Reinforcing Loops and Growth

I have often seen the following causal loop used in system dynamics presentations to explain a reinforcing loop:

Figure 1: Causal Loop Diagram of Simple Birth Process

The argument then runs: the more population, the more births, hence more in the population; thus the population grows. Fortunately, I never hear people reverse the argument: the fewer in the population, the fewer births, hence fewer in the population! Clearly not true. If the only process on the population is births, it must grow. In fact, the population will grow even if births stay constant.

The problem with a causal loop diagram is that it does not give any information about which variables are stocks, and thus accumulate. Every causal loop must have at least one stock; otherwise, time does not advance, and there is a circular definition. In the above, Population is a stock, and births are a flow. Thus, the argument should read: the more population, the more births, thus the more are added to the population.

The + sign on the link to births means “same way” that is the births change the same way as the population. If the population goes up, then so do births; if the population goes down so do the births.

However, the + sign on Population means “add to”. If the births go up, more are added to the population; however, if births go down, less are added to the population. But the population still increases because it is being added to.

The stock-flow diagram gives more information about the system:

Figure 2: Stock-Flow Diagram of Simple Birth Process

Now it is clear that the stock Population is being added to. The reinforcing loop describes a process where the births being added to the population is increasing. Thus the population growth accelerates:

Figure 3: Accelerating Growth for 1-Stock Reinforcing Loop (per capita rate of growth 0.2 per unit time)

The reinforcing loop gives accelerating growth. Acceleration is the characteristic behaviour of a reinforcing loop containing only one stock. Acceleration is portrayed as a curve becoming more vertical, figure 3. If, however, the reinforcing loop is broken:

Figure 4: Stock-Flow diagram of Constant Growth

then the resulting growth has no acceleration and appears as a straight line:

Figure 5: Uniform Growth of a Stock with a Constant Flow (births = 1 person per year)

The absence of the loop does not mean the absence of growth, but the absence of acceleration. If there is growth, then it is uniform.

In this way a reinforcing loop (figure 2) can be pictured as a force on a stock, producing acceleration (figure 3) – the equivalent of Newton’s second law of motion. The absence of a loop (figure 4) is like the absence of a force – Newton’s first law of motion – producing uniform growth (figure 5). This analogy is an example of the Newtonian Interpretative Framework which lies at the heart of Sociomechanics, which seeks to explain social behaviour using ideas from mechanics.

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