
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): 0.05, 0.1
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, 1.1
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): 0.05, 0.1
We assume that the implementation of the size limit is relatively consistent between years.
Imp Plots
Implementation Parameters
TAC Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in TAC implementation error (TACSD) and persistent bias in TAC implementation (TACFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
TAE Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in TAE implementation error (TAESD) and persistent bias in TAC implementation (TAEFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Size Limit Implementation
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in size limit implementation error (SizeLimSD) and persistent bias in size limit implementation (SizeLimFrac), with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
Historical Simulation Plots
Historical Time-Series
Spawning Biomass
Depletion
Absolute
Vulnerable Biomass
Depletion
Absolute
Total Biomass
Depletion
Absolute
Recruitment
Relative
Absolute
Catch
Relative
Absolute
Historical Fishing Mortality
Historical Time-Series
References
Gulland, J. A. (1978). Fish population dynamycs. Wiley-Interscience Publication.
Haigh, R., Olsen, N., and Starr P. 2005. A review of rougheye rockfish Sebastes aleutianus along the Pacific coast of Canada: biology, distribution and abundance trends’. Research Document 2005/096.
Walters, C. J. & Martell, S. J. D. (2004) Fisheries ecology and management, Princeton University Press, Princeton
Walters, C.J, Martell, S. J. D. & Korman, J. 2006. A stochastic approach to stock reduction analysis. Canadian Journal of Fisheries and Aquatic Sciences, 63:212-223.