growth modelling is a research project that attempts to understand
the growth and decline of the Christian Church using
the techniques of mathematical sociology.
models give valuable insights into the way the churches grow
or decline at either a congregational, denominational, national
or international level. They are particularly helpful in describing
the dynamics of growth in times of revival.
This web site is aimed at church practitioners who wish to understand and enhance the growth of their churches, as well as academics looking for a quantitative understanding of the spread of religion.
Some important results are summarised below
and on the Results Summary page.
A Blog contains short articles and commentaries on the project.
Loughor, near Swansea, South Wales.
of the starting places of the 1904-5 revival in Wales and home
church of revivalist Evan Roberts.
revival is a sovereign work of God, giving new life to Christians.
It leads to the conversion of many unbelievers and the transformation
John Hayward. Postal
Research details on the Social Dynamics web page.
What is Church Growth?
is the discipline that seeks to analyse why Christian churches,
at various levels of organisation, grow or decline. This includes
both their spiritual growth as well as their numerical growth.
can be divided into two strands:
Church Strand, which is based with Christian
denominations and exists to serve their needs. It is based on
theological principles, organisational pragmatism, and ideas from the church growth movement.
Social Science Strand whose focus is primarily academic
research and has a basis in the sociology of religion.
strands use data gathering and statistical analysis to understand
the nature of quantitative church growth.
is Church Growth Modelling?
is an attempt to understand the dynamics of church growth using
mathematics and system dynamics methods.
produce theories of how churches grow, in the sense of why the
numbers of people in churches change the way they do;
discover broad principles that describe the growth;
provide a theoretical framework that can both suggest and assess strategies of
help decide what sort of data should be gathered to best reflect
a church's effectiveness;
The project uses the techniques of mathematical sociology: differential equations and computer simulation. Significant use is made of the system dynamics methodology because of the quality of its model building processes and its accessibility to a non-technical audience. There is also input from statistics, sociology of religion, church history and christian belief.
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- Limited Enthusiasm Model. Based on social diffusion theories. Church grows through the activity of enthusiasts who are alone responsible for the recruitment/conversion of unbelievers into the church. Believers are only enthusiasts for a limited period after their conversion. Only new believers become enthusiasts. A basic model of revival growth. Model, Results. Application to revival.
Congregational Models. Applied to the individual congregation only. Designed to assist church leaders. Based on ideas from business modelling.
- Limited Enthusiasm with Births Deaths and Reversion. Model extended to include births, deaths, people leaving church and perhaps rejoining at a later date. Useful for analysing the long term survival of denominations and congregations. Model, Growth results. Decline results.
- Renewal Model. As above but enthusiasts can also be made out of existing inactive believers. Models a range of renewal movements that start within the church. Shows that renewal is the key to seeing revival growth in the church. Model, Results.
- Membership Model. Extension of the limited enthusiasm model to include the differences between church attendance and membership. Delays in joining and leaving a church cause attendance to run ahead of membership in a growing church, but run behind it in a declining church. This difference can be used as an indicator of future growth or decline, or of strictness in the church. Model, Results.
- Effective Believers Model. An extension to the limited enthusiasm model where effectiveness depends on the production of spiritual activity. Explains the dynamics of how dying churches can be turned to living and growing ones through enthusiasts engaging in activities that bring spiritual life. Model started as a student project. Model, Results, blog post.
- Church Planting. Extension of the limited enthusiasm model to include church planting strategies . Shows that growth in new churches can burn out due to a lack of enthusiasts rather than a lack of places to plant. The Migration model is a subset of this model. Model started as a student project. Migration Model, Migration Results.
Sociological Models. Based on theories in the sociology of religion.
- Discipleship Model. A model of how the discipleship process progresses following conversion. This model was developed as part of the CICC Church Growth Cafe in Cardiff, UK. Model, Results.
- Congregational Lifecycle Model. A model of a single congregation rather than a denomination or the whole church, linking the activity of church members and their ability to build "spiritual capital" as a resource to aid growth. Predicts the eventual slow decline of the church due to complacency and the need to spend more time on maintaining the resource and less on recruitment. Outlined in "Modelling Church Growth- Micro and Macro Models".
- Strictness Model. Explores the effect that the strictness of a church has on the growth of the church encapsulating Kelley's thesis that strict churches are strong and hence grow, but lenient ones are weaker and more likely to decline. See "A Dynamical Model of Strictness and its Effect on Church Growth 2002". Blog post Liberal and Conservative Churches Part 1.
- Church and Society Model. An attempt to build current sociological theories such as secularisation, neo-secularisation and the new paradigm into a dynamic model and explore their relative effects. This acts as a useful macro-sociological comparison with the other micro-sociological models based on the activities of groups of people. Model is still in development.
The core models are published in peer reviewed journals and conferences in mathematics, sociology and system dynamics.
Models are built mainly using mathematics, or the System Dynamics methodology. This powerpoint presentation shows how System Dynamics is used to build a simple church growth model. (Also as a PDF).
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Summary of Limited Enthusiasm Model
faith is largely spread through enthusiasts, or "active"
believers. These are active in recruitment distinguishing them
from "inactive" believers who play little role in recruitment.
conversion growth comes from contact between an enthusiast and
an unbeliever. The numbers converted being proportional to the
numbers of both.
enthusiastic phase of a believer only lasts a certain length
of time, after which they become inactive.
is a threshold over which large scale "revival-type"
growth occurs. This depends on the number of unbelievers.
number of enthusiasts does not affect whether such substantial
growth occurs. If there are smaller number enthusiasts the same
growth occurs over as longer period.
threshold depends on the number of people converted per enthusiast. Thus
it is the "amount of enthusiasm" that governs the growth.
will end because the church runs out of enthusiasts, not
because the number of unbelievers runs out. As people are converted
enthusiasts are less likely to meet unconverted people, leading
to a failure to make sufficient enthusiasts.
is more beneficial for growth to increase the effectiveness
of enthusiasts than to increase their numbers. A small number
of effective evangelisers are better than a large number of less
the population of a church is small compared to the surrounding
unbelieving society it can be a long time before a revival among
believers can see significant growth in the church.
summary it is the spiritual vitality of the enthusiasts that
drives the growth of the church. More life gives more growth,
provided that life is directed into contact with unbelievers.
Acts 2:42-47 & 4:12-16 for a Biblical understanding of this
to Summary of Results for more.
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