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Church Growth Modelling

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Model Results

Growth Limited by Reputation

Related Models

Bounded Resource

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

Self-Enhancing Resource Model

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 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 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 it church size or reputation are below critical values the church declines to extinction, and thus cannot grow by these means alone.

This is a metaphorical model whose purpose is to illustrate limits to church growth.

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. That is the type of popularity that gets a church reported in newspapers, secular or Christian. The type 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. It could also apply in a more local setting when one congregation is mentioned frequently on the local grapevine, especially if that spills over into the non-Church attending community.
  2. Reputation. In addition 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. In addition 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.


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:

Dynamic Hypothesis

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).

system dynamics model of bounded resource

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.

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:


people recruited per resource year The potential rate of recruitment given the resource is at its maximum capacity.
leaving rate The fraction of church members who leave each year.
max resource per person per year The fractional amount of resource one person could potentially generate in a year, given there is no slowing effect due to B3.
depletion rate The fractional rate of loss of resource per year.
max resource The capacity or upper limit to the resource. With a scale transformation this 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. That is the accelerator R2 is too small to accelerator the resource enough for its growth.

See Self-Enhancing Resource Model Results.

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Church Growth Modelling