The model consists of one group of people: Church, measured by attendance or membership. There is no model of those outside church as demand is assumed potentially unlimited. In addition there is one variable Resource to represent the self-enhancing resource that also enhances growth. Zero resource will mean no conversion/recruitment to the church is possible. It will also mean that no growth in resource is possible, the assumption being that other mechanisms not in this model/scenario have started the growth in this particular resource. The resource has a maximum capacity.
The dynamic hypotheses are:
|Church supplies religion in proportion to its resource (R1).||The larger the resource the more people are recruited from outside the church. This may be achieved directly through contact with unbelievers, or indirectly via advertising, social networks, rumour on the street, or any combinations of methods. The reputation/resource generated by the church is instrumental in making any of the means of recruitment effective.|
|Church generates the resource in proportion to its size (R1).||The larger the church, the more resource is generated. This may be because financial giving increases and thus more money can be used on staff, church buildings and advertising. There are more people to advertise the church through their lives, church work and work in the community.|
|People leave church at a constant proportional rate (B1).||This includes people giving up the church, and deaths. The reason people leave are personal, thus the rate is proportional to the church size, i.e. "per capita". Those who leave may rejoin as the source of recruits is potentially infinite.|
|The larger the resource becomes the more it self-enhances (R2). The "Accelerator".||The more resource level then the more external agencies take note of the church and the easier reputation/resource becomes to generate. Low levels of resource make it hard to generate. As it increases that generation becomes easier as popularity breeds popularity. R2 acts as an accelerator on the resource. Its full effect must be understood by comparing it with the brake below.|
|The closer the resource gets to capacity, the harder it becomes to generate (B3). The "Brake".||When the resource gets larger it becomes harder to generate, because there is a limit to popularity which cannot be exceeded. Once a church is the most popular, has the highest reputation etc. then it cannot increase further. The higher it rises in the rankings, the harder it is to approach the top. High levels of resource make it hard to generate. B3 acts as a brake on the resource. Its full effect must be understood by comparing it with the accelerator above. Moderate levels of resource give the fastest increase in resource|
|If there is no resource generated, the remaining resource depletes at a constant rate (B2).||Popularity legitimacy and reputation deteriorate unless maintained. A church needs to continued to advertise its reputation, whether through word or deed, it needs itself in the news with fresh stories. With no such input both media and society will gradually forget the church over time.|
|Unlimited pool of unbelievers.||The size of society outside the church is infinite.|
Births are ignored but children born to church members can be assumed recruited with the same resource as those outside the church.
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 becomes easier as it increases as the growth is enhanced by an accumulation of resource (R2). As it 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 to increase a low popularity 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 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.