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.

Self-Enhancement

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 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.

Prediction

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.

Model Results

Type of Resource

The type of resource in the model is very specific and requires an external agency for it to function. Three suggestions:

  1. Popularity. Specifically, thus concept refers to the type of popularity that gets a church reported in newspapers, secular or Christian. For example, the kind of church that is discussed on social media and has many followers. Thus, the church is “well known” and mentioned frequently. Many mega-churches could come in this category. A popular church could also apply in a more local setting when one congregation is talked about often on the local grapevine, especially if that spills over into the non-Church attending community.
  2. Reputation. In addition to popularity, the church may gain a reputation for quality in its delivery of religion: its worship, services, Bible teaching, social programmes, and opportunities to serve.
  3. Legitimacy. Further, the church may be seen as a trusted defender of one or more aspects of the Christian faith. Its delivery of religion is conducted with integrity and honesty.

Assumptions

The model consists of one group of people: “Church”, measured by attendance or membership. There is no model of those outside churches as demand is assumed potentially unlimited. In addition, there is one variable “Resource” to represent one or more of the resources that enhance growth. A zero resource will mean no conversion/recruitment to the church is possible. The resource has a maximum capacity. The self-enhancing feature requires a non-zero initial value to resource to start its growth. It is assumed this value has been achieved by some process outside the model.

The dynamic hypotheses are:

Dynamic HypothesesDescription
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 reasons 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 produce more. 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 continue 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.


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 becomes easier to produce 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 for a church to increase its popularity when it is low 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.


Model Parameters

The behaviour of the model is controlled by a number of parameters that reflect the church’s effectiveness, and the response of society:

ParameterDescription
people recruited per resource yearThe potential rate of recruitment given the resource is at its maximum capacity.
leaving rateThe fraction of church members who leave each year.
max resource per person per yearThe amount of resource one person could potentially generate in a year, given the resource starts at zero. That is there is no slowing effect due to B2.
depletion rateThe fractional rate of loss of resource per year.
max resourceThe capacity or upper limit to the resource. With a scale transformation, this limit can be set to 1 without affecting the behaviour of the model. This fixes the resource units as a fraction of its capacity.

If the parameters remain constant then it is assumed all people have the same ability to build the resource, including the new recruits.


Results of the Self-Enhancing Resource Model

Church starts by growing (R1), with the resource also growing (R1). However, resource growth slows when the impact of B2 and B3 exceeds that of R1. Church growth slows as the impact of R1 falls below the fixed impact of B1. Eventually, both the church and resource reach equilibrium with the latter falling short of capacity. There may be a critical mass of church size, or resource, under which a church cannot grow. Instead, the church heads for extinction. This is a direct consequence of the lack of self-enhancing popularity at low resource levels, that is, the lack of help by outside agencies. Put another way, the accelerator R2 is too small to accelerate the resource enough for its growth.

See Self-Enhancing Resource Model Results.