This model is a specific variation on the bounded resource model applied to growth through popularity, reputation or legitimacy where external agencies and media have enhanced their growth.
The central hypothesis of the bounded resource model is that church members generate resources that, in turn, drive the growth of the church through conversion/recruitment. Conversion is proportional to resource size. Resource generation is proportional to church size but is increasingly harder to generate at higher resource levels. The resource is assumed to have an upper bound. Essentially, the church supplies religion to society in proportion to a generated resource.
A self-enhancing resource is one that also relies on its own levels to help accelerate the growth, a mechanism that may come about through external agencies, whose details are not required for the model. Thus at low levels of the resource, acceleration is much slower. This mechanism captures the concept that a church with low popularity, reputation or legitimacy finds it hard to capture the attention of the media or social networks, whereas a highly popular one, which has a degree of “fame”, will benefit from such agencies. Popularity breeds popularity, with the help of outside agencies such as media. This is the self-enhancing popularity effect.
In addition, losses to the church, whether deaths or people leaving, are at a constant rate per person. The resource will naturally deplete over time if not generated.
The model predicts a limit to the growth of the church, with growth slowing as the limit is reached. Initially, both church growth and resource generation may accelerate, but eventually, each slows down until the conversion rate matches the leaving rate. The resource always falls short of its upper bound. Additionally, the model predicts that if the church’s size (or its reputation) is below critical values, then the church declines to extinction, and thus cannot grow by these means alone.
This model is metaphorical, whose purpose is to illustrate limits to church growth.
System Dynamics Model
Unbelievers are added to the church according to the amount of resource (R1). Church members leave at a constant rate per person (B1). The resource is generated according to the size of the church (R1). The resource is hard to generate at low levels but it becomes easier to produce as it accumulates (R2). As resource gets even higher, it becomes harder to generate (B3), measured next to its maximum resource (capacity). Resource depletes at a constant per capita rate (B2).
For example, it is hard for a church to increase its popularity from a low level as outside agencies have little interest in such churches. However, as popularity increases, the outside agencies become interested and accelerate its reputation growth, and it only slows as capacity is approached, usually falling short of capacity due to depletion.
The leaving feedback loop B1 has a constant impact. However, because loop B3 slows, the generation of the resource, the reinforcing loop R1, has a diminishing impact on recruitment. The limit to church growth is reached when the recruitment rate matches the leaving rate.
If the church subsequently declines because, for example, the leaving rate increases, then the smaller church will generate less reputation/resource as some of the existing resource will deplete in time, B2. A new lower equilibrium would be reached.
Results of the Self-Enhancing Resource Model
Church starts by growing, with the resource, representing popularity, also growing. Loop R1 dominates. However, the resource becomes harder to generate as it gets closer to capacity, thus its growth slows, loop B3. The slowing resource growth slows the increase in recruitment until it matches the losses from the church, loop B1. Thus, the church stops growing. This behaviour is represented by the solid blue curves in the two graphs below.
If the initial resource starts lower, there is insufficient popularity to assist its growth, and both it and the church numbers collapse. Self-enhancing resources such as popularity or reputation need a critical value to enable church growth. Alternatively, a church has to work harder in the early stages, e.g. higher recruitment drives or lower losses, to overcome the initial lack of resource.