Global Systems Thinking week 2: Systems

This week, we’re looking at systems; a lot of this is through the lens of population change.

World population and exponential growth

Note, the decreasing amount of time between each 1 billion increase.

What is the limit to human population growth? James Dyke suggested that this may be a thermodynamic limit, other limits may include food production, freshwater availability, energy resources, environmental degradation and climate change.

Malthus had an interest in what was happening in the UK. He observed the relationship between urbanisation and population growth, and speculated on a runaway effect (shown in the graph above. Furthermore, he reasoned that if you have an exponential population increase, you need an exponential increase in food production to support it – but while population increases geometrically, resources grow only arithmetically, creating an unsustainable imbalance. Anything less than exponential increase in food production would mean overshoot, starvation and death. To avoid this, it was necessary to stop an increase in the population – Malthus advocated for moral restraint (delayed marriage and fewer children) as a means to control population growth and mitigate its impacts. Relevant work: An Essay on the Principle of Population (1798).

Comment from James: we need systems thinking to separate out knotted, wicked problems.

Population change system dynamics

Population change at its simplest level is the result of the balance between births and deaths in the human population. These are elements in a system, which brings us on to stocks and flows.

Stocks change because of flows.

If the rate of births is higher than the rate of deaths, population increases. If the rate of deaths is higher than the rate of births, population decreases. Population change is the flow in of births compared with the flow out of deaths. Births are a source. Deaths are a sink. If the flow in balances the flow out, we have steady stock (a stable population).

The graph shows a model for population change. Early in the development of a society (pre-industrial), there are fluctuations of population with high rates of births and deaths, but these appear to balance each other out. So the population is low, even though it fluctuates.

Stage two might be where science and medicine start to play a part in reducing mortality rates, With a commensurate increase in total population. This increase in total population happens despite there being a decrease in the birth rate.

It may take time for societies to notice and respond to an increase in population rate, says James. This reminded me of hara hachi bun me (腹八分目), the Confucian teaching that instructs people to eat until they are 80 percent full. There’s a solid logic to it, which is that it takes time for food to pass through the stomach and into the duodenum, where satiety receptors tell the brain that we’ve had enough to eat. So, if we stop eating when we feel 80 per cent full, we’re probably already full. At the scale of a society, it takes a while for the signals of population growth pressure to make it back to the ‘brain’.

Eventually, both birth and death rates reduce, and as a society declines, death rates may exceed birth rates, leading to a drop in the total population. Japan is one of the best examples of this, where the population is ageing due to increased lifespans and a drop in the birth rate.

Back to stocks and flows, and a bathtub, because flows are illustrated in systems diagrams with taps.

The bathtub is used as an example of a coupled system because the water level in the bath depends on the tap, and the tap, according to the example, depends on the water level – but I don’t see how this works. The tap doesn’t care about the level of the water unless I’ve chosen to turn it off because the water in the bath is overflowing. The point here – individual components of a system may be interdependent. There also seems to be a distinction to make between tightly and loosely coupled systems; in the case of the latter, changes in one component of the system may have a less immediate effect on others. Meadows refers to feedback loops and expresses the idea of a coupled system quite simply – if A has an effect on B, is it also possible that B has an effect on A?

For a better example of a coupled system, I like plants and pollinators.

1. Plants rely on pollinators (such as bees, butterflies, or birds) to help them reproduce by transferring pollen from one flower to another.
2. Pollinators depend on plants as a food source, using nectar and pollen to sustain themselves.

If pollinators decline (due to habitat loss, pesticides, or disease), plants that rely on them for pollination will also be affected, reducing their ability to reproduce. Similarly, if the number of flowering plants decreases, pollinators will have less food, threatening their survival.

This is a coupled system because both elements (plants and pollinators) are interdependent: changes in one directly affect the other. Systems thinking encourages us to consider both sides of this relationship to maintain balance and health in the ecosystem.

Different feedback loops

Positive feedback / reinforcing feedback / runaway feedback

The systems thinking in joke here is that positive feedback is quite likely not to be positive.

Positive feedback continues until either

1. overshoot or collapse, or
2. a negative feedback loop is entered

Negative feedback / stabilising feedback / balancing feedback

The example given here of negative feedback was a toilet cistern.

A toilet cistern operates using a simple mechanical system to control the filling of the cistern after flushing:

1. Flush valve: When you flush the toilet, a valve opens to release water from the cistern into the toilet bowl, emptying the cistern.
2. Float (ball): The float is a hollow ball attached to a rod. As the cistern refills, the float rises with the water level.
3. Fill valve (cock): The float is connected to the fill valve. When the cistern is empty, the float is low, and the valve opens to let water in. As the water rises, the float rises too.
4. Shutoff: Once the float reaches a certain height (as the cistern fills), it triggers the fill valve to close, stopping the water flow. This prevents the cistern from overfilling.

If this were a positive feedback scenario, the water would continue to flow into the cistern until the cistern flooded (overshoot). The float provides balancing feedback.

Functions

The reassuring news, firstly, that maths is a sausage machine.

Linear and non-linear functions

A below is linear, B is non-linear and C is also non-linear, but exponential. This graph was explaining population increase as an illustration of Malthus’s concern about unchecked population growth.

Exponential function

f(x) = 2^x-1

From one grain of rice on the first square of the chessboard, with an exponential increase the amount increases to the point that by the time you get to square 64, there are over 9 quintillion grains of rice on the board.

A, B and the seesaw

I struggled to understand this. If B goes up, A goes up. If B goes down, A goes down. But if A goes up, B goes down and if A goes down, B goes up. I think I need to go back to James for that one.