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Church Growth Modelling

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Model Results

Growth Limited by Lack of Resource Generation


Related Models

Self-Enhancing Resource

The bounded resource is also self-enhancing making it easier to generate once resource levels become moderate, but hard to generate when low.

Related Blog

Church Growth Limited by Inadequate Resource Production

Blog on limits to church growth.

Bounded Resource Model

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.

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.

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

Types of Resource

The type of resource in the model is left general, but could include:

  1. The physical buildings, whether purchased or rented, especially if the buildings are attractive, or historic.
  2. The worship space whose limited capacity discourages new attenders as it gets harder to find seating without arriving early.
  3. The time of key pastoral staff.
  4. The reputation and legitimacy of the church.
  5. The spiritual life of the church.
  6. The opportunities to serve in the church.
  7. The resourcing of children and adult teaching, beginners courses and discipleship.
  8. Social networks and social capital.
  9. The social engagement and programmes of the church.
  10. Life services such as marriage preparation classes or bereavement support.
  11. The organisational complexity of the church.

Assumptions

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 one or more of the resources that enhance growth. Zero resource will mean no conversion/recruitment to the church is possible. The resource has a maximum capacity.

The dynamic hypotheses are:


Dynamic Hypothesis
Description

Church supplies religion in proportion to its resource (R). 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 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 (R). 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 resource Sunday Schools, Bible studies, social programmes and other lay ministries. There are more people to encourage each other, engage in spiritual conversation and pray. There are more people to befriend and build social networks and capital.
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 closer the resource gets to capacity, the harder it becomes to generate (B3). The "Brake". When the resource is small it is relatively easy to generate. When the resource gets larger it becomes harder to generate, perhaps because of the organisational complexity involved. Staff and ministers may become individually less effective when working in groups. There may be a greater drop out rate in larger Sunday Schools and Bible classes because of the increased pastoral difficulties due to size. There is a capacity to the church building/worship area size affecting attendance and class provision. There is a capacity to the number of contacts and friends in social networks. There is a limit to what a person can receive of the spiritual life. Reputation and legitimacy effectively have a maximum. There is greater scope for strife and division undermining effectiveness. B3 acts as a brake on the resource.
If there is no resource generated, the remaining resource depletes at a constant rate (B2). Organisations, networks, legitimacy and reputation deteriorate unless maintained. Staff naturally leave with a delay in replacement. People who service Sunday School and classes leave either the church, or no longer volunteer for that role. Spiritual life fades without input from the church.
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.


Flows

Unbelievers are added to the church according to the amount of resource (R). Church members leave at a constant rate per person (B1). The resource is generated according to the size of the church (R). The resource is harder to generate the larger it becomes (B3), measured next to its maximum resource (capacity). Resource depletes at a constant per capita rate (B2).

system dynamics model of bounded resource

The leaving feedback loop B1 has a constant impact. However because loop B3 slows the generation of the resource, the reinforcing loop R 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 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:


Parameter
Description

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 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 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 Bounded Resource Model

Church starts by growing (R), with the resource also growing (R). However resource growth slows when the impact of B2 and B3 exceeds that of R. Church growth slows as the impact of R falls below the fixed impact of B1. Eventually both the church and resource reach equilibrium with the latter falling short of capacity.

See Bounded Resource Model Results.

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Church Growth Modelling