2.2. Sudden changes and cyclicity

Changes in the functioning of systems are rarely smooth. There may be a substantial gradual change in system stocks, but these changes will manifest in the system behaviour with a time lag or only when the change crosses a critical threshold. When system behaviour is not directly proportional to the size of the system's stocks, system behaviour is said to be non-linear.

For example, if we think of the bathtub in the previous example as a system and the water in the tub as a stock, it is relatively unimportant whether the tub is half full or nearly full: the water stays in the tub. But when the amount of water exceeds the volume of the tub, the water spills onto the floor and wets the house. The size of the stock, i.e. the amount of water in the tub, therefore has a concrete threshold above which the system's behaviour changes radically. Such thresholds exist in all systems, but it is very difficult to study them without stressing the system to the limit.

Particularly difficult are systems that appear on the surface to be very stable and predictable, but which, once a critical point is reached, change abruptly and more or less permanently. After a change in the system, it can be very difficult for the system to return to the state it was in before the change. A critical point in the system is also called a tipping-point. 

A very simple example of a critical point in a system is the breaking of ice under increasing stress. A five centimetre thick lake ice can easily support a single person, but as more and more people gather on the ice, it suddenly breaks and those on the ice are thrown into the water. Crucially, it takes time and suitable weather conditions for a new ice sheet to form, so the system may not recover once the load is removed.

Tipping points in natural systems and related system changes have been identified, for example, in the context of ancient climate change (more on these in the next section) and in shallow lakes, where prolonged nutrient inputs turn previously clear lakes into turbid, phytoplankton-dominated lakes. Even if nutrient inputs are stopped, it will be very difficult to restore lakes to their former clear water state.

Reinforcing feedbacks, delays and cyclicity

Reinforcing feedbacks accelerate the change in system stocks. A good example of this is the population growth rate. Consider, for example, voles, where changes in population size (i.e. population dynamics) have been studied extensively. When there are few voles, the population grows slowly because a small number of voles will produce only a small number of offspring. But as the vole population grows, the number of offspring produced increases. A reinforcing feedback loop between population size and the number of offspring quickly leads to an explosion in the number of voles.

However, the number of voles does not grow indefinitely, as eventually either the increase in predators or the decrease in available food places a limit on population growth. The decrease in the amount of food and the increase in predators acts as a balancing feedback mechanism limiting the size of the population.

However, the number of voles does not settle into a high equilibrium state, but tends to collapse to a very low level. These " vole cycles ", i.e. years of very high numbers of voles every few years, with very few voles in between, are due to delays in the system of voles and voles-eating predators.

When voles are abundant, the reproductive output of voles-eating predators such as weasels and owls increases, because in good vole years the predators produce high numbers of offspring. The offspring also survive because there is plenty of food available for them. However, the increase in predator numbers follows the increase in vole numbers with a time lag, as predator numbers can only increase once vole numbers have increased. The reproduction of predators is also slow compared to that of voles, as they produce only one litter per year, while voles can produce up to 5-7 litters.

The predatory pressure of numerous predators eventually leads to a collapse in the number of voles. Once the number of voles has collapsed, the food situation of the predators is very poor, and predator populations start to decline - again with a time lag in relation to the number of voles. Once the number of predators is down and the food supply of voles has recovered, the number of voles starts to increase again and the cycle starts afresh.

In general, reinforcing feedbacks and delays easily cause cycling in systems and, in extreme cases, unpredictable, even chaotic, behaviour.

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