Troy and Jim Norris would like to remove the requirement for the code to be flexible enough to iterate over multiple time steps, as was done for the PSC Selective Fishery Model. Robert Kope agreed that it seemed to be an unreasonable constraint.

Jim Scott, however, questioned how the current multiple timestep analysis would be incorporated. Jim Norris suggested three alternatives. The first is using the PSC Selective Fishery Model approach. Here a ceilinged fishery that spans multiple time steps would use an algorithm that simply subtracts the catch in each time step from the overall ceiling until the ceiling is reached. This method would not be able to exactly duplicate the existing PSC Chinook Model algorithm.

A second alternative is to allow for iterations over all the time steps within a single year. The basic idea would be to do the computations for the whole year, compare the results with some objective function that spanned multiple time steps (e.g., catch allocation objectives), adjust appropriate fishery control variables, repeat calculations for the entire year, etc. until the objective function was met. Jim stated that he and Troy plan on using this second alternative.

A third alternative would be to develop some type of fishery management object that would allow for iterations over selected time steps within a year. The main advantage of this approach is faster overall computation time. Jim stated that this third alternative proved to be too complicated, and felt that it should be explored only if the second alternative proved to be unacceptably slow.


4. Future code development (Jim Norris).

Jim stated that the next major code development will be to make the existing fishing mortality algorithms generic for variable timesteps and locations. Once these fishing algorithms are in place, Jim will attempt to duplicate the existing FRAM coho configuration by configuring the maturation rates as Maturation and Migration processes. The next logical step will be to expand the number of areas and time steps and introduce new Migration data estimated from Ken Newman's State Space Model work.


5. State Space Model update (Ken Newman).

Ken presented an overview of the State Space Model (SSM) and compared it to the code development presented earlier by Jim and Troy. The "working abundance" vector for each cohort in the new code corresponds to the SSM abundance vector times the survival matrix (which includes both fishing and natural mortality). The goal of the SSM is to estimate the parameters for the migration matrices, including the degree of uncertainty, and the parameters for the mortality components.

Ken described the hierarchical nature of the SSM he is now using. At the top level is a set of hyperdistributions which are probability density functions (PDFs) that generate the initial distribution, movement, and mortality parameters for a given stock in a given year. Namely, to run the SSM for a given stock and year, one randomly draws a set of values from which one can sequentially generate abundances and catches over time and space using the SSM (with or without natural variation included).

In its present form the hyper-distribution has 3 fixed and 5 free parameters that must be estimated. Ken showed results for the 5 free parameters; initial survival, initial location, US fishing survival, Canadian fishing survival, and movement.

At the August meeting Ken reported that his Empirical Bayes (EB) estimates of initial survival were below the minimum estimated from CWT cohort analysis, and Gary Morishima questioned those results. Ken reported that after the August meeting he found a code error in his program. Once the code was corrected, the results were more consistent with those derived from cohort analysis.

Ken received 3 more years of Humptulips CWT data, so he now has data for 1983-88. He still doesn't have all the effort data, but he's getting closer.

Ken has been working on a new SSM formulation that does not assume normally distributed error terms. The problem with normally distributed errors is that it is possible to get negative catches and abundances. He has been experimenting with an alternative non-normal SSM, where the initial distribution is

(1) multinomial: n ~ M(R*s, P1, P2, ...)

where R*s(i) is the initial abundance at the start of the fishing season (Releases times survival rate), and Pi = probability of residing in region i.

Then the state equation of abundances evolves according to a lognormal distribution,

(2) lognormal: n(t)|n(t-1) ~ lognormal(ln(M*S*n(t-1)), Sigma)

where M and S are the migration and survival matrices, respectively, and n(t) is the abundance vector at time t, and Sigma is the covariance matrix.

Finally the observation process (catch) is linked to the abundance by a Poisson PDF:

(3) Poisson: c(t)|n(t) ~ Poisson(H*n(t))

where c(t) is catch vector at time t, n(t) is the abundance vector at time t, and H is the harvest matrix.

The main problem in implementing these non-normal error structures is that his program is too inefficient--it requires too much computation time. This remains an unsolved problem for SSMs.


6. Model comparison update (Jim Norris).

Jim Norris gave an update on further analysis of the PM model. At the June 97 meeting Jim gave a report showing a matrix notation for the PM model, which does not have a migration algorithm per se. Based on this notation, Jim concluded that: "… the PM model makes the tacit assumption that for a given cohort and time step, fish migrate from all donor regions at the same rate." Rich Comstock noted (at the June meeting) that this assumption may not be correct, because the transition matrix in the PM model is not directly analogous to the migration matrices of the other models. Jim agreed to delete the statement from the report and requested suggestions for a more intuitive description of the PM matrix terms.

Jim described his most recent analysis approach for investigating the question: What is the proper biological interpretation of the Transition Matrix elements for the PM Model? The approach consisted of the following steps:

1. Define a mathematical model of a biological system having 4 regions, 4 fisheries, one stock composed of marked and unmarked components, and Transition Matrices (TMs) such that fish migrate from region 1 to region 4 over time.

2. Define a base period harvesting policy and assume the manager has perfect knowledge of the resulting base period data (i.e., catches and harvest rates).

3. Define new harvesting policies by scaling base period harvest rates (e.g., for the first two fisheries reduce the harvest rate on the unmarked stock component to 10% of the base period rate) and compare "true" results based on the biological model defined in step 1 with predicted results using the PM methods (using correct base period catches and harvest rates).

The results indicated that when there were base period catches in all fisheries and timesteps, the PM model predicted catch for the unmarked stock component was 330 compared to the "true" value of 322. When only half of the fishery/timestep cells had base period catches, the PM model predicted catch was 295 compared to the "true" value of 272.

Jim's conclusion was that the PM model is a biased estimator, and the degree of bias is affected by the distribution of base catches in time and space.

A lengthy discussion followed. Several committee members pointed out that the results should not be too surprising, since all models (including FRAM) are biased to some degree. Jim noted that his frustration in evaluating the PM model performance is that the current documentation does not describe in mathematical terms an underlying model of a biological system. Without an underlying model, it is difficult to determine the biological meaning of intermediate parameters estimated by the PM algorithm (e.g., the adjustment factors used to scale the base period abundances when estimating catches under new harvesting policies).

Jim stated that he plans to add the FRAM model algorithms to the analysis approach to determine relative biases of the PM and FRAM models.


7. Miscellaneous Items.

7.1. Anchorage Conference.

Jim Anderson reported that the conference held in Anchorage was excellent. Of interest to the NMFS model committee was a talk by Jim Ianelli on risk analysis and conversations with Dave Hankin on relating ocean conditions and survival. Jim also talked with Dave Fournier about his AD Model Builder software--it may have some application for our work. Next year's meeting will be held in November in Anchorage.

7.2. Santa Rosa Workshop.

Robert Kope reported that this workshop was organized by the NMFS Southwest Regional Office to help explain to California fishermen (mostly trollers) and non-technical managers (e.g., PFMC members and staff) how several computer models (e.g., Klamath Ocean Harvest Model, Sacramento Winter Chinook Model, FRAM) are used to evaluate salmon management alternatives. At the end of the meeting Jim Norris gave a presentation on the NMFS model work. The workshop was successful in raising the level of understanding by everyone.

7.3. NerkaSim.

Jim Norris showed some slides on the NerkaSim model developed at UBC. This is a user-friendly model (for the Windows 95 platform) that incorporates individual based models (IBMs) for fish behavior (movement) and bioenergetics (growth and survival) with the NMFS Ocean Surface Currents (OSCURS) model and oceanographic data (sea surface temperature and zooplankton abundance). The model is described in the October issue of Fisheries and can be found on the web at:

http://www.eos.ubc.ca/salmon/nerkasim/

7.4. Development Schedule.

Troy reported that the bulk of the design work is done and we now are mostly coding. Building the GUI will be time consuming. He thinks that sometime in the middle of next year we will have a usable model with a crude GUI.

The meeting adjourned at 3:20 p.m. and the next meeting is scheduled for Tuesday, January 20th, at NMFS Montlake.