small logo

Church Growth Modelling

What's New | About | Contact

Model Construction

Bounded Resource

Church supplies religion according to the size of a resource generated by the church.

Related Results

Growth Limited by Reputation

Related Blog

Church Growth Limited by Inadequate Resource Production

Blog on limits to church growth.

Church Growth Limited by Lack of Resource

Results of the Bounded Resource Model

A church which relies on a resource alone to generate its growth will always be limited as that resource becomes harder to produce. The resource may include, paid staff, lay ministries, spiritual life, social engagement, social capital, social networks, reputation and legitimacy.

Limit Determined by Resource

Consider a church of initially 10 people with a total leaving rate of 6% per year, including deaths. Church members are assumed to be very effective at building the resource which enables growth at 19 recruits per year per resource unit. However the resource starts low, at 12% of capacity, due to the small size of the church. The resource is an easily depletable one at 50% per year. It is built at a rate of 0.0075 per person per year assuming there is no resistance to building from the resource itself.

Such a highly effective church grows over 60 years to get near its equilibrium value of 250. This is an upper limit that becomes increasingly harder to approach due to the difficulty in generating the resource, figure 1.

Figure 1: Church Growth Through Resource. 1 = Church, 2 = Equilibrium, 3 = Dominance of Feedback Loops

Initially the growth of the church accelerates as the recruitment reinforcing loop has the strongest impact on the church. By time 20 this impact has fallen so that the leaving loop dominates, figure 1. Church growth now slows. The slowing period is much longer than the acceleration period and occurs when the church is 85 much less than half its final equilibrium value. When growth is through a resource the pattern is often not symmetric, with most of the church growth coming while it is slowing down.

The resource follows a similar pattern, figure 2, and approaches its equilibrium at 79% of is possible maximum faster than the church approaches its limit.

Figure 2: Resource Generation by Church. 1 = Resource, 2 = Equilibrium, 3 = Dominance of Feedback Loops

For the first 10 years growth in the resource accelerates as resource generation has the highest impact. This is the same reinforcing loop that causes the church growth, however its dominance ceases 10 years before it ceases on the church. Thus the resource starts slowing down before the church number. If the resource is measurable then its slowing down could be used as advanced warning that the church growth will slow in the future.

If the resource is interpreted as spiritual life then the church could be deemed to be in revival while that resource is increasing faster. Revival would then be seen to be over when the spiritual life is slowing down. In this case the revival has ended before the church growth has slowed down. If the church's attention is on the growth in numbers, rather than in life, then it may not realise that the revival is waned for a few years. This may be quite applicable to charismatic renewal whose churches had carried on growing for some time even though the life in the churches and conference had stopped increasing rapidly.

At time 10 the combination of two balancing feedback loops, the "brake" and depletion, dominates and the increase in resource starts slowing down, figure 2. The "brake" is the increasing difficulty of generating the resource as it gets large. It can be shown that this increasing difficulty is the cause of the church reaching a limit, not that actual bound on the resource. At 79% the resource has stopped well short of this bound.

The impacts of the three loops on the resource are given in figure 3, along with a vertical line at time 10 where loop dominance on the resource changes. The impact of a loop is the measure of the force of the loop on the resource measured relative to its rate of change. The net impact is a measure of the curvature of the graph. Note the impact of resource generation, curve 1, initially drops but then starts increasing again. It is a positive impact. However the brake, curve 2, increases in magnitude faster, and together with the constant depletion impact, more than counters the resource generation. Thus the increasing difficulty of resource generation is the source of slowing resource and slowing the church growth.

Figure 3: Impacts of the 3 Feedback Loops on the Resource

Extinction Through Lack of Resource Generation

Consider a church whose equilibrium value is 70 with resource just over 50%. After 20 years let the ability to generate the resource drop to 40% of the equilibrium value, perhaps due to the loss or unavailability of key personnel. The church is tipped into extinction with equilibrium now at zero, figure 4. Initially the resource declines sharply, then slows to a modest fall. The church declines steadily for the next 80 years to have 17 remaining members. If aging had been taken into account the decline in the last 40 years would be much sharper.

Figure 4: Extinction Caused by Lack of Resource Generation

Thus reduction in resource generation could be a cause of congregational decline. It is not that the resource generation has ceased at time 20, but that it has fallen below a critical level that would have avoided extinction. Perhaps the prayer meetings have become poorly attended and spiritual life generation is reduced. Perhaps the church is advertising itself less, for example discontinuing a regular home leaflet drop. Perhaps it has reduced its presence in the local street pastors or food bank. Perhaps it no longer provides refreshments after services thus reducing networking opportunities. Perhaps it has reduced "capacity" at services by having less services at varying times. These give some ideas of how a church may reduce resource generation and tip itself into future extinction.


The effect of secularisation on church growth can be illustrated in this model by allowing the number recruited per resource to drop as secularisation rises. This scenario reflects the increasing difficulty the church has convincing a more hardened population to become believers, assuming the resource remains the same. In addition the effect of secularisation on the church can be modelled by allowing the depletion rate of the resource to rise. This represents the pressures on society for church members to be less committed to church, and thus less committed to resource production.

Consider a church with the same parameter values as figures 1-3 starting with a size of 10. The parameters remain constant for 45 years after which secularisation starts and increases steadily until 150 years in total have elpased. The effect on the church is given in figure 5. Note at 45 years the church, line 1, is still short of its equilibrium, line 2, although its growth is slowing. Despite the effects of secularisation the church continues to grow until time 60, as secularisation has not reduced the accumulated resource sufficiently to initiate decline. From time 60 onwards the church starts to decline with the equilibrium value is well below the church numbers at any given time. Church decline is moderate not dramatic as both the church and the resource are accumulations and take time to reduce. At time 125 the church equilibrium has dropped below zero indicating the church is now heading for extinction, even though it will still take many years to reach that point.

Figure 5: Effect of Secularisation on Church Numbers

Once the equilibrium value, line 2, has fallen below the current value of the church, line 1, the church has accelerated decline. This is caused by the reinforcing loop R, the recruitment link. Once the recruitment rate falls below the leaving rate, the loop R has negative effect on church numbers and its brief dominance accelerates the decline. Once its effect is positive again leaving dominates and the decline is more gradual. The impact of a loop directly affects the curvature of the graph rather than its numbers, which are influenced indirectly.

Once secularisation starts, time 45, the resource quickly drops as it was much closer to its equilibrium/saturation value. The resource continues to drop, lagging its equilibrium value. As that equilibrium value becomes zero it can be concluded that church heads for extinction as its resource generation is heading for zero.

Figure 6: Effect of Secularisation on Resource

The R feedback loop (generation) briefly dominates, as it has negative affect. Then the brake dominates as church numbers are still high, eventually assisted by the depletion loop as church numbers drop. The resource continues to curve downwards because of the effect of secularisation on the church.

Strategies to Raise Limit to Growth

This model suggests 5 strategies that raise the limit the church numbers reach.

1. Fewer Resources Done Well are Better than Many Resources Done Poorly

Easy to generate resources with little potential to recruit should be avoided. For example a few high quality social engagement projects are better than many projects where the quality and effectiveness suffers.

2. Do Not Rely on One Resource Alone

Relying on one resource for most of the growth is risky. If for any reason factors outside the church's control affect that resource, for example sudden loss of reputation, loss of a key pastor, or Sunday school teachers, then there is no alternative driver of growth. Thus two or three good resources enable a church to get through a difficult patch if one of those resources is suffering.

3. Improve the Quality of the Resource Before its Quantity

Give due attention to improving the effectiveness of the resource. The parameter number recruited per year per resource is more sensitive than the resource generated per person. Thus improvements in the effectiveness of the resource will better aid growth than generating more of the resource. For example a higher quality Sunday School that attracts more people is better than just making it bigger. The higher quality which gives higher church recruitment will naturally increase church size. Likewise improvements in the quality of pastoral care, the sort that people outside the church find helpful, will aid growth more than just making more care available.

4. Reduce the Leaving Rate

Closing the back door of the church always helps raise the capacity limit of the church. A lower leaving rate makes the resource more effective on net growth.

5. Prevent Resource Depletion

Many resources deplete, people leave the church for natural reasons, leaving Bible studies, Sunday Schools, social programmes etc. But others leave due to events in the church that hurt them, hinder them serving God etc. Good pastoral care of people will help reduce this resource depletion, and of course make more contented people. As church grows the likelihood of such adverse effects on people increases and leaders should be on the look out for early signs of difficulties.

Home | Models | Results | Simulations | Articles | Revival | References | Publications | Modelling | Blog | About | What's New | Contact

Church Growth Modelling