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 the Limited Enthusiasm Model for a 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, ageing and people leaving the church. The unbelievers are split into those open to conversion and those hardened. Thus, the model can also describe secularisation in society.

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

System Dynamics Model

Stocks and Flows

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. Alternatively, they may revert and be hardened to rejoining (only inactive reversion is shown). See the assumptions for further model details.

demographics model
Figure 1


The reinforcing loop R1 drives church growth, where enthusiasts reproduce 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, the church may decline rather than plateau once revival growth is over. Likewise, 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. Additionally, a reinforcing loop R2 is formed using the connectors of loops B1-B4, creating long growth and decline cycles.

A balancing loop controls open unbelievers becoming hardened (not shown), the effect of secularisation. The model includes loops to govern 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 population 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; see the graph below. These oscillations occur for two reasons. Firstly, some people who leave the church rejoin at a later time. Secondly, ageing causes a delay between those born into the church and those who die.

demographics result

Enthusiasts take 70 years to reach a peak, and 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.

Further Results

Applications to UK Denominations

Church of EnglandChurch of ScotlandChurch in Wales
United Reformed ChurchMethodist ChurchWelsh Presbyterians
Welsh IndependentsElim PentecostalUK Baptists
NewfrontiersRoman CatholicFIEC
Scottish Episcopal Church
Growth, Decline and Extinction of UK Churches