Long Term Growth Results of the General Limited Enthusiasm Model (Births, Deaths, Reversion)
Principles Established Equilibrium Revival-Type Growth Threshold Extinction Threshold Delayed Growth Recurring Growth    Applications UK New Churches Wales Calvinistic Methodist   Details of Models Limited Enthusiasm  Births, Deaths & Reversion  Renewal   Details of Results Summary of Results Short Term Revival  Long Term Growth Long Term Decline Growth via Renewal   References & Bibliography  Mathematics of Church Growth Church Growth Revival System Dynamics  Sociology of Religion Epidemics  Social Diffusion Publications Articles Models for Download	Long term growth in the General Limited Enthusiasm Model is typical of the church attendance and membership patterns seen in the growing denominations particularly, Pentecostal and New Paradigm Churches Principles Established Equilibrium After a sufficiently long period of time the numbers in the church will stabilise to some equilibrium value, be it zero or non-zero (figure 1). If the church is part of a growing population then the proportion of the church in society will stabilise to equilibrium. The value of this equilibrium and the length of time taken to stabilise depends on the parameters in the system. Generally the reproduction potential has the biggest effect on 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 the loss of children only has a minor affect on the ultimate size of the church as they 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.   Figure 1 Return to Top Revival-Type Growth Threshold As in the case of 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 growth of the church becomes rapid (figure 2). The number of enthusiasts starts declining once the threshold is exceeded. However, unlike in short term growth, the number of enthusiasts never completely dies away as the pool of unbelievers is replenished by new people being born, and people who have left the church. The number of enthusiasts eventually settles to some equilibrium value, like that of the churches numbers.   Figure 2 Note that the revival growth threshold (curve 1 in the right hand graph of figure 2) rises as the church rises as there are less unbelievers to convert. Eventually the revival growth threshold will equal the reproduction potential. this is equilibrium. It is harder to get revival-type growth in a church that is a large proportion of society compared with one that is small in comparison to society. If the losses from the church are higher the revival growth threshold will be correspondingly higher. It is harder to get revival-type growth if the losses from the church are high. Return to Top Extinction Threshold There is also a threshold, also determined by the loss rates and the duration of the enthusiastic period, which determines whether a church survives. If the reproduction potential is under this extinction threshold the enthusiasts are not reproducing themselves fast enough to survive as such the church ends up declining to extinction at a speed proportional to its losses. The extinction threshold is line 3 in the graph of figure 2. This discussed further on the long-term decline page. Return to Top 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 a growth in the number of enthusiasts (red curve in figure 3) can lead to a growth in the church. In figure 3 it takes nearly 25 years for the rise in enthusiasts to turn the church around.   Figure 3 Return to Top Recurring Growth An intense period of growth can be followed by a significant decline, if the growth has exceeded the equilibrium value. The growth has occurred so fast that there are insufficient unbelievers left to sustain the number of enthusiasts, thus the church starts to decline. That decline will fall below the equilibrium value leading to further growth again although not so intense this time (figure 4). The result is revival-type growth recurring at intervals with decreasing intensity.   Figure 4 The period of recurrence and the intensity of subsequent periods of growth depends on the various parameter values. Note that this mechanism alone cannot account for the recurrence of revivals in a country like Wales as the later revivals (159 and 1904) were the most intense. Also in the case of Wales there was no period of decline between revivals only slower periods of growth. Return to Top Applications UK New Churches An example of revival-type growth is given by the New Paradigm churches in the UK. These include churches once described as house churches such as New Frontiers, Pioneer, Icthus and Covenant Life, and churches influenced by the USA such as Vineyard. Based on membership data during the 1990's it can be seen that their reproduction potential is well above the revival threshold (figure 5). This indicates that if current patterns of reproduction of enthusiasts and losses continue then substantial growth will occur for these groups during the 21st century.   Figure 5 The graph for the growth in numbers in the church is very similar to curve 1 in figure 5. Thus the fastest growth in these churches is yet to occur, if things remain the same. However there is no guarantee that parameter values will remain the same. For example the current estimated reversion level of 4% could increase if the congregations increase in size and become less informal. This would raise the revival threshold towards the reproduction potential. Also the currently high value of the reproduction potential of around 1.275 may drop because the general level of enthusiasm for recruitment declines. If such enthusiasm is partly determined by a work of the Holy Spirit in the enthusiasts the church will not have any direct control over maintaining this level. Return to Top Welsh Calvinistic Methodists 19th Century This church was the result of the Methodist revival in Wales of the 18th century. In the latter part of the 19th century the church was still growing but the number of enthusiasts was declining (figure 6). It is a good example of a church whose reproduction potential, although above the extinction threshold, was below the threshold of revival-type growth.   Figure 6 The church had benefited greatly from the revival in 1859, but once the revival ceased the growth continued along more ordinary lines with the number of enthusiasts declining. If this pattern had continued beyond 1904 the church would have declined to reach an equilibrium value - in this case a set percentage of the growing Welsh population. It would have reached its natural balance for its now lower reproduction potential and losses. In reality the church benefited greatly from the 1904-5 revival, but fell away later.