Operating Model

The OM rdata file can be downloaded from here

Download and import into R using myOM <- readRDS('OM.rdata')

Species Information

Species: Mallotus villosus

Common Name: Capelin

Management Agency: DFO

Region: Gulf of St Lawrence

Latitude: 46.9

Longitude: -60.8

OM Parameters

OM Name: Name of the operating model: Capelin GSL OM

nsim: The number of simulations: 80

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: 1.5

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 2003

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): 8

Here we assume a maximum age of 8. This is simply to encompass a suitable number of ages for simulation purposes. The age corresponding to 1% survival is around 6.

R0: The magnitude of unfished recruitment. Single value. Positive real number

Specified Value(s): 1000

Determined by StochasticSRA. See Build.r script.

M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number

Specified Value(s): 0.61, 0.91

The workbook Capelin_GSL.xlsx includes a sheet ‘M calcs’. This is used to determine a tentative range in M given age samples in the period 1984-1993. The model assumes logistic selectivity and optimizes for 3 parameters: M, the selectivity inflection point and selectivity slope given a user defined ratio of apical fishing mortality rate to natural mortality rate. Here we assume a range for F ratio of between 1 and 2 times that of M leading to estimates of M in the range of 0.611 to 0.907.

the M calcs sheet of Capelin_GSL.xlsx

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 size-invariant M.

Msd: Inter-annual variability in natural mortality rate expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers

Specified Value(s): 0.1, 0.4

Given that M is very poorly quantified in most fishery settings, the annual variability in M is poorly known. However capelin are a principal prey species for a large number of marine predators in the GSL. Fluctuations in predator abundance and overlap with Capelin are likely to drive fluctuations in M among years. Here, moderate interannual variability is specified with a CV of 0.2 to 0.4.

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): 0.4, 0.95

The steepness of the stock-recruitment curve (unfished recruitment at 20% unfished spawning biomass). This parameter is a fundamental determinant of stock resilience and poorly quantified even in data-rich assessments. Here we assume a very wide range from 0.4 - 0.95. A potential robustness test.

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 small pelagics such as capelin.

Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers

Specified Value(s): 0.5, 0.9

Determined by StochasticSRA.

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): 0.6, 0.9

Determine by StochasticSRA.

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): 190, 195

‘Eye-balled’ for Female fish from Figure 2 of the DFO 2003 assessment report (see figure below).

K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 0.43, 0.55

The spreadsheet Capelin_GSL.xlsx include a sheet ‘K calcs’. This sheet calculates K from mean length at age of Figure 2 of DFO 2003 and four scenarios for L-infinity and t0 parameters. The lower value of 0.429 arises from a t0 value of -0.75 and an Linf of 195mm. The upper K value of 0.551 which is the product of t0 value of -0.25 and an Linf of 190mm.

t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers

Specified Value(s): -0.75, -0.25

Theoretical age at length zero. In the absence of a growth curve a t0 value of between 0.429 and 0.551.

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): 0.15, 0.2

The length CV is set to 0.15-0.2 reflecting size sample data presented in DFO 2003.

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

Inter-annual variability in growth rate expressed as a log normal standard deviation. No variability in growth rate is assumed.

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 Value(s): 100, 140

DFO 2003 cites divergence in female weight before 140mm following gonadal development

L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 15, 20

A guess (in the absence of maturity at length data) at the length increment from 50 percent to 95 percent maturity, 15-20mm

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): 0.05, 0.9

Derived from Stochastic SRA

Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers

Specified Value(s): 1, 1

We assume that all fish are discarded dead since gill netting is the primary fishing metier.

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

Derived from ‘W-L calcs’ sheet of Capelin_GSL.xlsx and Figure 2 of DFO (2003)

b: Length-weight parameter beta. Single value. Positive real number

Specified Value(s): 3.06

Derived from ‘W-L calcs’ sheet of Capelin_GSL.xlsx and Figure 2 of DFO (2003)

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

A mixed stock with half of the biomass in each of two areas is simulated.

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 mixed stock with half of the biomass in each of two areas 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): 0.6, 0.9

High to moderately high mixing is simulated. A probability of staying in each area of 60 to 90 percent.

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): 53

Determined by StochasticSRA (below 1960-2012, a total of 53 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

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 SSRA for each historical year.

EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers

From the StochasticSRA.

EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers

From the StochasticSRA.

EffYears EffLower EffUpper
1961 1 2
1962 1 2
1963 1 2
1964 1 2
1965 1 2
1966 1 2
1967 1 2
1968 1 2
1969 1 2
1970 1 2
1971 1 2
1972 1 2
1973 1 2
1974 1 2
1975 1 2
1976 1 2
1977 1 2
1978 1 2
1979 1 2
1980 1 2
1981 1 2
1982 1 2
1983 1 2
1984 1 2
1985 1 2
1986 1 2
1987 1 2
1988 1 2
1989 1 2
1990 1 2
1991 1 2
1992 1 2
1993 1 2
1994 1 2
1995 1 2
1996 1 2
1997 1 2
1998 1 2
1999 1 2
2000 1 2
2001 1 2
2002 1 2
2003 1 2
2004 1 2
2005 1 2
2006 1 2
2007 1 2
2008 1 2
2009 1 2
2010 1 2
2011 1 2
2012 1 2
2013 1 2

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

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

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, 0.2

This is essentially the variability in interannual catches from similar fishing effort given stable biomass. This is unknown but may be substantial for stocks such as capelin that may be more or less vulnerable to gear depending on the particular spatio-temporal distribution in a given year.

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): 10, 10

From the StochasticSRA.

LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 70, 70

From the StochasticSRA.

Vmaxlen: The vulnerability of fish at . 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 . 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

There is general discarding across all size-classes in some fisheries. We assume that this is not the case in the capelin 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): 2013

The current calendar year (most recent)

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. If interannual variability in catches is a function of variability in effort, catchability, vulnerabl biomass and observation error the the catch data imply that the maximum level of observation error in catches is probably in the range of 10 to 20 per cent.

Inter-annual variability in catches

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 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, 500

A total of 5000 age samples were provided over a 10 year period. We presume that a similar degree of sampling is possible in the future.

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): 50, 100

Since age sampling may come from hauls that are age monospecific we consider a potentially low effective sample size.

CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers

Specified Value(s): 300, 500

In the absence of data on sampling intensity in MPO 2013 we assume the same potential sampling rate 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): 25, 100

As age sampling.

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 indices are assumed to be observed more precisely than the Generic_Obs model with a CV of around 5 to 10 per cent following reported standard errors in MPO 2013

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): 0.1

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. Relatively high observation error in estimates of current biomass

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): 0.33, 1

Since the survey is based on CPUE data from a purse seine fishery targetting aggregations it is likely to be hyperstable (respond more slowly to changes in real biomass)

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): 0.05

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): 0.25

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): 0.05

As Generic_Obs.

t0biascv: Log-normal coefficient of variation for sampling persistent bias in observed t0. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 0

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): 0.05

As Generic_Obs.

Bias in length at first capture, length at full selection: LFCbiascv, LFSbiascv

LFCbiascv: Log-normal coefficient of variation for sampling persistent bias in observed length at first capture. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 0.1

As Generic_Obs.

LFSbiascv: Log-normal coefficient of variation for sampling persistent bias in length-at-full selection. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 0.1

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): 0.3

FMSY is likely to be known inaccurately.

FMSY_Mbiascv: Log-normal coefficient of variation for sampling persistent bias in FMSY/M. Uniform distribution lower and upper bounds. Positive real numbers

Specified Value(s): 0.2

Similarly the ratio of FMSY to M may be highly inaccurate.

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): 0.4

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

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 0.5 which means that assume depletion could up to quadruble or one-fourth 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): 0.3

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

MPO. 2013. Assessment of the Estuary and Gulf of St. Lawrence (Divisions 4RST) Capelin Stock in 2012. DFO Can. Sci. Advis. Sec., Sci. Advis. Rep. 2013/021.

DFO, 2003. Capelin of the Estuary and the Gulf of St. Lawrence (4RST) in 2002. DFO-Science, Stock Status Report. 2003/009.