The following sections provide examples of the several of the fishing processes operating in the deterministic mode.
The following lines of text illustrate the definition of six stocks and an effort fishery operating on the stocks during time period "33" with 1,000 units of effort and a catchability, q = 0.00001. Each of the stocks are given the same initial abundance. The items on each stock definition line are: the key word "STOCK", followed by the stock name, a yes or no flag indicating whether the stock is mass marked, the total number of fish in the stock, and the number of fish that are CWT. The fishery specifications are split between two lines with a "+" character indicating continuation on the next line.
The corresponding model output is shown below:
In this example, total catch is given by:
C = N(1 - e-qf) = 2,400,000(1 - e-[(0.00001)(1,000)]) = 23,880.4
In the deterministic version, total catch is allocated among the six stocks simply in proportion to their abundance.
3.3.2 Seasonal and Time Step Specific Ceilings
Operation of the ceiling mechanisms is illustrated in the following examples. The first set of instructions defines six stocks of equal size and a sequence of six effort fisheries, each with identical effort and catchability except that the first instruction also contains a seasonal catch ceiling of 40,000 pieces for the fishery.
The seasonal ceiling constrained the fishery to only two "time periods" as shown in the output records below:
A second set of inputs identical to the first except that the second fishery instruction contains a ceiling limited to just the scope of a single instruction. The second ceiling operates in addition to the overall seasonal ceiling:
The constraint in the second instruction limits the harvest during that "time" and prolongs the fishery over three instruction steps:
The total catch is the same (40,000 pieces), only the duration of the fishery is different.
The current form of the escapement goal fishery specifications is shown in the next example. Six stocks have been defined with equal abundance and two fisheries are designated escapement goal fisheries, each operating on two different lists of stocks. The first stock in each of the lists is designated the controlling stock. For the ELLIOT_BAY_NET fishery the controlling stock is SSOUND_NORMAL_NORTH while the controlling stock for SKAGIT_BAY_NET is SKAGIT_RIVER_NORTH. The escapement goal in the first fishery is set to 10,000 while the goal in the second is set at 50,000. There are no time designations on the fishery instructions since the fishing process is presumed to occur at the end of the year and represents the accumulated harvest over a number of time periods. It is further presumed that the stocks in the list are to be completely fished out since all fish are either caught or go to escapement. This command is typically used in conjunction with the SEPARATE command. The user previously allocates fish from a main stock to these terminal area stocks periodically throughout the fishing process. The number of fish in the first (controlling) stock for each escapement goal fishery is compared with the goal and if there are fish in excess of the goal, fishing is permitted on the stocks available to the fishery.
The model output corresponding to these instructions is shown below.
The designated goal of the SSOUND_NORMAL_NO is 10,000 fish. Since the stock abundances are equal in this example, the allowable harvest in the ELLIOT_BAY_NET fishery on each of the stocks is: 30,000 - 10,000 = 20,000. There are insufficient fish in the SKAGIT_RIVER_NO stock to meet the 50,000 fish goal, so all the fish go to escapement (designated by the "E" flag near the beginning of each record). Note that for these terminal fisheries, the process operates on sums accumulated over all instructions so the "time" value in the output record is set to some meaningless value, 99 in this case.
To illustrate operation of selective fishing rules, the first instruction set for the effort fishery is modified to make one of the stocks mass-marked and the "SELECTIVE" command is added to the fishery instruction with a mortality rate of 10% and error rates on identification/compliance for both marked and unmarked fish set to 1%:
The resulting output shows the landed catch for the mass-marked stock (QUINSAM_NORTH) decremented by 1% (i.e., 3980.1 - 39.801 = 3940.3) to account for error in identification of marked fish with 10% of the fish thrown back ( = 4) placed in the selective mortality column. The error rate applied to the catch of unmarked stocks results in a catch of about 40 fish, and of the 3980.1 - 39.801 = 3940.3 fish thrown back for each stock, 10% or 394 fish die as shown in the selective mortality column.
If a continued dropoff rate/dropoff mortality of 5% is added to these same instructions, the resultant shaker mortality of 23,880.4 X 0.05 = 1,194 is distributed among all stocks (i.e., 199 = 1194/6) without affecting the other values:
The example can be further complicated by adding a minimum size limit command. The case below shows the size limit equal to the population mean. This results in one half of the population below the legal size limit since the distribution of fish lengths is assumed to be normal and symmetric about the mean.
The landed catch and selective mortality categories are halved since the selective fishing rules apply only to the legal half of the population. The mortality rate of 50% applied to the sublegal component and divided among stocks (995 = (11,940.2 X 0.5)/6) then added to the 199 fish dropoff mortality yields a total shaker mortality of 1,194 for each stock.
Finally, a case where the landed catch is constrained by a daily bag limit is shown in the last example. The parameters for the previous fishery controls remain the same but a daily bag limit of 3 fish is added. Since this is a selective fishery, the bag limit applies to marked fish in the catch plus any unmarked that are inadvertently included due to incorrect identification. The last value in the daily bag limit instruction indicates the ratio of variance:mean in the underlying distribution of catch per angler-day. It's important to remember that the catch level generated in a fishery with a daily bag limit control is presumed to result under the condition of no bag limit. If the data are censored or truncated, Porch and Fox (1991) provide some approaches for obtaining distribution parameter estimates that approximate the result without the bag limit.
The effect of the 3 fish daily bag limit is to constrain the landed catch to just over 3/4 of the original catch (marked catch plus unmarked kept = 2069.6 = 1970.1 + 5(19.9)). The ratio is 0.774598 and is applied to the shaker and selective fishery mortalities as well.
