such as the weather. In the game, as in real life, the fish population is not known accurately, although it can be estimated. Also, in the game, as in real life, the process of fish regeneration is not fully understood by those in the system (players or fishermen). Regeneration is related to the (unknown) fish population, but the relationship is complex and may involve other external factors.
Figure 1.4 An imaginary fishery – the game board of the original FishBanks, Ltd
Source: Meadows, et al., 2001
Model of a Natural Fishery
I have taken the situation and factors outlined above and used them to create a simple fisheries model (though the scaling I use is different from Fish Banks and there are no competing fishing companies). Figure 1.5 shows the fishpopulation and regeneration. For now there are no ships or fishermen – they appear later. So what you see is a natural fishery, free from human intervention.11 The fish population or fish stock, shown as a rectangle, accumulates the inflow of new fish per year (here the inflow is defined as births minus deaths). Initially, there are 200 fish in the sea and the maximum fishery size is assumed to be 4000 fish. Incidentally, the initial value and maximum size can be re-scaled to be more realistic without changing the resulting dynamics. For example, a fishery starting with a biomass of 20 thousand tonnes of a given species and an assumed maximum fishery size of 400 thousand tonnes would generate equivalent results.
Figure 1.5 Diagram of a natural fishery
The flow of new fish per year is shown by an arrow. The size of the inflow varies according to conditions within the fishery, as explained below. This idea of a modulated flow is depicted by a tap or ‘flow regulator’ placed in the middle of the arrow. At the left end of the arrow is another special symbol, a pool or cloud, depicting the source from which the flow arises – in this case fish eggs.
A very important relationship is the effect of fish density on net regeneration, a causal link shown by a curved arrow. Since fish density itself depends on the number of fish in the fishery region, the result is a circular feedback process in which the size of the fish stock determines, through various intermediate 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.
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
