Results of the Limited Enthusiasm Model with Demographics
The model has four population variables: Unbelievers, who are open to conversion; Hardened Unbelievers; enthusiasts, believers who drive the growth; and inactive believers, who are inactive in recruitment, though may be active in other areas of church life. Principles can be established for the dynamics of long-term church growth:
- Equilibrium in the proportions in each population category.
- The threshold of revival growth.
- The extinction threshold.
- Delayed growth.
- Recurrent growth.
The term “revival growth” refers to rapid exponential growth in the church’s numbers and the number of enthusiasts. It is similar to the epidemic phase of a disease’s spread.
Equilibrium
After a sufficiently long time, the numbers in the church will stabilise to an equilibrium value, whether zero or non-zero; see Figure 1. If the church is part of a growing population, then the church’s proportion of society will stabilise at equilibrium.
The value of this equilibrium and the time taken to stabilise depend on the system parameters. Generally, the reproduction potential has the biggest effect on the ultimate size of the church. The loss rates have a more moderate effect. Indeed, as long as the reproduction rate is high and new people are being converted, then the loss of children only has a minor effect on the ultimate size of the church, as they are converted later in life. However, for most church situations, the growth and loss rates are more finely balanced. In this case, the loss of children has a very significant effect on the future size of the church.
Threshold of Revival Growth
As with short-term growth, there is a threshold determined by the loss parameters, the duration of the enthusiastic period, and the proportion of society not in the church. If the reproduction potential exceeds this threshold, the number of enthusiasts increases, and the church’s growth becomes rapid (Figure 2). The number of enthusiasts begins to decline once the threshold is exceeded. However, unlike in short-term growth, the number of enthusiasts never completely dies out, as the pool of unbelievers is replenished by new people being born and by people who have left the church. The number of enthusiasts eventually settles at an equilibrium value, like the church’s numbers.
Note that the revival growth threshold (curve 1 in the above graph) rises as the church rises, as there are fewer unbelievers to convert. Eventually, the revival growth threshold will equal the reproduction potential. This is equilibrium. It is harder to achieve revival growth in a church that is a large proportion of society than in one that is small relative to society.
If the losses from the church are higher, the revival growth threshold will be correspondingly higher. It is harder to achieve revival-type growth when church losses are high.
Extinction Threshold
A second threshold, also determined by the loss rates and the duration of the enthusiastic period, determines whether a church survives. If the reproduction potential falls below this extinction threshold, the enthusiasts are not reproducing fast enough to survive. As such, the church ends up declining to the point of extinction at a rate proportional to its losses. The extinction threshold is the dotted line in Figure 2. This is discussed further on the long-term decline page.
Delayed Growth
When the church is small and declining, an increase in reproduction potential can bring it back to growth and survival. However, it can take some time before growth in the number of enthusiasts (Figure 3) can lead to growth in the church. In this case, an enthusiastic period = 5 years; it takes nearly 25 years for the rise in enthusiasts to turn the church around.
Recurring Growth
An intense period of growth can be followed by a significant decline if the growth has exceeded the equilibrium value. Growth has been so rapid that there are now too few unbelievers to sustain the number of enthusiasts. Thus, the church starts to decline. That decline will fall below the equilibrium value, leading to further growth, though not as intense this time (Figure 4). The result is revival-type growth recurring at intervals with decreasing intensity.
The recurrence period and the intensity of subsequent growth periods depend on the parameter values. Note that this mechanism alone cannot account for the recurrence of revivals in a country like Wales, as the later revivals (1859 and 1904) were the most intense. Also, in Wales, there was no period of decline between revivals, only slower periods of growth.