The model has two thresholds: the revival growth threshold - over which rapid growth occurs; and the extinction threshold. The extinction threshold is always below the revival-growth threshold. Both are determined by the loss rates and the duration of the enthusiastic period. The revival-growth threshold is discussed on the long-term growth page.
If the reproduction potential is under the extinction threshold the enthusiasts are not reproducing themselves fast enough to survive. The number of enthusiasts keeps declining, curve 2, in the graph below. Thus the church ends up declining to extinction at a speed proportional to its losses, curve 1.
The extinction threshold is line 3 in the next graph. Unlike the revival-growth threshold, the extinction threshold does not drop as the proportion of unconverted people rises. Thus the church has no chance of recovery. Ultimately it will become extinct. Extinction occurs when the revival threshold equals the extinction threshold, as indicated by the arrow
Equilibrium at a non-zero value of church numbers can only occur when the reproduction potential equals the revival threshold. In the above case this cannot happen as the church becomes extinct first, as seen by line 3 being above line 2 in above graph.
Not all decline leads to extinction. If the reproduction potential is above the extinction threshold then the church numbers will stabilise at some non-zero value. Thus decline doesn't necessarily mean extinction.
Long Term Church Decline
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.
Long term decline is typical of the church attendance and membership patterns seen in the older denominations particularly, Methodist, Anglican and United Reformed in the UK. Decline comes about because enthusiasts do not make converts faster than the losses from the church such as to aging, reversion, and retention of the children of believers. Thus falling birth rates can expose an inadequate supply of converts. Once the church is in decline enthusiasts do not reproduce themselves fast enough for growth to recover. The church ages, thus having a higher average death rate and thus accelerating decline.
Generally church decline is slow as most people, once committed as Christians, attend church for the remainder of their lifetime.
Principles can be established for the dynamics of long term church growth:
- 1. Extinction threshold.
- 2. Percentage of enthusiasts can rise during decline
- 3. Churches with low reproduction potential are sensitive to child loss.
One unusual effect of decline in church numbers, especially if the church is heading for extinction, is that the percentage of enthusiasts in the church can rise. The actual number are falling - enthusiasts are not reproducing themselves fast enough. However the church overall is declining even faster, thus the fraction of the church that is enthusiastic becomes greater. See next graph.
Thus as the church declines, and individual congregations, get smaller, they may appear more enthusiastic, even more committed. However unless the enthusiasts reproduce themselves faster then the appearance of enthusiasm is misleading. The church is still becoming extinct.
A church with a low reproduction potential (well under the extinction threshold) can survive if it has no adult or child losses. The church survives on biological production alone. However, in this case, church numbers are very sensitive to losses.
Consider an extreme case of a church with no enthusiasts, accounting for 20% of the community, and with no adult reversion. With no child losses the church stays at 20% (line 1 following graph). If 25% of the children of believers are lost from the church then the decline sets in (curve 2. The church will eventually become extinct, but it takes a very long time to do so. It has halved in 200 years. It is not losing 25% of its people, but only its children. The 75% retained go on to have children of their own thus decline is slower than one might imagine at a first glance.
A church with a 50% child loss is halved in about 100 years. If all the children are lost the church is extinct in 70 years.