Catch Ceiling Algorithm. Currently, the input catch ceilings for each ceilinged fishery (in the *.cei file) are given for each year (i.e., over all timesteps and regions). These input values are then used to compute scalars that relate catches prior to the 1985 treaty to catches after 1985:

                     input ceiling(y,f)
  scalar(y,f) = -----------------------------------
                SUM(input ceilings(y = 79 to 84,f))

During forward simulation, the program sums the Preterminal and Terminal model predicted catches for each fishery during the years 1979-1984 (called the "base period"). The Preterminal and Terminal catch ceilings for years beyond 1984 are computed by multiplying the scalar(y,f) by the appropriate sum for the 1979-1984 period. That is,

  ceiling(y,f,phase) = scalar(y,f)*SUM(model catch(y = 79 to 84,f,r)

where phase is either Preterminal or Terminal.

The problem with the above algorithm is that Preterminal and Terminal do not specifically refer to time or space. We need an algorithm that will compute catch ceilings by timestep and region for each fishery.

To generalize this process to multiple timesteps and regions, the scalar(y,f) values can be computed as before. In fact, the scalars can be computed outside the simulation program and then input directly. During forward simulation, the program can sum the model predicted catches for each fishery during the years 1979-1984 by timestep and region, instead of by Preterminal or Terminal phase. The catch ceilings for years beyond 1984 can then be computed by multiplying the scalar(y,f) by the appropriate sum for the 1979-1984 period. That is,

  ceiling(y,f,t,r) = scalar(y,f)*SUM(model catch(y = 79 to 84,f,t,r)

where t = timestep and r = region.


Adult Equivalent Factors In Production Functions. The production functions in the PSC Chinook Model relate spawners to ADULT recruitment. Adult recruitment is converted back to "Age1Fish" by a factor called "RectAtAge1". In essence, the RectAtAge1 factor defines the relationship between adult recruitment and Age1Fish in the equilibrium condition with no harvesting. Thus, the RectAtAge1 factor is defined by the maturation and natural mortality schedules for each stock. For the new model, three situations need to be considered.

(1) If the maturation and natural mortality schedules do not change over time and space, each stock has a unique RectAtAge1 factor. About 2/3 of the stocks in the PSC Chinook Model fall in this category. Note that the RectAtAge1 factors could be computed before a model run and passed in as input data along with other production function parameters.

(2) If the schedules do change over time and space, then each stock will have a different RectAtAge1 factor for each year. About 1/3 of the stocks in the PSC Chinook model fall in this category. These stocks have constant natural mortality schedules, but variable maturation schedules. At the start of each year, a new RectAtAge1 factor is computed for each stock. As with case (1), since all schedules are included with the input data, the RectAtAge1 factors could be computed before a model run and passed in as input data along with other production function parameters.

(3) Cases (1) and (2) can be generalized to variable timesteps and regions, provided the timestep and region definitions and the maturation and natural mortality schedules for each stock are all defined during the model configuration. We envision the new model will have timesteps and regions defined during configuration, but we would like to allow for the possibility that maturation and survival schedules may be determined dynamically based on model predicted environmental conditions.

Jim and Troy proposed that for forward simulation runs RectAtAge1 factors be considered as part of the production parameters for each stock and should become part of input data. This should be the case even if natural mortality and maturation schedules are determined dynamically. In other words, the model user must have some previously estimated relationship between adult recruits and Age1Fish for each stock and year. If a model dynamically computes natural mortality and maturation schedules, the model predicted RectAtAge1 factors could be stored reported as output.


Pre-Spawning Mortality And Production Functions. The PSC Chinook Model uses a truncated Ricker function for natural stocks. The Ricker A parameter and an optimum escapement level are the input parameters. The Ricker B parameter is determined from the Ricker A parameter using Hilborn's Approximation. If there is no additional mortality after all harvesting (this is true for all but 3 stocks), the maximum escapement level at which to truncate the function is given by RickerB/RickerA.

For three Columbia River stocks, the escapement from the fisheries is adjusted by a pre-spawning survival factor (called the IDL, or "inter-dam loss", factor). For these stocks, the maximum escapement level is increased to account for pre-spawning mortality. Here's the code.

FUNCTION FRicker (ESC, Stk%, Yr%)
  A = RickerA(Stk%)
  B = Optimum(Stk%) / (.5 - .07 * A)
  FRicker = ESC * EXP(A * (1 - ESC / B))
  '..... If escapement exceeds level producing maximum recruitment,
  '..... keep recruits at maximum. cf Ricker 1975, p. 347, eq. 10
  MaxEsc! = B / (A * IDL!(Stk%, Yr%))
  IF ESC > MaxEsc! THEN
    FRicker = B * EXP(A - 1) / A
  END IF
END Function

There was a lot of discussion about this algorithm. The main point of contention was why the maximum escapement value should be adjusted if the escapement value ("ESC") being passed into the function already had been adjusted for pre-spawning escapement. My understanding (readers please correct me if I'm wrong!) is the following.

The Ricker function parameters are estimated from observed spawners and observed recruitment to the fisheries. Thus, the parameters do not incorporate any non-fishing mortality after fishing but before spawning. Since the parameters do not incorporate pre-spawning survival, the computed maximum escapement doesn't incorporate it either. That is, the maximum escapement parameter assumes there is no pre-spawning mortality. Thus, adjusting the maximum escapement level by pre-spawning mortality is to correct the maximum escapement parameter value, not to correct the escapement passed into the function.

In the new model we treat the pre-spawning mortality as a form of non-fishing, or natural, mortality that may occur during any timestep and in any region, depending on how the user configures the natural mortality process. Thus, the new model may be configured to have pre-spawning mortality during several timesteps and regions, depending on the model resolution. For example, separate "natural" mortalities could be assessed as fish pass each dam.

To extend the concept of pre-spawning mortality to variable timesteps and regions, we need a parameter that represents natural mortality of the escapement (all age classes) from the fisheries to the spawning grounds. Currently, the stock/year specific IDL parameters serve this purpose. An analogous parameter for the generalized case is the weighted average of the IDLs for each age class in the escapement, where the weights are the relative contributions of each age class to the total escapement. The current algorithm is a special case of the wieghted average algorithm. Troy reported that he has already implemented this general structure and it validates with the old code.


3. Prototype model code update (Troy Frever).

Troy reported that the full prototype is not quite ready yet, but he is very close. At this point, the prototype code has the following new features currently implemented:

 - variable timesteps
 - variable regions
 - variable age classes
 - variable cohort characteristics (marked, tagged, etc.)
 - variable dimensionality for most data parameters
 - transition matrix migration

Work to be completed prior to prototype delivery:

 - cohort configuration options from input data
 - harvest management (policy) framework
 - simple catch ceilings
 - completion of new data input file capabilities
 - expansion of output options (possibly data dump - see below)
 - internal code cleanup

Remaining work after prototype delivery (next contract period):
 - addition of other harvest processes (selective fishery, etc.)
 - different shaker process?
 - addition of other management processes (escapement goals, etc.)
 - speed optimization
 - documentation

Gary Morishima suggested that we have one large output file (in text format) from which other stand alone programs (e.g., Excel, Access) can create formatted reports. He said this has worked well for the PSC Chinook Model.


4. State Space Model update (Ken Newman, Alan Hicks).

Ken described a new migration module he has implemented in the State Space Model. A complete description of the new module can be obtained at:

/harvest/newman/migmod3.pdf

Briefly, the model assumes that the probability distribution for the location at time t+1 of a fish at location p(t) at time t is a Beta distribution with parameters alpha(p(t),t) and beta(t). The alpha parameter is a function of time and location while the beta parameter depends only on time.

The expected value of the next location, mu, is a product of the current location and a multiplier <= 1.0 (a logit function), that early in the time period (i.e., t near 0) is made arbitrarily near to 1.0 by choosing an appropriate parameter in the logit function (see the reference doc for details). As time increases, the multiplier shrinks towards zero, which is the location on the line of the natal area. Movement beyond the natal area, whether north or south of the natal area, is not allowed, assuming the freshwater influence will attract the fish back to spawn. Nor is movement outside the line segment (to the far north or south) allowed--thus the system is closed.

Ken reported the following results from the new module (relative to the old module) for the six years of Humptulips data he has been working with:

-- No change in the initial survival estimates;
-- The initial distributions are now very stable (i.e., consistent across the six years). The previous module had a very odd initial distribution for the 1988 data;
-- Fishing effort parameters still don't show a consistent pattern between US and Canada;
-- The overall goodness of fit improved by up to 40%.

Robert Kope asked if Ken had tried fitting the model using a common catchability coefficient for the US and Canada harvest processes. He had not.

Jim Anderson suggested that Ken might try a more traditional migration model and gave three examples that Rich Zabel (UW Columbia Basin Research) has been working with.

Alan Hicks (UI graduate student) presented some preliminary results showing correlations between upwelling index (lagged to ocean entry year) and survival to the first week of the SSM.


5. Model comparisons update (Jim Norris).

Jim reported that he added a second FRAM model configuration to the model comparisons program to (1) demonstrate the flexibility of the underlying code structure and (2) validate two different migration process algorithms. After a Base Model is run to generate synthetic catch and escapement data, the FRAMAnalyst object estimates the FRAM parameters (harvest rates and maturation rates). The FRAMAnalyst then creates two independent models from the same parameter estimates.

The first model (FRAM1) configures a model in which each cohort has a number of immature schools with equal initial abundance and are initially distributed uniformly over a narrow range in the Preterminal region. Throughout the forward simulation, the immature cohorts have no migration (i.e., their schools never change location). However, at appropriate times during the simulation, each immature cohort goes through a maturation process that creates a new mature cohort with the same number of schools as the associated immature cohort. The maturation rate determines the fraction of fish from each immature school that is transferred to its associated mature school. The migration process for the mature cohort moves its schools through the Terminal region and, after suffering fishing mortality, on to the Spawning region.

The second model (FRAM2) configures a model in which each cohort has only three schools--one for each region (Preterminal, Terminal, and Spawning). Thus, the schools can be thought of as the regional abundances of a cohort (i.e., the abundance vector in the State Space Model). The total initial abundance of the cohort is given to the school located in the Preterminal region; the initial abundances of the schools located in the Terminal and Spawning regions are zero. The migration process for this model uses the transition matrix approach used in the State Space Model. That is, fish from a given cohort are transferred among its schools based on the transition matrix for that cohort during that timestep. The elements of the transition matrix are determined by the maturation rates.

Thus, FRAM1 and FRAM2 utilize the same estimated parameters to configure models with radically different configurations. Theoretically, both models should produce the same results if given the same FRAM parameter estimates.

Jim showed preliminary results of how well each model fit the synthetic data. A Base Model was run in deterministic mode using the "Constant" migration pattern and "Base" harvest plans described at the last meeting. The resulting synthetic catch and escapement data were aggregated over 30 day time periods, FRAM parameters were estimated, and FRAM1 and FRAM2 models were configured. The Base and FRAM models were then run using all combinations of two migration patterns ("Constant" and "Increasing") and three harvest plans ("Base", "Low Ocean", and "Selective"). For the "Low Ocean" harvest plan, the models reduced the harvest rates for the Ocean Troll fishery to 15% of the "Base" plan. For the "Selective" harvest plan, the models reduced the harvest rates for the Unmarked Cohort in the Ocean Troll and all sport fisheries to 15% of the "Base" plan.

For each of the six comparisons, the square root of the sum of squared differences between the Base model catches for each fishery and the corresponding predicted catches from each FRAM model were computed (labeled RMSE in the table below). Jim distributed printed results from each run; the RMSE results are below:

Config Migration Harvest Plan RMSE FRAM1 RMSE FRAM2

  1 Constant Base 19 14
  2 Constant Low Ocean 58 58
  3 Constant Selective 70 69
  4 Increasing Base 192 195
  5 Increasing Low Ocean 234 233
  6 Increasing Selective 203 204

The results from the two FRAM models were nearly identical, and, thus, the code algorithms were assumed to be working properly. Also, both FRAM models accurately predicted the configuration from which the FRAM parameters were estimated (Config 1).

In Config 2, most of the FRAM error was caused by underestimating the South Sound Net fishery catches. Apparently the FRAM models did not accurately simulate the movement of increased abundance (due to low ocean harvest) into Puget Sound.

For Config 3, the FRAM models predicted the Marked Cohort catches very accurately, but underestimated the Unmarked Cohort catches in the South Sound Net fishery.

Configs 4 - 6 simulated a change in migration pattern from the base year to the predicted year. For the "Increasing" migration pattern the fish start moving about a month earlier (although at a very slow rate) and the rate increases as time progresses. This change in migration pattern increased the FRAM errors. For each of these configurations the main source of error was in overestimating the South Sound Net catches.

Jim reported that he had most of the code running to include the SSM in the analysis, but the code had an obvious bug that he was unable to correct before the meeting.


6. September Pacific Fishery Management Council meeting report (Robert Kope).

Robert reported that the September PFMC meeting did not have any significant topics for this project.


7. Ecosystem/Fisheries Symposium report (Jim Norris, Ken Newman, Norma Jean Sands).

Jim reported that the plenary speakers emphasized how difficult it is (and will be) to bring together all types of ecological information (not just computer models) into the decision-making process. For example: How do you include knowledge of indigenous people with computer models?

There were several papers using the ECOPATH model. This seems to be a popular model for complete ecosystems. The results (predictions) are still pretty general (e.g., removing species A will increase some species and decrease others). There also was a presentation using the Facet Decision System.

Several papers noted the importance of salmon carcasses in bringing marine elements into the terrestrial system. Main conclusion--rotting fish are more valuable than you might think.

Milo Adkison did a pretty detailed analysis of 32 possible models to predict Bristol Bay salmon runs. The environmental factors he considered were of relatively little value compared to "sibling" information (i.e., number of age 2, 3, and 4 fish in previous years). His "best" model fit all of the past 40 years well ... even the big production jump during the regime shift in the late 70s. However, the predictor completely missed the last 3 years ... over-estimated by about 2 times. Main conclusion--even 40 years of good data and good model fits aren't enough to predict some changes. As Stuart Pimm noted in his plenary remarks: "Things go bump in the night!"

There was a special evening session to demonstrate models, including the Crisp Harvest Model and NerkaSim. During the discussion period some members of the audience wanted to know why we didn't have an optimization routine in Crisp Harvest to search for one or more harvest plans that would meet all the management constraints (e.g., escapement goals, allocation goals, etc.). They were pretty shocked to learn that the stakeholders preferred to do such a search in the political arena where they could hope to get a better deal.

Ken Newman reported that he found Randall Peterman's paper on sources of uncertainty in marine fish management very interesting.


8. Next meeting.

No date was selected for the next meeting due to uncertainty about a PSC Chinook Technical Committee workshop tentatively scheduled for November 16-20. I recommend that we schedule the next model committee meeting for Friday December 11 at NMFS Montlake. Please advise ASAP if this date is not acceptable.