Understanding the environment: Complexity and chaos
Understanding the environment: Complexity and chaos

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Activity 5B: Engaging with a system dynamics model of exponential human population growth (and decline)

In this activity the aim is to explore a system dynamics model of human population growth and investigate the effects on population growth when positive feedback dominates negative feedback.

Since the time of Thomas Malthus [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] , many commentators have considered the growing human population as the root cause of all environmental and, consequently, socio-economic problems. Taking a systems view, we recognise that this is not as straightforward as it may seem, as there are many feedback processes that contribute to global environmental, social and economic crises, including our per capita consumption of resources and the rate of technological innovation (for which the environmental impacts are not always clear e.g. biofuels). However, the confusion may arise because limiting population growth seems to be one of the most straightforward actions to take which does not put into question a high consumption lifestyle. For example, within a couple of generations Italy went from showing the greatest increase in population of any country in the world to having the lowest sustained population growth rate in recent years (0.1 per cent in 2007), while being one of the most affluent countries in the world.

Unfortunately, the average ecological footprint of an Italian in 2008, 4.8 ha/capita, still far outstrips the country’s biophysical carrying capacity, 1.2 ha/capita ( Living Planet Report, 2008 ). In order to maintain the same consumption levels while staying within the country’s carrying capacity, the Italian population would have to shrink by three quarters (from 58 million to just under 15 million) and this would have to be done quite rapidly since the footprint is already in overshoot (or somebody better come up with some techno-fix fast!).

The core of this exercise is to make you aware, using the system dynamics modelling approach, of the complex and increasingly unpredictable outcomes when a series of positive and negative feedback loops operate in concert i.e. how difficult it is for anyone, however sophisticated their models are, to predict the future. If anything, observing the dynamic complexity emerging from a few simple relationships should teach us to adopt a precautionary principle to decision making, i.e. reducing our current environmental impact to within sustainable levels first, rather than hoping for a techno-fix in the future.

Activity 2

Run NetLogo and open the system dynamics model, Activity_5B.nlogo. The System Dynamics Modeler should open and you should see the following system dynamics diagram (Figure 5.9).

Figure 5.9
Figure 5.9 System dynamics diagram of population stock, plus birth and death rates and associated variables

In this model the ‘Birth_Percentage’ is a constant that is set to a value of ‘0.027’ – i.e. 2.7% addition to the global population from births based on data from the year 2000. The ‘Death_Percentage’ is another constant and this is set at a value of ‘0.014’ – i.e. 1.4% decrease in the global population from deaths also based on data from the year 2000

Before you carry out your first simulation for this activity, look at your system dynamics diagram and identify the type of feedback loop represented on the left-hand side, i.e. the ‘birth loop’. Is this the same type of feedback loop as the right-hand side ‘death loop’? Which feedback loop do you think will dominate? What do you think will happen to population numbers as a result of this dominant feedback loop? Sketch on a piece of paper a graph of population number against time. What shape is the resulting line?

Now, run the model and see if your predictions are correct. Press the ‘setup’ button in the NetLogo interface area and then the ‘go’ button. Look at the resulting graph and compare it to your predictions. You will need to press the ‘go’ button again to stop the simulation.

After your first simulation, change the birth percentage value to ‘0.014’ and the death percentage value to ‘0.027’. What do you think will happen now? Run the model again for 100 years.

Finally, make the birth and death percentage values equal and run the model for a further 100 years. What happens now?

Answer

You can gain significant insights by visually exploring the implications of a system dynamics diagram, but following through this initial exploration with an actual simulation can help to validate your mental models. In this case, the ‘birth loop’ represents a positive feedback loop: the greater the births, the larger the population; and the greater the population, the greater the number of births. Unchecked, this positive feedback loop will result in exponential population growth (Figure 5.10).

Figure 5.10
Figure 5.10 Graph showing the results of the first Activity_5B.nlogo simulation

The ‘death loop’ combined with the ‘birth loop’ introduces a negative feedback relationship within the model. So, when the model is run with the birth percentage greater than the death percentage, the resulting population grows exponentially. However, when the death rate is greater than the birth rate, then the population gradually runs down to extinction (Figure 5.11). ‘Homeostasis’ is only reached when the birth and death percentages are equal, thus growth and decline in population cancel each other out to achieve a steady state.

Figure 5.11
Figure 5.11 Graph showing the results of the second Activity_5B.nlogo simulation

This simulation shows us that if current birth and death rates remain unchanged at 2.7 per cent and 1.4 per cent respectively, then the human population will continue to grow exponentially. A significant point to note here is that positive feedback causes increasing rates of change so that loops dominated by positive feedback can also result in exponential rates of decline. The overfishing example in Reading 3.1 is a clear case of a positive feedback loop (e.g. the lower the fish catch, the greater the fishing intensity) resulting in an increasingly rapid decline in the fish stock. Stability is only reached when a negative feedback loop kicks in, which counterbalances the effects of positive feedback (e.g. the lower the fish stock, the lower the fishing quota).

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