Strategic Modelling and Business Dynamics - Morecroft John D.

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steps, its own rate of inflow.12 The relationship is non-linear as shown in Figure 1.6.

Figure 1.6 Net regeneration as a non-linear function of fish density

      When the fish density is low there are few fish in the sea relative to the maximum fishery size and net regeneration is low, at a value of less than 50 fish per year. In the extreme case where there are no fish in the sea, the net regeneration is zero. As fish density rises the net regeneration rises too, on the grounds that a bigger fish population will reproduce more successfully, provided the population is far below the presumed theoretical carrying capacity of the ocean region.

      As the fish density continues to rise, there comes a point at which net regeneration reaches a peak (in this case almost 600 fish per year) and then begins to fall because food becomes scarcer. Ecologists say there is increasing intraspecific competition among the burgeoning number of fish for the limited available nutrient. So when, in this example, the fish population reaches 4000 the fish density is equal to one and net regeneration falls to zero. The population is then at its maximum natural sustainable value.

Simulated Dynamics of a Natural Fishery

If you accept the relationships described above then the destiny of a natural fishery is largely pre-determined once you populate it with a few fish. To some people this inevitability comes as a surprise, but in system dynamics it is an illustration of an important general principle: the structure of a system (how the parts connect) determines its dynamic behaviour (performance through time). A simulator shows how. The simulation in Figure 1.7 shows the dynamics of a ‘natural’ fishery over a period of 40 years, starting with a small initial population of 200 fish. Remember there are no ships and no investment. Fishermen are not yet part of the system.

Figure 1.7 Simulation of a natural fishery with an initial population of 200 fish and maximum fishery size of 4000

      The result is smooth S-shaped growth. For 18 years, the fish stock (line 1) grows exponentially. The population grows from 200 to 2500 fish and regeneration (new fish per year, line 2) also increases until year 18 as rising fish density enables fish to reproduce more successfully. Thereafter, crowding becomes a significant factor according to the non-linear net regeneration curve shown in Figure 1.6. The number of new fish per year falls as the population density rises, eventually bringing population growth to a halt as the fish stock approaches its maximum sustainable value of 4000 fish.

Operating a Simple Harvested Fishery

      Imagine you are living in a small fishing community where everyone's livelihood depends on the local fishery. It could be a town like Bonavista in Newfoundland, remote and self-sufficient, located on a windswept cape 200 miles from the tiny provincial capital of St Johns, along deserted roads where moose are as common as cars. ‘In the early 1990s there were 705 jobs in Bonavista directly provided by the fishery, in catching and processing’ (Clover, 2004). Let's suppose there is a committee of the town council responsible for growth and development that regulates the purchase of new ships by local fishermen. This committee may not exist in the real Bonavista but for now it's a convenient assumption. You are a member of the committee and proud of your thriving community. The town is growing, the fishing fleet is expanding and the fishery is teeming with cod.

Figure 1.8 shows the situation. The fish stock in the top left of the diagram regenerates just the same as before, but now there is an outflow, the harvest rate, that represents fishermen casting their nets and removing fish from the sea. The harvest rate is equal to the catch, which itself depends on the number of ships at sea and the catch per ship. Typically the more ships at sea the bigger the catch, unless the fish density falls very low, thereby reducing the catch per ship because it is difficult for the crew to reliably locate fish. Ships at sea are increased by the purchase of new ships and reduced by ships moved to harbour, as shown in the bottom half of the diagram.

Figure 1.8 Diagram of a simple harvested fishery

Figure 1.9 Interface for fisheries gaming simulator

The interface to the gaming simulator is shown in Figure 1.9. There is a time chart that reports the fish stock, new fish per year, catch and ships at sea over a time horizon of 40 simulated years. Until you make a simulation, the chart is blank. The interface also contains various buttons and sliders to operate the simulator and to make decisions year by year. There are two decisions. Use the slider on the left for the purchase of new ships and the slider on the right for ships moved to harbour. You are ready to simulate! Open the file called ‘Fisheries Gaming Simulator’ in the learning support folder for Chapter 1. The interface in Figure 1.9 will appear in colour. First of all, simulate natural regeneration over a period of 40 years, a scenario similar, but not identical, to the simulation in Figure 1.7. The only difference is that the initial fish population is 500 fish rather than 200. What do you think will be the trajectories of the fish stock and new fish per year? How will they differ from the trajectories in Figure 1.7? Would you expect any similarities? To find out, press the button on the left labelled ‘Run’ (but don't alter either of the two sliders, which are deliberately set at zero to replicate a natural fishery). You will see a five-year simulation. The fish stock (line 1) and new fish per year (line 2) both grow steadily. You can observe the exact numerical values of the variables by placing the cursor on the time chart, then selecting and holding. Numbers will appear under the variable names at the top of the chart. At time zero, the fish stock is 500 and new fish are regenerating at a rate of 63 per year. If you look carefully you will see that the catch (line 3) and ships at sea (line 4) are, as expected, running along at a value of zero, alongside the horizontal axis of the time chart. Press the ‘Run’ button again. Another five simulated years unfold showing further growth in the fish stock and in new fish per year. Continue until the simulation reaches 40 years and then investigate the trajectories carefully and compare them with the time chart in Figure 1.7. Why does the peak value of new fish per year occur so much earlier (year 10 instead of year 16)? Why is the final size of the fish stock identical in both cases?

Harvesting in Bonavista, Newfoundland – A Thought Experiment

      Back to Bonavista, or at least a similar imaginary fishery, scaled to the numbers in the simulator. The fishing fleet has been growing and along with it the catch and the entire community supported by the fishery. As a member of the town's growth and development committee you want to explore alternative futures for the fishery and the simulator is one way to do so. You conjure up a thought experiment. Starting as before with an initial stock of 500 fish, you first simulate growth, through natural regeneration of fish, for a period of 10 years. The result is a well-stocked fishery similar to the one existing some 20 years ago when the hamlet of Bonavista, as it was then, began to expand commercial fishing. You know from the previous experiment that this scenario will lead to plenty of fish in the sea, but in reality you and the fishermen themselves don't know how many.

      To replicate this fundamental uncertainty of fisheries you should ‘hide’ the trajectories for fish stock and new fish per year by colouring them grey so they blend into the background of the time chart. Some playing around with the software is necessary to bring about this change, but the result is important and worthwhile. First, press the ‘Reset’ button on the left of the time chart. The trajectories will disappear to leave a blank chart. Next move the cursor to the tiny paintbrush icon at the right of the tools bar at the top of the interface. Select and hold. A palette of colours will appear.

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Interestingly, some people dispute the existence of this circularity. They argue that the number of juveniles reaching fishable size each year has nothing to do with the number of parents in the sea because fish such as cod can produce upwards of seven million eggs in a season – most of which perish due to predation and environmental factors. However, the number of fish eggs is certainly related to the population of fish.