The computation algorithm is similar to that for multi-phase ceiling management in that catches are computed by an iterative procedure. The fixed escapement algorithm is implemented after all initial terminal catches are taken but before final escapements are computed. If multiple stocks in the same river are being managed via fixed escapements, three types of policies may be implemented: (1) strong stock managment in which the river is managed to meet the stongest stock's escapement goal; (2) weak stock management in which the river is managed to meet the weakest stock's escapement goal; or (3) combined stock management in which the escapement goal is based on the sum of all stocks.

Step 1.

Compute the river catches using the formula:

[4.48]

where Ratio is the relative increase or decrease in the river fishing effort required to adjust the river catch to meet the escapement goal. Note that Ratio = 1 on the first iteration.

We also compute the river shaker mortalities for each stock, age, and fishery in the usual manner. Note that for each cohort it is possible for the catch plus the shakers to exceed the true terminal run. This is accounted for in Step 3.

Step 2.

We create a new variable for the total river mortalities, called RivMorts, which can not exceed the available fish. This is a temporary variable and is only used within this algortihm. For each stock and age we compute

[4.49]

where and are summed over all river fisheries. Thus, cannot exceed the total available fish.

Step 3.

Compute another temporary variable called TempNewScale. If strong or weak stock management is being implemented, the algorithm computes separate adjustment values for each stock using the following formula:

[4.50]

where

[4.51]

• = River catches plus incidental mortalities for stock s, age a, in river fishery f.
• = Escapement goal for stock s;
• = Interdam survival rate for stock s after all harvesting mortalities to the point where the escapement goal is measured.

For strong or weak stock management, the largest or smallest TempNewScal is used to compute the adjustment ratio to be applied to all catches by the river fisheries, respectively.

If combined stock management is used, TempNewScal is computed as follows:

[4.52]

Step 4. Compute NewScal

We compute NewScal as follows:

[4.53]

where the WgtAvgP terms are the weighted average of the adjusted harvest rates (i.e., P*PScal values). The weights are the terminal run sizes divided by the total terminal run for the managed stocks. Thus, if weak or strong stock management is being used, the weights are simply the fraction each age cohort contributes to the strong or weak stock. If combined stock management is being used, the weights are the fraction each stock/age cohort contributes to the total terminal run (ages 3, 4, and 5) for the river managed stocks.

Step 5. Update the adjustment ratio

The final step is to multiply Ratio by NewScal to get a new ratio. Then go to Step 1 and repeat until NewScal is close to one.

Ratio = Ratio · NewScal [4.54]