Stone’s sheep in WMU7-42 (Peace Region of British Columbia, Canada): a case study for terrestrial mammal harvests
Term project for Murdoch McAllister`s FISH 505 Graduate Course at the Unversity of British Columbia, Spring 2018
Mairin Deith, University of British Columbia
[email protected]
Introduction
This operating model was built to explore the applicability of traditional fisheries assessments to terrestrial ungulate harvests. Stones sheep, a subspecies of thinhorn sheep, are subject to a male-only trophy harvest based on horn length. In British Colubmia, only sexually mature males with fully curled horns can be harvested legally during the open season (from August to mid-October).
Curl of the Stone’s sheep horn as an indicator of maturity and legal status. Image from the Ministry of Forests, Lands and Natural Resource Operations, British Columbia.
Hunted rams are subject to compulsory inspections by Conservation Officers in the province. Therefore the primary data source used to specify this operating model came from records of the compulsory inspections, which list the age, horn size, and other characteristics of each ram that was legally harvested. These catch-at-age data were used to inform a stock reduction analysis (SRA) that estimated a number of parameters specified in this operating model (i.e. R0, h, and D). Airbourne counts of Stone’s sheep in this region were conducted in 1994, 2002, 2007, and 2012, and these population estimates were also incorporated in this model (data available upon request from British Columbia’s Ministry of Forests, Lands, and Natural Resource Operations).
The remaining parameters, particularly those regarding horn growth patterns and natural mortality rates, were taken from existing literature on hunted and unhunted populations of Stone’s sheep.
Numbers based model
Unlike conventional fisheries models, ram harvests are numbers-based rather than biomass-based. Therefore the weight of all males is equal to 1 in this analysis, and harvested biomass can be considered synonymous to the number of hunted rams.
Similar to fish-based MSEs, this analysis also considers length and growth with age. However, rather than modeling changes to body length over time, this model calculates asymptotic increases to horn size over time. Maturity at length and hunter selectivity at length are therefore based on horn size at age.
The major uncertainty in this analysis is recruitment patterns. As trophy hunting is restricted to fully matured males, it is unclear if any of the population’s reproductive capacity is reduced by male removals. It is believed that even if all legal males are harvested from the population, younger males would still be able to impregnate all ewes (Ian Hatter, personal communication). However, rampant male harvests can lead to population collapse in ungulates if the proportion of males in the population drop below some critical threshold (Milner-Gulland et al. 2003). At this time, it is unclear what this threshold may be for Stone’s rams. This analysis assumes a Beverton-Holt recruitment pattern with high steepness to reflect the weak link between male numbers and reproduction.
Robustness tests:
Robustness OM2: Recruitment follows a 10-year periodic cycle (following wolf population and sunspot cycles)
Robustness OM3: Artificial selection as a result of hunting pressure has caused a gradual reduction in early horn growth (as per Douhard et al. 2016)
Robustness OM4a: True hunter selectivity at age is biased towards younger/shorter-horned males than seen historically
Robustness OM4b: True hunter selectivity at age is biased towards older/larger-horned males than seen historically
Robustness OM5a: Recruitment compensation is steeper (higher bounds for h)
Robustness OM5b: Recruitment compensation is less steep (lower bounds for h)
Operating Model
The OM rdata file can be downloaded from here
Download and import into R using myOM <- readRDS('OM.rdata')
Species Information
Species: Ovis dalli stonei
Common Name: Stone’s sheep
Management Agency:
Region: Peace River, BC
Latitude: 57.824
Longitude: -124.228
OM Parameters
OM Name: Name of the operating model: StonesSheep_WMU42
nsim: The number of simulations: 200
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
SRA and literature review
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): 16
16, from the maximum age of horns identified during compulsory inspections.
R0: The magnitude of unfished recruitment. Single value. Positive real number
Specified Value(s): 294.05
Value taken from SRA estimates of recruitment at unharvested levels.
M: Natural mortality rate. Uniform distribution lower and upper bounds. Positive real number
Specified Value(s): 0.54, 0.07, 0.03, 0.04, 0.05, 0.06, 0.1, 0.15, 0.26, 0.41, 0.77, 1.2, 1.2, 1.2, 1.2, 1.2
Age-specific mortality from Hoefs and Bayer, 1983.
M2: (Optional) Natural mortality rate at age. Vector of length maxage . Positive real number
Specified Value(s): 0.55, 0.08, 0.04, 0.05, 0.06, 0.07, 0.11, 0.16, 0.27, 0.42, 0.78, 1.21, 1.21, 1.21, 1.21, 1.21
The same values for M, but increased slightly (by 0.01, as per the gray seal example).
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
Slot not used.
Msd: Inter-annual variability in natural mortality rate expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.05, 0.15
Assumes low variability in natural mortality between years.
Natural Mortality Parameters
Sampled Parameters
Histograms of 48 simulations of M, Mexp, and Msd parameters, with vertical colored lines indicating 3 randomly drawn values used in other plots:
Time-Series
The average natural mortality rate by year for adult fish for 3 simulations. The vertical dashed line indicates the end of the historical period:
M-at-Age
Natural mortality-at-age for 3 simulations in the first historical year, the last historical year (i.e., current year), and the last projected year:
M-at-Length
Natural mortality-at-length for 3 simulations in the first historical year, the last historical year (i.e., current year), and the last projected year:
Recruitment: h, SRrel, Perr, AC
h: Steepness of the stock recruit relationship. Uniform distribution lower and upper bounds. Values from 1/5 to 1
Specified Value(s): 0.75, 0.9
Value taken from SRA estimates of Beverton-Holt steepness.
SRrel: Type of stock-recruit relationship. Single value, switch (1) Beverton-Holt (2) Ricker. Integer
Specified Value(s): 1
Beverton-Holt relationship chosen (1) instead of the Ricker relationship (2).
Perr: Process error, the CV of lognormal recruitment deviations. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.01, 0.02
Indicates very low interannual variability in recruitment
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): 0.25, 0.65
Value calculated from the lag-1 autocorrelation of recruits in the historical time series.
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): 100, 135
Numbers taken from distribution of horn lengths at age (in cm) from trophy horns, which were used to calculate a von Bertalaffy growth curve for ram horns.
K: von Bertalanffy growth parameter k. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.32, 0.42
From the von Bertalaffy model.
t0: von Bertalanffy theoretical age at length zero. Uniform distribution lower and upper bounds. Non-positive real numbers
Specified Value(s): -0.1, 0.1
From the von Bertalaffy model.
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): 0.1, 0.12
From the von Bertalaffy model.
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
Unknown, default value maintained in the OM.
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
Unknown, default value maintained in the OM.
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): 65, 80
Horn length at 50% maturity is between 3/4 and full curl males (who are typically legal to hunt if their horns are >90cm).
Stress-case OMs 4a and 4b investigates an alternative selectivity curves.
L50_95: Length increment from 50 percent to 95 percent maturity. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 10, 30
The rate of horn growth decelerates with age, and little horn growth distinguishes males at 50% maturity with those 95% vulnerable.
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): 0.65, 0.75
Value from SRA, which indicated the stock to be at 71% of unharvested levels.
Fdisc: Fraction of discarded fish that die. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
Unknown, default value maintained in the OM.
Depletion and Discard Mortality
Sampled Parameters
Histograms of 48 simulations of depletion (spawning biomass in the last historical year over average unfished spawning biomass; D) and the fraction of discarded fish that are killed by fishing mortality (Fdisc), with vertical colored lines indicating 3 randomly drawn values.
Length-weight conversion parameters: a, b
a: Length-weight parameter alpha. Single value. Positive real number
Specified Value(s): 1
Numbers-based model, not weight-based.
b: Length-weight parameter beta. Single value. Positive real number
Specified Value(s): 0
Numbers model - by setting b to zero, each individual’s weight = 1, and harvested ‘biomass’ becomes harvested numbers instead.
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
Unknown, default value maintained in the OM.
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
Unknown, default value maintained in the OM.
Prob_staying: The probability of inviduals in area 1 remaining in area 1 over the course of one year. Uniform distribution lower and upper bounds. Positive fraction.
Specified Value(s): 0.5, 0.5
Unknown, default value maintained in the OM.
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): 42
Catch-at-age data from compulsory inspections range from 1975 to 2016.
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
Unknown, default value maintained in the OM.
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
No justification provided.
EffLower: Lower bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
No justification provided.
EffUpper: Upper bound on relative effort corresponding to EffYears. Vector. Non-negative real numbers
No justification provided.
| EffYears | EffLower | EffUpper |
|---|---|---|
| 1975 | 0.0375 | 0.0375 |
| 1976 | 0.0236 | 0.0236 |
| 1977 | 0.0467 | 0.0467 |
| 1978 | 0.0438 | 0.0438 |
| 1979 | 0.0450 | 0.0450 |
| 1980 | 0.0444 | 0.0444 |
| 1981 | 0.0426 | 0.0426 |
| 1982 | 0.0277 | 0.0277 |
| 1983 | 0.0276 | 0.0276 |
| 1984 | 0.0240 | 0.0240 |
| 1985 | 0.0262 | 0.0262 |
| 1986 | 0.0326 | 0.0326 |
| 1987 | 0.0315 | 0.0315 |
| 1988 | 0.0428 | 0.0428 |
| 1989 | 0.0457 | 0.0457 |
| 1990 | 0.0526 | 0.0526 |
| 1991 | 0.0479 | 0.0479 |
| 1992 | 0.0533 | 0.0533 |
| 1993 | 0.0664 | 0.0664 |
| 1994 | 0.0468 | 0.0468 |
| 1995 | 0.0467 | 0.0467 |
| 1996 | 0.0423 | 0.0423 |
| 1997 | 0.0471 | 0.0471 |
| 1998 | 0.0445 | 0.0445 |
| 1999 | 0.0524 | 0.0524 |
| 2000 | 0.0400 | 0.0400 |
| 2001 | 0.0351 | 0.0351 |
| 2002 | 0.0333 | 0.0333 |
| 2003 | 0.0260 | 0.0260 |
| 2004 | 0.0161 | 0.0161 |
| 2005 | 0.0280 | 0.0280 |
| 2006 | 0.0325 | 0.0325 |
| 2007 | 0.0266 | 0.0266 |
| 2008 | 0.0327 | 0.0327 |
| 2009 | 0.0246 | 0.0246 |
| 2010 | 0.0248 | 0.0248 |
| 2011 | 0.0300 | 0.0300 |
| 2012 | 0.0352 | 0.0352 |
| 2013 | 0.0358 | 0.0358 |
| 2014 | 0.0523 | 0.0523 |
| 2015 | 0.0387 | 0.0387 |
| 2016 | 0.0406 | 0.0406 |
Esd: Additional inter-annual variability in fishing mortality rate. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No justification provided.
Historical Effort
Sampled Parameters
Histograms of 48 simulations of inter-annual variability in historical fishing mortality (Esd), with vertical colored lines indicating 3 randomly drawn values used in the time-series plot:
Time-Series
Time-series plot showing 3 trends in historical fishing mortality (OM@EffUpper and OM@EffLower or OM@cpars$Find):
Annual increase in catchability, interannual variability in catchability: qinc, qcv
qinc: Average percentage change in fishing efficiency (applicable only to forward projection and input controls). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No justification provided.
qcv: Inter-annual variability in fishing efficiency (applicable only to forward projection and input controls). Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0, 0
No justification provided.
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): 75, 75
Length taken from percentile distribution of catch-at-age data from compulsory horn inspections.
LFS: Shortest length that is fully vulnerable to fishing. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 90, 90
See above.
Vmaxlen: The vulnerability of fish at Stock@Linf . Uniform distribution lower and upper bounds. Fraction
Specified Value(s): 1, 1
At maximum length, vulnerability to hunting is 1.
isRel: Selectivity parameters in units of size-of-maturity (or absolute eg cm). Single value. Boolean.
Specified Value(s): FALSE
Default value.
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
Assume that 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
Assume that 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
Assume that retention follows selectivity.
DR: Discard rate - the fraction of caught fish that are discarded. Uniform distribution lower and upper bounds. Fraction
Slot not used.
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
Existing Spatial Closures: MPA
MPA: (Optional) Matrix specifying spatial closures for historical years.
Slot not used.
Obs Parameters
Catch statistics: Cobs, Cbiascv, CAA_nsamp, CAA_ESS, CAL_nsamp, CAL_ESS
Cobs: Log-normal catch observation error expressed as a coefficient of variation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.01, 0.02
Because all hunters must present trophy rams for compulsory inspection, this OM assumes that catches are observed without bias.
Cbiascv: Log-normal coefficient of variation controlling the sampling of bias in catch observations for each simulation. Uniform distribution lower and upper bounds. Non-negative real numbers
Specified Value(s): 0.01
See above.
CAA_nsamp: Number of catch-at-age observation per time step. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 40, 60
Assumes an average of 50 rams are harvested each year and inspected by governmental agents.
CAA_ESS: Effective sample size (independent age draws) of the multinomial catch-at-age observation error model. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 40, 60
See above.
CAL_nsamp: Number of catch-at-length observation per time step. Uniform distribution lower and upper bounds. Positive integers
Specified Value(s): 41, 59
See above.
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): 41, 60
See above.
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
Default value.
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
Default value, not used.
Btobs: Log-normal coefficient of variation controlling error in observations of current stock biomass among years. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.05, 0.1
Default value.
Btbiascv: Uniform-log bounds for sampling persistent bias in current stock biomass. Uniform-log distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.02, 0.05
Default 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): 1, 1
Default value.
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
Default value.
Mbiascv: Log-normal coefficient of variation for sampling persistent bias in observed natural mortality rate. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default value.
Kbiascv: Log-normal coefficient of variation for sampling persistent bias in observed growth parameter K. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default 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): 0.1
Default value.
Linfbiascv: Log-normal coefficient of variation for sampling persistent bias in observed maximum length. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default 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): 0.1
Default value.
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
Default value.
Bias in fishery reference points, unfished biomass, FMSY, FMSY/M ratio, biomass at MSY relative to unfished: FMSYbiascv, FMSY_Mbiascv, BMSY_B0biascv
FMSYbiascv: Not used. Log-normal coefficient of variation for sampling persistent bias in FMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.4
Default value.
FMSY_Mbiascv: Log-normal coefficient of variation for sampling persistent bias in FMSY/M. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default value.
BMSY_B0biascv: Log-normal coefficient of variation for sampling persistent bias in BMSY relative to unfished. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default value.
Management targets in terms of the index (i.e., model free), the total annual catches and absolute biomass levels: Irefbiascv, Crefbiascv, Brefbiascv
Irefbiascv: Log-normal coefficient of variation for sampling persistent bias in relative abundance index at BMSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5
Default value.
Crefbiascv: Log-normal coefficient of variation for sampling persistent bias in MSY. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.5
Default value.
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
Default value.
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
Default 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): 0.2, 0.4
Default value.
Recruitment compensation and trend: hbiascv, Recbiascv
hbiascv: Log-normal coefficient of variation for sampling persistent bias in steepness. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1
Default value.
Recbiascv: Log-normal coefficient of variation for sampling persistent bias in recent recruitment strength. Uniform distribution lower and upper bounds. Positive real numbers
Specified Value(s): 0.1, 0.1
Default value.
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
All TAC taken without SD in implementation.
TACSD: Log-normal coefficient of variation in the fraction of Total Allowable Catch (TAC) taken. Uniform distribution lower and upper bounds. Non-negative real numbers.
Specified Value(s): 0.01, 0.02
Default 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
No justification provided.
TAESD: Log-normal coefficient of variation in the fraction of Total Allowable Effort (TAE) taken. Uniform distribution lower and upper bounds. Non-negative real numbers.
Specified Value(s): 0.01, 0.02
No justification provided.
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
Assume that 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): 0.01, 0.02
Assume some minor variation in size limits.
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
Douhard, M., Festa-Bianchet, M., Pelletier, F., Gaillard, J.M., and Bonenfanti, C. 2016. Changes in horn size of Stone’s sheep over four decades correlate with trophy hunting pressure. Ecological Applications 26(1): 309-21.
Hoefs, M., and Bayer, M. 1983. Demographic characteristics of an unhunted Dall sheep (Ovis dalli dalli) population in southwest Yukon, Canada. Canadian Journal of Zoology 61(6): 1346-1357.
Milner-Gulland, E.J., Bukreevea, O.M., Coulson, T., Lushchekina, A.A., Kholodova, M.V., Bekenov, A.B., and Grachev, I.A. 2003. Conservation - Reproductive collapse in saiga antelope harems. Nature 422: 135.