Introduction

This is a supporting document for the application of the openMSE framework to the Antarctic Krill fishery. The primary objective of the analysis was to configure the openMSE components in a manner that closely approximates the methodology applied by the Grym framework (D. Maschette et al. 2020) for determining sustainable harvest rates for Krill. Specifically, the aim was to replicate the base-case implementation of Grym for the Krill stock as specified in CCAMLR’s code repository.

Here we focus on the specification of the main component of the openMSE framework, the Operational Model (OM), which sets up the parameters required to simulate the stock dynamics. In particular, we provide a description of the parameter values that underpin the OM for one of the input scenarios considered in the main analysis, referred to as scn-1.

Further discussions and considerations regarding the configuration of the OMs to approximate the Grym framework are presented in the main document of the analysis.

Operating Model

Species Information

Species: Euphausia superba

Common Name: Antarctic Krill

Management Agency: CCAMLR

Region: FAO Area 48

Sponsor: Norwegian Polar Institute

Latitude: -60

Longitude: -40

OM Parameters

OM Name: Name of the operating model: krill_grym_approx_scn-1

nsim: The number of simulations: 10001

proyears: The number of projected years: 50

interval: The assessment interval - how often would you like to update the management system? 1

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

Custom Parameters

M and Perr

Simulation values for annual natural mortality (M) and recruitment process error (Perr) were obtained from a Proportional Recruitment (PR) model (Pavez et al. 2021) fitted to survey data specified under input scenario scn-1 (see main documentation for details on input parameters for the PR model). The PR method produces random draws of natural mortality $M$ and recruitment natural variability (expressed as CV, $CV_R$) expressing the uncertainty about those parameters.

Generated draws of $M$ were used directly as simulation values of the OM parameter M.

Draws of $CV_R$ were converted to log-normal standard deviations and plugged in as simulation values of Perr (i.e. $\texttt{Perr} = \sqrt{log(CV_R^2 + 1)}$).

Age-plus group (plusgroup)

openMSE defaults to use the maximum age-class maxage as a plus group. However, in the Grym’s base-case configuration, the final age class is not treated as an age-plus group. Therefore, to align with the Grym’s specifications, the plus group option was switched off by setting the custom parameter as OM@cpars$plusgroup <- 0.

Depletion optimization

The depletion optimization step in simulations for the historical period was switched off (OM@cpars$qs <- rep(1, n_iter)). This forces the derivation of the current depletion state to be based on selectivity and annual fishing mortality pattern. Therefore, values defined below for parameter D are ignored during simulations.

Stock Parameters

Mortality and age: maxage, R0, M, Msd

maxage: The maximum age of individuals that is simulated. There are maxage+1 (recruitment to age-0) age classes in the storage matrices. maxage is the plus group where all age-classes > maxage are grouped, unless option switched off with OM@cpars$plusgroup=0 . Single value. Positive integer.

Specified Value(s): 7

Value from Constable and de la Mare (1996).

In addition, as explained in section Custom Parameters above, age-class 7 is not an age-plus group.

Thus, the assumption is that all individuals do not survive beyond the age of 7 years (D. Maschette and Wotherspoon 2021).

R0: Initial number of unfished recruits to age-0. This number is used to scale the size of the population to match catch or data, but does not affect any of the population dynamics unless the OM has been conditioned with data. As a result, for a data-limited fishery any number can be used for R0 . In data-rich stocks R0 may be estimated as part of a stock assessment, but for data limited stocks users can choose either an arbitrary number (say, 1000) or choose a number that produces simulated catches in recent historical years that are similar to real world catch data. Single value. Positive real number.

Specified Value(s): 1

Based on the value assumed for mean recruitment in Grym’s base-case application.

M: The instantaneous rate of natural mortality. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified in cpars: 0.563, 1.291

Simulation values for M provided in cpars (see Custom Parameters). The text above on values being drawn from an uniform distribution should be ignored.

Msd: Inter-annual variation in M expressed as a coefficient of variation of a log-normal distribution. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. If this parameter is positive, yearly M is drawn from a log-normal distribution with a mean specified by log(M) drawn for that simulation and a standard deviation in log space specified by the value of Msd drawn for that simulation. Uniform distribution lower and upper bounds. Non-negative real numbers

Specified Value(s): 0, 0

Assuming natural mortality in krill is constant over time, in alignment with Grym’s base-case application.

Natural Mortality Parameters

Sampled Parameters

Histograms of simulations of M, 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. Steepness governs the proportion of unfished recruits produced when the stock is at 20% of the unfished population size. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years of a given simulation. Uniform distribution lower and upper bounds. Values from 1/5 to 1.

Specified Value(s): 0.9, 0.95

Selected range of h values chosen to provide an approximation to Grym’s approach of simulating annual recruitment. In Grym’s base-case, simulated number of recruits are mostly independent of stock size, unless when they are penalised by a depletion factor if the stock size in the preceding year falls below 20% of its pre-exploitation levels.

Specifying high values of parameter h results in strongly concave stock-recruitment curves, characterized by a steep increase in recruitment at low levels of stock size that approaches an asymptote. This implies that the simulated values of recruitment will be nearly independent of stock size, except when the stock is at 20% of its pre-exploitation size or below.

SRrel: Type of stock-recruit relationship. Use 1 to select a Beverton Holt relationship, 2 to select a Ricker relationship. Single value. Integer

Specified Value(s): 1

Grym’s base-case does not incorporate density dependence in recruitment success, making the Ricker model less suitable as an approximation. Instead, the Beverton–Holt stock-recruitment model, with the values for parameter h specified as above, is expected to provide a better approximation to the Grym approach.

Perr: Recruitment process error, which is defined as the standard deviation of the recruitment deviations in log space. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified in cpars: 0.255, 1.183

Simulation values of Perr provided in cpars (see Custom Parameters). The text above about values being drawn from an uniform distribution should be ignored.

AC: Autocorrelation in the recruitment deviations in log space. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided, and used to add lag-1 auto-correlation to the log recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified Value(s): 0, 0

Assuming no autocorrelation between consecutive annual recruitments.

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

Time-series plot showing 3 samples of recruitment deviations for historical and projection years:

Growth: Linf, K, t0, LenCV, Ksd, Linfsd

Linf: The von Bertalanffy growth parameter Linf, which specifies the average maximum size that would reached by adult fish if they lived indefinitely. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless Linfsd is a positive number. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 60, 60

Value from Constable and de la Mare (1996), in millimeters. As in Grym’s base case, the $L_\infty$ parameter is treated as known (i.e. no uncertainty).

K: The von Bertalanffy growth parameter k, which specifies the average rate of growth. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless Ksd is a positive number. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 0.48, 0.48

Value from Thanassekos et al. (2021). Parameter $K$ is assumed to be known without error.

t0: The von Bertalanffy growth parameter t0, which specifies the theoretical age at a size 0. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Uniform distribution lower and upper bounds. Non-positive real numbers.

Specified Value(s): 0, 0

Value from Constable and de la Mare (1996). As in Grym’s base-case, age at size-0 assumed as known (i.e. no uncertainty).

LenCV: The coefficient of variation (defined as the standard deviation divided by mean) of the length-at-age. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided to specify the distribution of observed length-at-age, and the CV of this distribution is constant for all age classes (i.e, standard deviation increases proportionally with the mean). Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 0.01, 0.01

Grym’s base case does not account for variation in length-at-age, implying that all individuals follow exactly the average growth curve. However, trial runs in openMSE indicated that simulations would crash if variation in length-at-age was set to zero.

Hence, to avoid simulation crashes, a very low level of variation (CV of 1%) in length-at-age was assumed in openMSE simulations.

Furthermore, variation in length-at-age treated as known without error, with fixed values across simulations.

Ksd: Inter-annual variation in K. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. If this parameter has a positive value, yearly K is drawn from a log-normal distribution with a mean specified by the value of K drawn for that simulation and a standard deviation (in log space) specified by the value of Ksd drawn for that simulation. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified Value(s): 0, 0

Assuming no inter-annual variation in growth parameter $K$.

Linfsd: Inter-annual variation in Linf. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. If this parameter has a positive value, yearly Linf is drawn from a log-normal distribution with a mean specified by the value of Linf drawn for that simulation and a standard deviation (in log space) specified by the value of Linfsd drawn for that simulation. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified Value(s): 0, 0

Assuming no inter-annual variation in $L_\infty$.

Growth Parameters

Sampled Parameters

Histograms of 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% maturity. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. The L50 and L50_95 parameters are converted to ages using the growth parameters provided and used to construct a logistic curve to determine the proportion of the population that is mature in each age class. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 32, 37

Same values as minimum and maximum length (mm) at 50% maturity as specified under scenario scn-1, originally provided in D. Maschette et al. (2021) (check main analysis document for further details).

L50_95: Difference in lengths between 50% and 95% maturity. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. The value drawn is then added to the length at 50% maturity to determine the length at 95% maturity. This parameterization is used instead of specifying the size at 95 percent maturity to avoid situations where the value drawn for the size at 95% maturity is smaller than that at 50% maturity. The L50 and L50_95 parameters are converted to ages using the growth parameters provided and used to construct a logistic curve to determine the proportion of the population that is mature in each age class. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 2.7, 2.7

Grym’s base-case formulates size-at-maturity using the ogive ramp function specified in terms L50 and the ramp’s width matrange (i.e. the range at which maturity occurs).

Thus, L95 (length at which 95% of individuals are matures) can be derived via the quantile function of the uniform distribution with limits L50 +- matrange/2.

For a (known) width of 6mm, as specified under input scenario scn-1, we derive the L50_95 parameter value as follows:

matrange <- 6 
L50 <- 35 # arbitrary as `matrange` is treated as independent of midpoint L50 in Maschette et al (2021) 
L95 <- qunif(0.95, L50 - matrange/2, L50 + matrange/2) 
L95 - L50

## [1] 2.7

Similarly to the Grym approach, where matrange is treated as known, L50_95 is also kept fixed across simulations.

Maturity Parameters

Sampled Parameters

Histograms of simulations of L50 (length at 50% maturity), and L95 (length at 95% maturity), 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: Estimated current level of stock depletion, which is defined as the current spawning stock biomass divided by the unfished spawning stock biomass. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This parameter is used during model initialization to select a series of yearly historical recruitment values and fishing mortality rates that, based on the information provided, could have resulted in the specified depletion level in the simulated last historical year. Uniform distribution lower and upper bounds. Positive real numbers (typically < 1)

Specified Value(s): 1, 1

Arbitrary values as depletion optimization step is not carried out (see Depletion optimization section above).

Fdisc: The instantaneous discard mortality rate the stock experiences when fished using the gear type specified in the corresponding fleet object and discarded. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Uniform distribution lower and upper bounds. Non-negative real numbers.

Specified Value(s): 0, 0

Zero discard mortality rate, as discards are assumed non-existent in the Krill fishery, similarly to the Grym’s base-case application.

Depletion and Discard Mortality

Sampled Parameters

Histograms of 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: The alpha parameter in allometric length-weight relationship. Single value. Weight parameters are used to determine catch-at-age and population-at-age from the number of individuals in each age class and the length of each individual, which is drawn from a normal distribution determined by the Linf , K , t0 , and LenCV parameters. As a result, they function as a way to scale between numbers at age and biomass, and are not stochastic parameters. Single value. Positive real number.

Specified Value(s): 0

Value from SC-CAMLR (2000). As in Grym’s base-case, the parameter a is assumed to be known without error (i.e. fixed values across simulations).

b: The beta parameter in allometric length-weight relationship. Single value. Weight parameters are used to determine catch-at-age and population-at-age from the number of individuals in each age class and the length of each individual, which is drawn from a normal distribution determine by the Linf , K , t0 , and LenCV parameters. As a result, they function as a way to scale between numbers at age and biomass, and are not stochastic parameters. Single value. Positive real number.

Specified Value(s): 3.31

Value from SC-CAMLR (2000). Parameter b assumed to be known without error (i.e. fixed values across simulations).

Spatial distribution and movement: Size_area_1, Frac_area_1, Prob_staying

Size_area_1: The size of area 1 relative to area 2. The fraction of the unfished biomass in area 1. Please specify numbers between 0 and 1. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. For example, if Size_area_1 is 0.2, then 20% of the total area is allocated to area 1. Fishing can occur in both areas, or can be turned off in one area to simulate the effects of a no take marine reserve. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 0.5, 0.5

Parameter value not allowed to be 1 (i.e. forcing one single area), so specifying that the two sub-areas have equal size.

Frac_area_1: The fraction of the unfished biomass in area 1. Please specify numbers between 0 and 1. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. For example, if Frac_area_1 is 0.5, then 50% of the unfished biomass is allocated to area 1, regardless of the size of area 1 (i.e, size and fraction in each area determine the density of fish, which may impact fishing spatial targeting). In each time step recruits are allocated to each area based on the proportion specified in Frac_area_1. Uniform distribution lower and upper bounds. Positive real numbers.

Specified Value(s): 0.5, 0.5

Parameter value not allowed to be 1 (i.e. forcing whole population to a single area), so specifying that population is evenly split between the two sub-areas.

Prob_staying: The probability of individuals in area 1 remaining in area 1 over the course of one year. Please specify numbers between 0 and 1. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. For example, in an area with a Prob_staying value of 0.95 each fish has a 95% probability of staying in that area in each time step, and a 5% probability of moving to the other area. Uniform distribution lower and upper bounds. Positive fraction.

Specified Value(s): 0.5, 0.5

Assuming 50% chance of movement between sub-areas.

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 simulation. Single value. For example, if the simulated population is assumed to be unfished in 1975 and this is the year you want to start your historical simulations, and the most recent year for which there is data available is 2019, then nyears equals 45.

Specified Value(s): 2

Minimum number of years allowed for the historical period in the current version of openMSE/MSEtools. Any value lower than 2 will cause simulation errors.

Spat_targ: Distribution of fishing in relation to vulnerable biomass (VB) across areas. The distribution of fishing effort is proportional to VB^Spat_targ. Upper and lower bounds of a uniform distribution. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This parameter allows the user to model either avoidance or spatial targeting behavior by the fleet. If the parameter value is 1, fishing effort is allocated across areas in proportion to the population density of that area. Values below 1 simulate an avoidance behavior and values above 1 simulate a targeting behavior.

Specified Value(s): 1, 1

Assuming fishing effort is allocated across areas in proportion to the population density in each area.

Trend in historical fishing effort (exploitation rate), interannual variability in fishing effort: EffYears, EffLower, EffUpper, Esd

EffYears: Vector indicating the historical years where there is information available to infer the relative fishing effort expended.This vector is specified in terms of the position of the year in the vector rather than the calendar year. For example, say our simulation starts with an unfished stock in 1975,and the current year (the last year for which there is data available) is 2019. Then there are 45 historical years simulated, and EffYears should include numbers between 1 and 45. Note that there may not be information available for every historical year, especially for data poor fisheries. In these situations, the EffYears vector should include only the positions of the years for which there is information, and the vector may be shorter than the total number of simulated historical years (nyears).

Arbitrary value. At least a single value required, otherwise the simulation will crash.

EffLower: Lower bound on relative fishing effort corresponding to EffYears. EffLower must be a vector that is the same length as EffYears describing how fishing effort has changed over time. Information on relative fishing effort can be entered in any units provided they are consistent across the entire vector because the data provided will be scaled to 1 (divided by the maximum number provided).

Stock assumed to remain unexploited during the historical period.

EffUpper: Upper bound on relative fishing effort corresponding to EffYears. EffUpper must be a vector that is the same length as EffYears describing how fishing effort has changed over time. Information on relative fishing effort can be entered in any units provided they are consistent across the entire vector because the data provided will be scaled to 1 (divided by the maximum number provided).

Stock assumed to remain unexploited during the historical period.

EffYears	EffLower	EffUpper
2021	0	0

Esd: Additional inter-annual variability in fishing mortality rate. For each historical simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. If this parameter has a positive (non-zero) value, the yearly fishing mortality rate is drawn from a log-normal distribution with a standard deviation (in log space) specified by the value of Esd drawn for that simulation. This parameter applies only to historical projections.

Specified Value(s): 0, 0

Population assumed to remain unexploited during the historical period, so variability in historical fishing mortality is ignored.

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: Mean temporal trend in catchability (also though of as the efficiency of fishing gear) parameter, expressed as a percentage change in catchability (q) per year. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Positive numbers indicate an increase and negative numbers indicate a decrease. q then changes by this amount for in each year of the simulation This parameter applies only to forward projections.

Specified Value(s): 0, 0

Assuming no change in mean gear efficiency over the projection period.

qcv: Inter-annual variability in catchability expressed as a coefficient of variation. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This parameter applies only to forward projections.

Specified Value(s): 0, 0

Assuming no inter-annual variability in gear efficiency over projection years.

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 at which 5% of the population is vulnerable to selection by the gear used in this fleet. Values can either be specified as lengths (in the same units used for the maturity and growth parameters in the stock object) or as a percentage of the size of maturity (see the parameter isRel for more information). For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless cpars is used to provide time-varying selection.

Specified Value(s): 25.05, 30.05

Analogously to the maturity ogive, the Grym approach specifies gear selectivity as a ramp function governed by two parameters: (i) the ramp’s midpoint L50, expressing the length at which 50% of the fish are vulnerable to selection by the fishery; and (ii) selrange, the width of the ramp.

Minimum and maximum values of L50 and selrange are provided in Thanassekos et al. (2021), which are used to derive the minimum and maximum values of L5 via the uniform quantile function, as follows:

selrange <- 11 
L50 <- c(30, 35) 
L5 <- qunif(0.05, L50 - selrange/2, L50 + selrange/2) 
L5

## [1] 25.05 30.05

LFS: Shortest length at which 100% of the population is vulnerable to selection by the gear used by this fleet. Values can either be specified as lengths (in the same units used for the maturity and growth parameters in the stock object) or as a percentage of the size of maturity (see the parameter isRel for more information). For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless cpars is used to provide time-varying selection.

Specified Value(s): 35.5, 40.5

Values derived from L50 and selrange, as above.

L50 + selrange/2

## [1] 35.5 40.5

Vmaxlen: Proportion of fish selected by the gear at the asymptotic length (‘Stock@Linf’). Upper and Lower bounds between 0 and 1. A value of 1 indicates that 100% of fish are selected at the asymptotic length, and the selection curve is logistic. If Vmaxlen is less than 1 the selection curve is dome shaped. For example, if Vmaxlen is 0.4, then only 40% of fish are vulnerable to the fishing gear at the asymptotic length.

Specified Value(s): 1, 1

All individuals considered to be selected at $L_{\infty}$.

isRel: Specify whether selection and retention parameters use absolute lengths or relative to the size of maturity. Single logical value (TRUE or FALSE).

Specified Value(s): FALSE

Selectivity parameters are in absolute units.

Fishery length retention: LR5, LFR, Rmaxlen, DR

LR5: Shortest length at which 5% of the population is vulnerable to retention by the fleet. Values can either be specified as lengths (in the same units used for the maturity and growth parameters in the stock object) or as a percentage of the size of maturity (see the parameter isRel for more information). For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless cpars is used to provide time-varying selection.

Specified Value(s): 0, 0

Analogously to the Grym’s base case, assuming no discards - i.e. all individuals selected by the gear are retained.

LFR: Shortest length where 100% of the population is vulnerable to retention by the fleet. Values can either be specified as lengths (in the same units used for the maturity and growth parameters in the stock object) or as a percentage of the size of maturity (see the parameter isRel for more information). For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. This value is the same in all years unless cpars is used to provide time-varying selection.

Specified Value(s): 0, 0

Idem to LR5 - Assuming no discards and hence all individuals selected by the gear are retained.

Rmaxlen: Proportion of fish retained at the asymptotic length (‘Stock@Linf’). Upper and Lower bounds between 0 and 1. A value of 1 indicates that 100% of fish are retained at the asymptotic length, and the selection curve is logistic. If Rmaxlen is less than 1 the retention curve is dome shaped. For example, if Rmaxlen is 0.4, then only 40% of fish at the asymptotic length are retained.

Specified Value(s): 1, 1

Same as Vmaxlen, i.e. 100% of fish are retained at $L_{\infty}$.

DR: Discard rate, defined as the proportion of fully selected fish that are discarded by the fleet. Upper and Lower bounds between 0 and 1, with a value of 1 indicates that 100% of selected fish are discarded. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided.

Specified Value(s): 0, 0

Assuming no discards.

Current Year: CurrentYr

CurrentYr: The last historical year simulated before projections begin. Single value. Note that this should match the last historical year specified in the Data object, which is usually the last historical year for which data is available.

Specified Value(s): 2022

Arbitrary value in the context of the openMSE-Grym approximation. Choosing the starting year of the project.

Existing Spatial Closures: MPA

MPA: Logical argument (TRUE or FALSE). Creates an MPA in Area 1 for all years if true is selected. Defaults to FALSE.

Specified Value(s): FALSE

Both areas assumed to be open to fishing at all times.

Obs Parameters

This section is not applicable in the context of the openMSE-Grym approximation, as the Management Procedures (MPs) that will be considered for the analysis (i.e. one MP for each of the considered $\gamma$ values) don’t require sampled data from the fishery. Therefore, all Obs parameters will be set to zero.

Catch statistics: Cobs, Cbiascv, CAA_nsamp, CAA_ESS, CAL_nsamp, CAL_ESS

Cobs: Observation error around the total catch. Observation error in the total catch is expressed as a coefficient of variation (CV). Cobs requires upper and lower bounds of a uniform distribution, and for each simulation a CV is sampled from this distribution. Each CV is used to specify a log-normal error distribution with a mean of 1 and a standard deviation equal to the sampled CV. The yearly observation error values for the catch data are then drawn from this distribution. For each time step the simulation model records the true catch, but the observed catch is generated by applying this yearly error term (plus any bias, if specified) to the true catch.

Specified Value(s): 0, 0

Catch assumed known without observation error.

Cbiascv: Log-normally distributed coefficient of variation controlling the sampling bias in observed catch for each simulation. Bias occurs when catches are systematically skewed away from the true catch level (for example, due to underreporting of catch or undetected illegal catches). Cbiascv is a single value specifying the standard deviation of a log-normal distribution with a mean of 1 and a standard deviation equal to the sampled CV. For each simulation a bias value is drawn from this distribution, and that bias is applied across all years.

Specified Value(s): 0

Catch assumed known without observation bias.

CAA_nsamp: Number of catch-at-age observations collected per time step. For each time step a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Positive integers.

Specified Value(s): 0, 0

No catch-at-age sampling.

CAA_ESS: Effective sample size of catch-at-age observations collected per time step. For each time step a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. CAA_ESS should not exceed CAA_nsamp. If greater than 1, then this is the multinomial distribution sample size. If less than 1, this is the coefficient of variation for the logistic normal distribution (see help doucmentation for simCAA for details).

Specified Value(s): 0, 0

No catch-at-age sampling.

CAL_nsamp: Number of catch-at-length observations collected per time step. For each time step a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Positive integers.

Specified Value(s): 0, 0

No catch-at-length sampling.

CAL_ESS: Effective sample size. For each time step a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. CAL_ESS should not exceed CAL_nsamp. Positive integers.

Specified Value(s): 0, 0

No catch-at-length sampling.

Index imprecision, bias and hyperstability: Iobs, Btobs, Btbiascv, beta

Iobs: Observation error in the relative abundance index expressed as a coefficient of variation (CV). Iobs requires upper and lower bounds of a uniform distribution, and for each simulation a CV is sampled from this distribution. Each CV is used to specify a log-normal error distribution with a mean of 1 and a standard deviation equal to the sampled CV. The yearly observation error values for the index of abundance data are then drawn from this distribution. For each time step the simulation model records the true change in abundance, but the observed index is generated by applying this yearly error term (plus any bias, if specified) to the true relative change in abundance. Positive real numbers.

Specified Value(s): 0, 0

No observation error in the relative abundance index.

Btobs: Observation error in the absolute abundance expressed as a coefficient of variation (CV). Btobs requires upper and lower bounds of a uniform distribution, and for each simulation a CV is sampled from this distribution. Each CV is used to specify a log-normal error distribution with a mean of 1 and a standard deviation equal to the sampled CV. The yearly observation error values for the absolute abundance data are then drawn from this distribution. For each time step the simulation model records the true abundance, but the observed abundance is generated by applying this yearly error term (plus any bias, if specified) to the true abundance. Positive real numbers.

Specified Value(s): 0, 0

No observation error in the absolute abundance index.

Btbiascv: Log-normally distributed coefficient (CV) controlling error in observations of the current stock biomass. Bias occurs when the observed index of abundance is is systematically higher or lower than the true relative abundance. Btbiascv is a single value specifying the standard deviation of a log-normal distribution with a mean of 1 and a standard deviation equal to the sampled CV. For each simulation a bias value is drawn from this distribution, and that bias is applied across all years. Positive real numbers.

Specified Value(s): 0

No bias in observations of stock biomass.

beta: A parameter controlling hyperstability/hyperdepletion in the measurement of abundance. For each simulation a single value is drawn from a uniform distribution specified by the upper and lower bounds provided. Values below 1 lead to hyperstability (the observed index decreases more slowly than the true abundance) and values above 1 lead to hyperdepletion (the observed index decreases more rapidly than true abundance). Positive real numbers.

Specified Value(s): 0, 0

Assuming no hyperstability/hyperdepletion in abundance estimation.

Bias in maturity, natural mortality rate and growth parameters: LenMbiascv, Mbiascv, Kbiascv,t0biascv, Linfbiascv

LenMbiascv: Log-normal coefficient of variation for sampling bias in observed length at 50 percent maturity. LenMbiascv is a single value specifying the standard deviation of a log-normal distribution with a mean of 1 and a standard deviation equal to the sampled CV. For each simulation a bias value is drawn from this distribution, and that bias is applied across all years. Positive real numbers.

Specified Value(s): 0