It does not matter how fast church congregations grow, there comes a point where growth slows and eventually stops. What has limited its growth? Many suggestions are made: lack of physical resource, human resources stretched too much, complacency, inability to organise for size, too few enthusiasts, and lack of demand. Rather than have one model that includes all barriers to growth, individual models are constructed, for each barrier. Each one tells a story as to why growth is limited and how the barrier can be raised. These are examples of metaphorical models.
Metaphorical Models
A metaphorical model is one which is not dependent on a specific situation, nor a domain being modelled. Instead, it is generic, giving transferable insight across a wide range of real-world situations. For example, the models that describe limits to church growth are not calibrated for a particular congregation and could be applied to growth barriers in other social organisations, businesses, populations or the environment. They are a metaphor for the types of processes that limit growth. Thus the models below have been “borrowed” from other domains.
As models become more fine-tuned to a given situation, they become less abstract and more concrete, capable of being calibrated from data. As well as explaining particular observed behaviour and make more general predictions (Illustrative Models), they may give detailed forecasts of future behaviour and quantify possible interventions (Analogue Models). See Model Fidelity in John Morecroft, Strategic Modelling and Business Dynamics, 2007.
The metaphorical models below are constructed to illustrate the different barriers to growth, and how they may be tackled.
The Models
Constant Demand
A church that makes no effort to supply religion, or interact with society, will stop growing at a limit determined by the demand and the church’s losses. If demand declines, the church will head for extinction.

Supply and Demand
If the demand for religion in society is independent of the church’s activities, that church will stop growing.
Increasing the supply of religion by the church is not enough to remove the growth barrier. What the church supplies and what society demands must match. The church needs to challenge society and increase its demand for religion, church, and God.
Bounded Resource
Church growth that depends on a resource, such as Sunday School provision, or opportunities to serve in the church, will be limited as the resource becomes harder to produce.

Having a small number of resources that effectively aid recruitment will maximise the limit and protect against resource loss.
Self-Enhancing Resource
Church growth that depends on a self-enhancing resource, such as its reputation, will be limited as that resource becomes harder to produce.
If the church, or its initial resource value, is below a critical mass, then the church will fail to grow and head for extinction.
