Births, Deaths, Reversion and Secularisation

The central hypothesis of the limited enthusiasm model is that conversion growth in the church is driven by a sub-group of church members called enthusiasts. See Limited Enthusiasm Model for full description. The analogy is with the spread of a disease, where the enthusiasts are “infected” believers passing the faith on to unbelievers who catch the “disease” of religion.

In addition, the demographics model includes births, deaths and reversion, allowing for church decline through, lack of child retention, aging and people leaving the church. The unbelievers are split into those open to conversion and those hardened, allowing for secularisation in society.

The model predicts two thresholds, one of revival-growth which depends on the size of the community that remains unconverted, and one of extinction, which depends on conversion and loss rates. If the potential for enthusiasts to reproduce themselves is over the revival threshold, then rapid growth results. If the threshold is under the extinction threshold, then the church will eventually decline to zero.


System Dynamics Model

The above hypotheses are expressed in a system dynamics model, with the central ones indicated in figure 1. Unbelievers convert to believers through contact with enthusiasts who have “spread the faith” to them. Some new converts become enthusiasts, whereas some become inactive believers. Enthusiasts only remain active for a limited length of time before becoming inactive and taking no further part in spreading the faith. Both types of believers may leave the church and be open to joining again, or revert and be hardened to rejoining (only inactive reversion is shown).

demographics model
Figure 1

Growth is driven by the reinforcing loop R1 where enthusiasts are reproducing themselves through conversion. The feedback: more enthusiasts, more conversions, more enthusiasts, gives exponential growth. Growth is opposed by B1, which reduces conversions, thus slowing the exponential growth. When conversions have been reduced below the number who lose enthusiasm, B2, the number of enthusiasts starts to decline, and therefore church growth slows and eventually halts.

B3 controls the unbelievers who leave the church and are open to rejoining. Thus once revival growth is over the church may decline rather than plateau. A similar loop, not shown, governs the enthusiasts who leave the church. People who leave become hardened to rejoining, but after a time they may soften, loop B4, and become open to re-conversion. Because of this rejoining effect, there is a reinforcing loop from recycling R2, which may help the church to survive. R2 is the combination of the 4 loops B1-B4, which create long cycles of growth and decline.

A balancing loop controls open unbelievers becoming hardened (not shown), the effect of secularisation. The model includes loops to governing the demographics, e.g. births, and how many remain in the population they were born into. These effects can contribute to church decline and secularisation. All populations groups have loops for deaths.


Results of the Limited Enthusiasm with Demographics Model

There are implications for the long-term growth and decline of the church. Like the basic limited enthusiasm model, there is a revival growth threshold over which the church will see rapid growth. However, there is also an extinction threshold under which the church will decline to zero members or attenders.

A typical simulation of the demographics model with the reproduction potential above the extinction threshold shows long-term oscillations due to some people who leave the church rejoining later in life, see graph below:

demographics result

Enthusiasts take 70 years to reach a peak, then they decline. They do not start rising again until 120 years. The church is initially declining. Its growth occurs much later than the start of the growth in enthusiasts. After that, the revival growth in the church is rapid. Hardened unbelievers are rising throughout. This demographic effect takes nearly 200 years to stabilise.

See Long-Term Growth Results

See Long-Term Decline Results