Main Calibration Procedures
The purpose of a calibration is to produce base period exploitation
rates for each stock and fishery in the FRAM model. To this end, marked
CWTs from base period years (brood years 2005-2008) were analyzed and
summarized to
reconstruct
cohorts.
At the completion of the base data development process,
each FRAM stock-age cohort is doubled, with half the cohort being
assigned to “unmarked” and the other half to “marked” components to
allow for processing of mark-selective fisheries in “forward-projection”
runs of FRAM used in preseason fishery modeling. The final step in the
calibration cycle is the development of a completed
base
period input file used by FRAM. This file contains stock abundances,
time-age-fishery specific exploitation rates, maturation rates, growth
rates, and various fishery related parameters such as hooking mortality
rates. A new calibration of FRAM is warranted when there are changes to
the input data and/or model structure. Examples include changes to
stocks, fisheries, CWT groups, time structure, and growth, natural, and
fishery related handling mortality rates. All of these elements
influence the estimates of the cohort sizes calculated during
cohorts analysis and the corresponding estimates of exploitation
rates.
Cohort reconstruction involves several steps described below and illustrated by Figurecalplotxxx. This process is augmented for stocks with insufficient CWT recoveries in the existing base period. For these out-of-base stocks, a different range of years with sufficient CWT recoveries stands-in to provide the needed tag recovery resolution. These tag recoveries are adjusted in an iterative process to simulate the recoveries that would have occurred given the magnitude of the fisheries in the selected base period (see out-of-base procedures ). Once adjusted, these CWTs are combined with the “in-base” recoveries and processed.
Figurecalplotxxx Calibration Overview
Variables and Notation
a: Age in years (2 to 5).
AEQs,a,t: Adult Equivalence by stock, age, and time step. The probability that a fish will survive to spawn in the absence of future fishing (calibration output). AEQs are a calibration output. For more information see AEQ Mortality Rates in the Data chapter.
BPEscapes:Marked as well as total escapements were provided by regional experts for each Chinook stock.For the purpose of calibration, escapement includes freshwater catch. Escapements are a calibration input. For more escapement information see Escapements in the “Data” chapter.
BPObsCatchf: Observed catch by fishery during the base period (input). Catches are a calibration input. For more information see Landed Catch in the “Data” chapter.
BPPTCatchs,a,f,t: Base period CWT recoveries in preterminal fisheries by stock, age, and time step. For more information see CWTs in the Data chapter.
BPTermCatchs,a,f,t: Base period CWT recoveries in terminal fisheries by stock, age, and time step. For more information see CWTs in the Data chapter.
CNRLegs,a,f,t: Legal size release mortality of a stock and age in a non-retention fishery and time step. This is calculated during calibration. For more information see Incidental Mortality in the Data chapter.
CNRMortss,a,f,t: Non-retention mortalities by stock, age, fishery, and time step. This is calculated during calibration. For more information see Incidental Mortality in the Data chapter.
CNRSubs,a,f,t: Sublegal size release mortality of a stock and age in a non-retention fishery and time step. This is calculated during calibration. For more information see Incidental Mortality in the Data chapter.
Cohorts,a,TerminalType,t: Pre-fishing abundance of a stock at age a and time step t. If terminal type =0 then abundance is before maturation, if terminal type =1 then after maturation. The cohort is a calibration output, calculated during cohort reconstruction procedures. For more information see Base Period Cohort in the Data chapter.
CVs,a: Coefficient of variation in length-at-age by stock and age. This is a calibration input. For more information see Growth Functions in the Data chapter.
CWTCatchs,a,f,t: CWT recoveries by stock, age, fishery, and time step expanded for sampling fraction. This is a data input. For more information see CWTs in the Data chapter.
CWTEscapes,a,t: CWTs by stock, age, and time step recovered in escapement and freshwater fisheries expanded for sampling fraction. This is a data input. For more information see CWTs in the Data chapter.
DropOfff: Dropoff mortality rate by fishery. For more information see Incidental Mortality in the Data chapter.
ExpRates,a,f,t: The fraction of the vulnerable (legal) cohort taken in a fishery. It is calculated as the mortality of a stock and age in a fishery and time step divided by the abundance of the stock and age. The denominator, the abundance, is the sum of all fisheries related moralities plus escapement. This is a calibration output. For more information see Base Period Exploitation Rates in the Data chapter.
f. Fishery. There are currently 74 FRAM Chinook Fisheries . Fishery 74 is escapement. Fisheries are a calibration input. For more information see Fisheries in the Data chapter.
LandedCatchs,a,f,t: Estimated total catch of a stock in a fishery by age and time step. This catch is calculated by expanding CWTCatch using the escapement expansion and the fishery expansion.
LegalEncs,a,f,t: Legal encounters in a non-retention fishery. Stock specific encounters are calculated during the calibration by splitting total encounters into stocks and ages. For more information see Non Retention Encounters in the Data chapter.
LegalProps,a,f,t: Proportion of the cohort which is above the legal size limit by stock, age, fishery, and time step. The legal proportion is caluclated during the calibration. For more information about the computation of the proportion legal/sublegal of a stock-age using the Von Bertalanffy growth equation see Size Limit Calculations.
LegalRelaseMortalityRate_f: Release mortality rate of legal sized Chinook in a fishery. This is a calibration input. For more information see Incidental Mortality in the Data chapter.
MatCohorts,a,t: The mature cohort, i.e., the number of fish by stock, age, and time step destined to spawn in the current year in the absence of further fishing. This is calculated during calibration. For more information see Maturation Rates in the Data chapter.
MatRates,a,t: The fraction of the cohort by stock and age that matures in a given time step. This is a calibration output. For more information see Maturation Rates in the Data chapter.
Means,a,t: Mean fork length of a fish by stock, age, and time step. For more information about the computation of the mean length using the Von Bertalanffy growth equation see Size Limit Calculations.
MinSizea,f,t: Minimum size limit in a fishery by age, fishery, and time step. The age subscript is carried but not used in computations. This is a calibration input. For more information see Minimum Size Limit in the Data chapter.
ModelRatiof: The proportion of the observed catch in a fishery that can be accounted for by stocks in the model. It is frequently referred to as the Mode Stock Proportion (MSP). This can either be a data input or output. For the calculation of the model ratio see Model Stock Proportion(MSP) .
MSPf,t: Model-stock proportion. Percentage of a fishery’s total catch that is accounted for by stocks modeled in FRAM. For the calculation of the model stock proportion see Model Stock Proportion (MSP) .
PEFs: Stock specific Production Expansion Factor. The ratio of total stock escapement to the escapement of the CWTed population. It is calculated during the calibration. For more information see Expand CWTs to Total Production.
PropLegCatchs,a The proportion of the legal catch in a fishery and time step that is of a given stock and age. This parameter is calculated during the calibration.
PropSubCatchs,a The proportion of the sublegal encounters in a fishery and time step that is of a given stock and age. This parameter is calculated during the calibration.
PTCohorts,a,t: The preterminal (immature) ocean cohort size by stock, age, and time step. This parameter is calculated during the calibration.
PTERs,a,f,t: Exploitation rate in preterminal fishery by stock, age, and time step. This parameter is calculated during the calibration. This parameter is output to the calibration database.For more information see Base Period Exploitation Rates in the Data chapter.
PTMortss,a,t: Total moralities of CWTed fish in preterminal fisheries by stock, age, and time step. This parameter is calculated during the calibration.
s: Stock number. There are currently 39 stocks in the model. This is a calibration input. For more information see Stocks in the Data chapter.
ScaleFactorf,t: Fishery and time step specific ratio of fishery exploitation rate during the CWT recovery year to the fishery exploitation rate during the base period. This is a calibration input derived during iterative validation runs. For more information see Fishery Scalers in the Data chapter.
Shakerss,a,f,t: Total mortalities of sublegal fish by stock, age, fishery, and time step. Shakers is calculated during the calibration. For a calculation of this parameter refer to Sublegal Stock-, Age-Composition.
ShakerReleaseMortalityRatef: Fishery specific shaker (sublegal) mortality rate. This is a calibration input. For more information see Incidental Mortality in the Data chapter.
SRatea,t: Survival rate by age and time step. The survival rate equals 1 minus natural mortality rate. For more information see Natural Mortality in the Data chapter.
SublegalEncs,a,f,t: Sublegal encounters in a non-retention fishery. This is calculated during the calibration. For a calculation of this parameter refer to Sublegal Stock-, Age-Composition.
SubLegProps,a,f,t: Proportion of the total cohort size by stock and age (terminal or preterminal) which is below the legal size limit in a given fishery and time step. This is calculated during the calibration.
t: Time step. There are 3 time steps per ‘year’: Oct – Apr, May – June, and July – Sept.
TargEncRatef,t: Sublegal to legal ratio in a fishery and time step. This rate is used to calculate the number of sublegal encounters when the legal retained catch is known. This is a calibration input. For more information see Target Encounter Rates in the Data chapter.
TermERs,a,f,t: Exploitation rate in terminal fishery by stock, age, and time step. This is derived though calibration calculations and becomes a calibration output. For more information see Base Period Exploitation Rates in the Data chapter.
TMortss,a,t: Total mortalities (landed plus incidental) in terminal fisheries by stock, age, and time step. It is calculated during calibration.
TotalBPEscs: Adult total escapement by stock during the base period. This is a calibration input. For more information see Escapements in the Data chapter.
TotalCohorts,a,t: The total cohort available at the start of each time period before natural mortality by stock, age, and time step. This is a a calibration output. For more information see Base Period Cohort in the Data chapter.
TotCatchf,t: Total landed catch summed over stocks and ages for a fishery and time step. This is calculated during the calibration.
TotEncountersf,t: Total encounters in a fishery and time step. For non-retention calculations this value can be provided as an input.
Expand CWTs to Total Production
The purpose of this expansion is to estimate the total size of the
stock aggregate by accounting for un-tagged segments of the aggregate;
i.e, the South Puget Sound Chinook stock aggregate is comprised of
tagged Nisqually and Chambers hatchery Chinook, but also includes
untagged Tumwater Falls hatchery and wild Nisqually Fall Chinook. To
make estimates for the entire stock aggregate, the production expansion factor (PEF) is calculated as the
ratio of adult escapement accounted for with CWTs to the total adult
escapement of a stock.
Equationxxx
$$ PEF_s=\frac{TotalBPEsc_s}{\sum_{a=3-5,t=1-3}CWTEscape_{s,a,t}} $$
Note that if a ‘large’ CWT group is used to represent the catch distribution of a ‘small’ hatchery stock, the expansion factors may be less than 1.0 MEW, 2008.
Expand CWTs to Match Fishery Catch
Depending on the setting of an input flag, observed base period CWT
recoveries are adjusted so that the sum across stocks in each fishery,
expanded by PEFs equals the total observed catch in
each fishery.
Equation for fisheries where model stocks account for 100% of the landed
catch:
Equationxxx $$ CWTCatch_{f,t}=\sum_{s,a}(CWTCatch_{s,a,f,t}{\times}PEF_{s})\phantom{\frac{1}{1}} $$
Equation22xxx
$$ FishExpansion_{f,t}=\frac{Catch_{f,t}}{CWTCatch_{f,t}} $$
The MSP is the percentage of a fishery accounted for by stocks included in the model. Chinook FRAM does not contain all the stocks impacted by FRAM fisheries. A portion of the stocks, particularly those affecting northern fisheries (Alaska, Canada) are missing from the model. For each of these fisheries, FRAM utilizes a constant proportion to account for non-model stock impacts, frequently using an independent estimate of this quantity, such as genetic data. While the calibration is conducted in a “marked frame of reference”, a FRAM run requires MSPs as a proportion of the total (marked + unmarked) catch (see Mass Marking and Mark Selective Fisheries paragraph). For this reason an input file was created processing CWT recoveries, catches, and escapements in a “total” frame of reference. Additionally, for the purpose of calculating exploitation rates in a “marked frame of reference”, MSP is also needed as the proportion of the marked catch. Tables Base Period Marked Catches and Base Period Total Catches contain model stock proportions and flags for marked and total (marked + unmarked) fisheries.
The previous calibration predominantly relied on estimating the MSP as the proportion of the catch accounted for by CWTs.
Where
Equationxxx
$$ BPObsCatch_f=\sum_{t}BPObsCatch_{f,t}\phantom{\frac{1}{1}} $$
Equationxxx
$$ CWTCatch_f=\sum_{t}CWTCatch_{f,t}\phantom{\frac{1}{1}} $$
Equatio33xxx
$$ MSP_f=\frac{CWTCatch_f}{BPObsCatch_{f}} $$
The landed catch of a stock at age a in a fishery and time step becomes:
Equationxxx
$$ LandedCatch_{s,a,f,t}=CWTCatch_{s,a,f,t}*PEF_s*\frac{1}{MSP_f} $$
The current calibration only uses the MSP calculation as described in equation33xxx for a few fisheries, because of the high variance associated with estimating the parameters entering the calculation of CWTCatchf,t. When flagged as “2”, if the MSP exceeds 100% of the BPObsCatchf, the program scales the CWTCatchs,a,f,t when summed over stocks and ages to 1.
Summary of MSP flags:
1: Adjust modeled catch to equal estimated catch
2: Adjust modeled catch to equal estimated catch if modeled catch exceeds estimated catch
3: Use external adjustment
A flag of “1” is the default setting for all Puget Sound fisheries. Using this flag will expand CWTs such that the CWTCatchs,a,f,t summed over stocks, ages, and time steps equals the BPObsCatchf.
For many fisheries outside Puget Sound a flag of “3” was used. This method relies on external estimates of MSP. CWT recoveries are then adjusted to sum to observed catch times MSP.
Equationxxx
$$ CWTCatch_f= BPObsCatch_f * ModelStockProportion_f\phantom{\frac{1}{1}} $$
External MSP Data Sources
As described above, the MSP can be calculated by the calibration program. This method was infrequently used due to the high variance associated with the estimates. The following external approaches were used depending on availability.
Default of 100% MSP
All Puget Sound fisheries were assumed to be completely represented by model stocks. This was also assumed for Georgia Strait net, North Washington Coast net, and Grays Harbor net. Additionally, the marked catch in most fisheries was assumed to be completely accounted for by the hatchery stocks in the model. This was frequently not the case for unmarked stocks in a fishery, particularly if comprised of difficult to enumerate wild stocks or stock components. To achieve an MSP of 100%, a fishery expansion factor was calculated as in equation (equation22xxx).
Chinook Technical Committee (CTC) MSP
For several northern fisheries, we used output from the 2014 calibration (CLB 1402) of the PSC Chinook model to calculate fishery model stock proportions. Details of this calibrationcan can be found in PSC Joint Chinook Technical Committee report TCCHINOOK (15)-1 V1 and V2. First, for each PSC Chinook Model stock we determined whether it was represented by FRAM model stocks. Then, for each relevant PSC Chinook model fishery, we summed the total stock specific catch across 2007 - 2013 (FRAM base period catch years) based on whether or not the stock was represented in FRAM. From this we calculated the FRAM base period fishery model stock proportion by dividing the total catch of stocks represented in FRAM by the total catch of the fishery.
Genetic Stock Identification (GSI)
Similar to the method evaluating the MSP using the CTC data, we
allocated GSI stock assignments to FRAM and non-FRAM model stock. For
Washington, Oregon, and California fisheries, GSI data originated from
Bellinger, 2015,
Moran, 2017 and personal communication with Dr. Michael O’Farrell.
We averaged fishing year 2012-2013 stock proportions for FRAM model
stocks (for more information please see “FRAM-GSI MSPs
new_Cent_Valley_Fix.xlsx”. An additional adjustment was made to
eliminate San Joachin stock from the GSI stock aggregate for Central
Valley.
For NCBC sport and troll we averaged 2007 to 2014 stock proportions for
FRAM model stocks (for more information please see
ModelStkPPN_9.27.20.
The number next to the source references associated files listed below the table.
Summary of CWT Expansions
Prior to the
PEF expansion and
the
fishery expansion described in the last two paragraphs, CWTs are
subjected to two other expansions.
The first expansion occurs in RMIS and is called a sampling expansion. It is calculated as the total catch in a fishery/time step divided by the sampled catch in a fishery/time step. This results in the number of CWTs that would have been recovered if 100% of the fishery had been sampled.
A second expansion, the brood year expansion, is applied within FRAMBuilder to CWTs that have already received a sampling expansion. The default method gives equal weight to all brood years within the model, but users can also specify brood year weights. The brood year expansion is specific to individual brood years. To calculate the expansion rate, the total number of tags for each brood year is summed. The brood year with the largest number of recoveries is then divided by the sum of tags from the brood year of interest. This expansion factor is then applied to all the CWT recoveries of the brood year to be adjusted. To better demonstrate the expansion process, an age 3 Mid Puget Sound tag (CWT code: 633285) that was recovered in Area 7 Sport on February 17th, 2008 will be used as an example. First, a sampling expansion is pre-applied within RMIS and is a function of the total number of Chinook caught during the sampling period divided by the number of Chinook sampled during the sampling period. The following information comes from RMIS Catch/Sample queries.
| Species | Year | Fishery | LocationCode | Catch | Sampled | Estimated |
|---|---|---|---|---|---|---|
| 1 | 2008 | 45 | 3M11107 | 2643 | 379 | 6.97 |
The sampling expansion of 6.97 is calculated as 2643/379. Further information pertaining to the sampling expansion can be found on page 14 of Overview of the Coded Wire Tag Program (Nandor, 2009).
For the example tag, the table below demonstrates that the brood year expansion applied should be 1.02. The brood year expanded value of the example recovery becomes 7.11 (6.97 * 1.02).
| Year | TotExpandedRecoveries | BY.Expansion |
|---|---|---|
| 2005 | 4383 | 1.02 |
| 2006 | 3018 | 1.63 |
| 2007 | 4930 | 1.00 |
| 2008 | 1179 | 4.18 |
After the expansion is applied, tags recovered for a given stock, age, fishery, time step are summed across brood years. At this point, three additional tags, including two from the 2007 brood year and one from the 2006 brood year are added to the example tag, resulting in a merged expanded value of 16.6.
The final two expansions are applied within the calibration program.
The first, an escapement expansion, adjusts the total number of CWTs in
escapement to match the escapement estimates provided by regional
biologists. This expansion accounts for untagged production, but also
grounds the brood year weighted recoveries by establishing a direct
linking to escapement. The escapement expansion is applied within the
CompExpFactMod.vb module. For the Mid-Puget Sound
aggregate, CWT escapement is 12,418 and observed escapement is 30,785.
Thus, the escapement expansion is 2.48.
The final expansion is a fishery expansion, which adjusts recoveries
in a specific fishery-time step combination to match actual fishery
catch. In this step, the actual fisheries catch is divided by the CWT
expanded catch. The fishery expansion can be found within the
calibration code in the AdjCatch.vb module. In the example
fishery-time step, the fishery expansion is 1.37.
$$ TotalExpansion = BroodYearExpandedTags * FisheryExpansion_{f,t} * EscapementExpansion_s\phantom{\frac{1}{1}} $$
$$ TotalExpansion = 16.6 * 1.37 * 2.48 = 56.4\phantom{\frac{1}{1}} $$
Estimating Sublegal Mortalities
Sublegal
or shaker mortalities result from the release of sublegal sized (below
the minimum size limit) Chinook encountered during a fishery. First, the
total number of sublegal encounters for the fishery-time step are
calculated by taking the
legal
catch from the fishery-time step (found in the
BasePeriodCatch
table for marked and
BasePeriodCatch_Tot
tables for total catches) and multiplying it by an externally provided
sublegal:legal ratio (found in the
TargetEncounterRates
table of the Calibration Support data base).
The
sublegal/legal ratio is often derived from sampling interviews or test
fisheries where the number of legal and sublegal Chinook encountered
during a fishing trip are reported.
Equationxxx $$ Encounters_{f,t}=\sum_{s,a}CWTCatch_{s,a,f,t} * TargetEncounterRate_{f,t}\phantom{\frac{1}{1}} $$ For more information about how to allocate total encounters to stocks and ages, please see Subegal Stock/Age Composition. For more information about the computation of the proportion legal/sublegal of a stock-age using the Von Bertalanffy growth equation see Size Limit Caluations.
Estimating Non-Retention Mortalities (CNR)
Tables
NonRetention
and
NonRetention_Tot
(the former for marked the latter for marked + unmarked) of the
calibration database contain non-retention inputs and flagging. The
primary non-retention input is an estimate of encounters rather than
landed catch. Depending on the value of the
NonRetentionFlag the inputs will either be modeled using
external values of legal and sublegal encounters (flag 3) or an external
value of total encounters (flag 4). CNR impacts can only be calculated
if a landed catch value and associated CWT recoveries exist for a
fishery. A CNR fishery without pre-existing landed catch can be modeled
with a catch of 1. This will only minutely affect cohort sizes, but
allow for the calculation of stock-specific BPERs. CNR calculations
assign encounter estimates to stocks and ages.
Calculations when legal and sublegal encounters are provided
(flag 3):
- Calculate the stock-, age-composition of legal encounters
Equation44xxx
$$ PropLegCatch_{s,a,f,t}=\frac{LandedCatch_{s,a,f,t}}{TotCatch_{f,t}} $$
- Calculate the stock-, age-composition of sublegal encounters
Equation45xxx
$$ PropSubCatch_{s,a,f,t}=\frac{SublegalEncounter_{s,a,f,t}}{TotSublegalEncounters_{f,t}} $$
- Calculate legal mortalities by stock and age
Equationxxx
$$
CNRLegal_{s,a,f,t}= LegalEnc_{f,t} * PropLegCatch_{s,a,f,t} *
LegalReleaseMortalityRate_{f} * MSP_f\phantom{\frac{1}{1}}
$$ * Calculate sublegal mortalities by stock and age
Equationxxx $$
CNRSub_{s,a,f,t}=SublegEnc_{f,t} * PropSubCatch_{s,a,f,t} *
ShakerReleaseMortalityRate_{f} * MSP_f\phantom{\frac{1}{1}}
$$ * Calculate total CNR mortality by stock and age
Equationxxx $$ CNRMorts_{s,a,f,t}=CNRLegal_{s,a,f,t}+CNRSub_{s,a,f,t}\phantom{\frac{1}{1}} $$
Calculations when total encounters are provided (flag
4):
For each fishery/time step, calculate PropLegCatch and PropSubCatch as in equations 44xxx and 45xxx above.
Calculate the proportion of the encounter that is legal as:
Equationxxx
$$ PropLeg_{f,t}=\frac{1}{1+TargEncRate_{f,t}} $$
Please see Target Encounter Rates for more information.
- Calculate legal and sublegal encounters
Equationxxx
$$ LegalEnc_{f,t}=TotEncounters_{f,t}*PropLeg_{f,t}\phantom{\frac{1}{1}} $$ Equationxxx
$$ SublegalEnc_{f,t}=TotEncounters_{f,t}*(1-PropLeg_{f,t})\phantom{\frac{1}{1}} $$
- Calculate legal mortalities by stock and age
Equationxxx
$$ CNRLegal_{s,a,f,t}=LegalEnc_{f,t} * PropLegCatch_{s,a,f,t} * LegalReleaseMortalityRate_{f} * MSP_f\phantom{\frac{1}{1}} $$
- Calculate sublegal mortalities by stock and age
Equationxxx
$$ CNRSub_{s,a,f,t}=SublegEnc_{f,t} * PropSubCatch_{s,a,f,t} * ShakerReleaseMortalityRate_{f} * MSP_f\phantom{\frac{1}{1}} $$
- Calculate total CNR mortality by stock and age
Equationxxx
$$ CNRMorts_{s,a,f,t}=CNRLegal_{s,a,f,t}+CNRSub_{s,a,f,t}\phantom{\frac{1}{1}} $$
Backwards Cohort Reconstruction
After all CWT expansions have been applied, a traditional cohort reconstruction occurs “backwards” such that for each stock, it begins with age 5 Chinook in the final time step, progressing through descending time steps and ages with the age 2, time step 1 cohort calculated last. First, escapement of age 5 Chinook in time step 3 for a given stock is calculated by summing over escapement CWT recoveries. Note that escapement recoveries also include recoveries from freshwater fisheries (see FRAMBuilder ). This is used as a starting value to which terminal fishery mortalities are later added. Total pre-terminal and terminal mortalities are calculated separately by looping through every fishery within a time step and adding expanded CWTs adjusted for other mortality (dropoff/dropout; expressed as a percentage of catch; found in the IncidentalRate table of the Calibration Support data base) and by adding sublegal mortalities (see sublegal mortality section below for additional details as to how this is calculated) and Chinook Non-Retention Mortality (CNR).
Cohort Reconstruction Steps
- Compute terminal and preterminal mortalities for each stock by
summing over fisheries within an age and time step. Summation is
performed on expanded CWT recoveries.
Equationxxx
$$ TMorts_{s,a,t} = \sum_{TFisheries} (LandedCatch_{s,a,f,t}*(1+DropOff_f)+Shakers_{s,a,f,t}+CNRMorts_{s,a,f,t})\phantom{\frac{1}{1}} $$
Equationxxx $$ PTMorts_{s,a,t} = \sum_{PTFisheries} (LandedCatch_{s,a,f,t}*(1+DropOff_f)+Shakers_{s,a,f,t}+CNRMorts_{s,a,f,t})\phantom{\frac{1}{1}} $$
- Compute the terminal or mature cohort by age and time step
Equationxxx
$$ MatCohort_{s,a,t}=TMorts_{s,a,t}+CWTEscape_{s,a,t}*PEF_s\phantom{\frac{1}{1}} $$
- Starting with age 5 time step 3, the preterminal cohort after
natural mortality is computed as:
Equationxxx
PTCohorts, a = 5, t = 3 = MatCohorts, a = 5, t = 3 + PTMortss, a = 5, t = 3 Assumption: 100% of the preterminal cohort matures.
- The cohort size for all ages in earlier time steps is computed
as:
Equationxxx
$$ PTCohort_{s,a,t}=\frac{PTCohort_{s,a,t+1}}{SRate_{a,t+1}}+MatCohort_{s,a,t}+PTMorts_{s,a,t} $$
- The cohort size for the younger ages in the final time step is
computed as:
Equationxxx
$$ PTCohort_{s,a,t=3}=\frac{PTCohort_{s,a+1,t=1}}{SRate_{a+1,t=1}}+MatCohort_{s,a,t}+PTMorts_{s,a,t} $$
- The starting cohort is calculates as:
$$ StartingCohort_{s,a}=\frac{PTCohort_{s,a,t=1}}{SRate_{a,t=1}} $$
Table xxx Cohort Reconstruction Example
Once an initial estimate of preterminal and terminal CWT cohort sizes have been made, sublegal (shaker) and CNR mortalities by fishery, age, and time period can be estimated. See Estimating Sublegal Mortalities and Estimating Non-Retention Mortalities for calculations.
The sublegal and non-retention mortalities by stock and age are a function of cohort size and cohort size is a function of sublegal and non-retention mortalities, hence an iterative process is required to calculate cohorts and incidental mortalities by stock and age.
Calculating Exploitation Rates
Once iterations have concluded and cohort sizes stabilized,
exploitation rates can be calculated. These exploitation rates are the
foundational data of a FRAM run. Preterminal ERs are calculated for
preterminal fisheries and have the preterminal cohort size in the
denominator. Terminal ERs are calculated for terminal fisheries and have
the cohort size post maturation in the denominator.
Equationxxx
$$ PTER_{s,a,f,t} = \frac{LandedCatch_{s,a,f=pterm,t}}{PTCohort_{s,a,t}*LegalProp} $$
Equationxxx
$$ TermER_{s,a,f,t} = \frac{LandedCatch_{s,a,f=term,t}}{MatCohort_{s,a,t}*LegalProp} $$
Maturation Rate Calculations
Once cohort sizes are available, maturation rates by age and time step can be computed. The maturation rate for the oldest age in the final time step is assumed to be 1.0
In the last time step, compute the total cohort after fishing mortality.
Equationxxx
$$ TotalCohort_{s,a,t=3}=MatCohort_{s,a,t=3}+\frac{PTCohort_{s,a+1,t=1}}{SRate_{s,a+1,t=1}} $$
The maturation rate is simply the proportion of the mature portion of
the total cohort after fishing.
Equationxxx
$$ MatRate_{s,a,t=3}=\frac{MatCohort_{s,a,t=3}}{TotalCohort_{s,a,t=3}} $$
For earlier time steps, maturation rates are computed in a similar way as: Equationxxx
$$ TotalCohort_{s,a,t} = MatCohort_{s,a,t}+\frac{PTCohort_{s,a,t+1}}{SRate_{s,a,t+1}} $$
Equationxxx
$$ MatRate_{s,a,t} = \frac{MatCohort_{s,a,t}}{TotalCohort_{s,a,t}} $$
Adult Aquivalency (AEQ) Calculations
Once maturation rates are available, adult equivalence (AEQ) can be computed. AEQ is the probability that a fish of a certain age will survive to spawn, in the absence of future fishing. AEQs are a function of the maturation rate of the stock and therefore are stock specific. AEQ is defined as 1.0 for the oldest age class at the final time step (MEW, 2008).
Equationxxx
$$ AEQ_{a=5,t=3}=1\phantom{\frac{1}{1}} $$
For younger ages, AEQ in time 3 is computed as:
Equationxxx
$$ AEQ_{a,t}=MatRate_{s,a,t}+(1-MatRate_{s,a,t})*SRate_{a+1,1}*AEQ_{s,a+1,1}\phantom{\frac{1}{1}} $$ For earlier time steps, for all ages, AEQ is computed as:
Equationxxx
$$ AEQ_{a,t}=MatRate_{s,a,t}+(1-MatRate_{s,a,t})*SRate_{a,t+1}*AEQ_{s,a,t+1}\phantom{\frac{1}{1}} $$
Out-of-Base Procedures
For stocks without representative CWT release groups during the base period, OOB CWT groups were used and their recoveries were simulated back into the base period in a process of calibration. Calibration involves iterative passes adjusting CWT recoveries for OOB tag groups back to the base period using FRAM derived fishery effort scalars from FRAM “validation” runs.
Figure xxx Out-of-Base Procedures
Forward Cohort Reconstruction
The “Forward Cohort Reconstruction” is unique to out-of-base procedures. The method is instrumental to calculating simulated CWT recoveries. Unlike the Backwards Cohort Reconstruction which starts with age 5 time step 3 the forward cohort reconstruction starts with age 2 time step 1. The purpose of the forward cohort reconstruction is to produce catches and escapements that are adjusted for in-base fishing effort (new base period) in order to combine them with in-base CWT recoveries.
- Begin with age-2 time 1 starting cohort and remove natural mortality $$ PTCohort_{a,t}=TotalCohort_{a,t} * SRate_{a,t}\phantom{\frac{1}{1}} $$
- Calculate adjusted exploitation rates (AdjustedER)
Forward cohort reconstruction requires fishery effort scalers that are derived from the new base period in a laborious iterative process.
Initialize fishery efforts scalers (FisheryScaler) with values derived from regular FRAM validation runs (using best estimates of actual catches and abundances). Runs need to be conducted for all fishing years affected by OOB brood years; i.e., if 2002-2005 brood years (BY) were selected for OOB recoveries, then 2004 (2-year-olds) to 2010 (5-year-olds) fishing years (FY) ) are required to obtain fishery effort scalers. These effort scalers are then manually transferred from the validation run database to the calibration database. Since effort scalers are a function of BPERs and OOB BPERs are influenced by effort scalers, the process is iterative, but requires a starting values for the OOB stock in the validation runs. These ERs can be initialized with a value of 1 or left at the values of the previous base period for the first model run. Subsequent runs use the OOB BPERs from the first completed calibration cycle. For more information of how fishery effort scalers are calculated see computational processes .
equationxxx $$ AdjustedER_{a,f,t} =\frac{OOB.ER_{a,f,t}}{FisheryScaler_{Year,f,t}} $$ Where, the “Year” equals brood year plus age; i.e., if the CWT was recovered for a 4-year old Chinook of brood year 2004, then the fishing year would be 2008 (2004 + 4).
- Sum adjusted OOB ER’s over all fisheries within an age and time step
and adjust if the sum exceeds 100%.
Do this separately for terminal and preterminal fisheries.
Equationxxx $$ AdjustedER_{a,t} = \sum_{f} AdjustedER_{a,f,t}\phantom{\frac{1}{1}} $$ When adjusting OOB ERs in the previous step by dividing by FishScaler, it is possible that ERs exceed 100% for the OOB stock and age when summed over all fisheries within a time step. To avoid this, the component ERs are scale to sum to 95%.
equationxxx $$ AdjustedER_{a,f,t}= AdjustedER_{a,f,t} * \frac{0.95}{AdjustedER_{a,t}} $$ - Compute preterminal catch
Equation xxx
$$ PTCatch_{a,f,t} = PTCohort_{a,t} * LegalProp_{a,f,t} * AdjustedER_{a,f,t}\phantom{\frac{1}{1}} $$ Where, LegalProp is computed as the proportion vulnerable (PV) .
Compute mature cohort
For an age and time step, the mature cohort is computed by subtracting the catch from preterminal fisheries from the preterminal cohort size and multipliying times maturation rate.
Equationxxx $$ MatCohort_{a,t} = (PTCohort_{a,t} - \sum_f PTCatch_{a,f,t}) * MatRate_{a,t}\phantom{\frac{1}{1}} $$Compute terminal catch
Equation xxx $$ TermCatch_{a,f,t} = MatCohort_{a,t} * LegalProp_{a,f,t} * AdjustedER_{a,f,t}\phantom{\frac{1}{1}} $$Compute escapement
Escapement is calculated by subtracting natural and fishery mortality from the mature cohort size.
Equationxxx $$ Escapement_{a,t} = MatCohort_{a,t} - \sum_f TermCatch_{a,f,t}\phantom{\frac{1}{1}} $$Compute the preterminal cohort for the next time step (if time step is less than 3)
equationxxx $$ TotalCohort_{a,t+1} = \frac{PTCohort_{a,t} - \sum_f PTCatch_{a,f,t}}{(1-MatRate_{a,t})} $$Compute the preterminal cohort for age+1 (if time step is 3) equationxxx $$ TotalCohort_{a+1,t} = \frac{PTCohort_{a,t} - \sum_f PTCatch_{a,f,t}}{(1-MatRate_{a,t})} $$
OOB Procedure Steps
Sum CWTs from FRAMBuilder over fisheries and escapement without further expanding (no escapement and fisheries expansions).
Compute sublegal mortalities
- For OOB stocks sublegal encounters of the stock in a fishery are set
at the landed catch; i.e., CWT recoveries from FRAMBuilder summed within
a fishery and time step. These encounters are then split into ages by
calculating the proportion of stock/age that is of sublegal size and
multiplying times the cohort size of the stock age.
Equationxxx
- For OOB stocks sublegal encounters of the stock in a fishery are set
at the landed catch; i.e., CWT recoveries from FRAMBuilder summed within
a fishery and time step. These encounters are then split into ages by
calculating the proportion of stock/age that is of sublegal size and
multiplying times the cohort size of the stock age.
$$ Sublegals_{a} = Cohort_{a} * SubLegProp_{a}\phantom{\frac{1}{1}} $$ Where the proportion sublegal (SubLegProp) is calculated as in chapter Size Limit Evaluations (equation xxx)
+ When summed over all ages, the age proportions are then calculated as:<br>
equation xxx$$ Proportion_{a} = \frac{Sublegals_a}{\sum_a Sublegals_a} $$
+ Sublegal mortalities are then calculated as: <br>
equation xxx$$ Shakers_{s,a,f,t} = Encounters_{s,f,t} * Proportion_a * ShakerReleaseMortalityRate_{f,t}\phantom{\frac{1}{1}} $$
Cohort Reconstruction
The cohort is reconstructed as described in chapter Backwards Cohort Reconstruction . The cohort size is needed to calculate sublegal encounters, legal exploitation rates, and maturation rates.Check convergence
Computing sublegal mortalities and calculating the cohort are iterative steps, because sublegal mortalities are a function of the cohort size and the cohort size is dependent on sublegal mortalities. These steps are repeated until age-2 abundances converge. This occurs when abundances differ by less than 1%.Calculate maturation rates and OOB exploitation rates
See Maturation Rates (xxx) and Exploitation Rates (xxx) for calculations.Start iterative cycle to integrate OOB catches with in-base CWTs
Conduct a Forward Cohort Reconstruction
Merge OOB CWTs over brood years
During the “Merge” subroutine OOB catches (CatchBY,a,f,t) will be combined over brood years (BY) for the same age, fishery, and time step. The user has the option to weight different brood years.
Equationxxx $$ MergedCatch_{a,f,t}=\sum_{BY}Catch_{BY,a,f,t}*Weight_{BY}\phantom{\frac{1}{1}} $$ Brood years can either be merged unweighted (BYFlag = 1). In this case catches will simply be summed (BYWeight = 1). Each brood year can receive equal weights (BYFlag = 0). In this case the catch from a brood year, when summed over all fisheries and time steps, is expanded to match the catch of the brood year with the highest catch. Or brood years can receive a custom weight (BYFlag = 2).
Equation xxx $$ Catch_{BY,a,f,t} = Catch_{BY,a,f,t} * BYWeight\phantom{\frac{1}{1}} $$Merge OOB CWTs with inbase CWTs
Combine simulated CWTs as computed in previous steps with inbase CWT recoveries.Run through regular (inbase) procedures to create new base period exploitation rates
This is accomplished by following the steps as outline under Main Calibration Procedures. During initial calibration steps CWTs are expanded to reflect the run size of the OOB stocks during in-base years.Import BPERs into validation runs
See chapter xxx for exporting base period data from the calibration database and importing the new base period into a validation run database.Produce new fishery effort scalers The new fishery effort scalers are stored in the validation run database in table “FisheryScalers” after running select years (OOB brood years plus age) of the validation runs. These scalers are copied into the calibration database.
Iterate
Iterate until OOB ERs stabilize