Application of the Limited Enthusiasm Model with Reversion, Written in 2022.

The Fellowship of Independent Evangelical Churches (FIEC) is a UK protestant church founded in 1922. It aims to bring unity to churches that believe in congregational independency and are firmly evangelical in faith. They are committed to church planting and to revitalising churches that are declining. It has grown continually since its inception. This analysis investigates how the church is experiencing revival growth and forecasts its potential future numbers.

Estimating Model Parameters

I will use the FIEC’s attendance data to estimate the parameters of the Limited Enthusiasm Model with Reversion. Using this cut-down version of the Demographics Model avoids estimating values for child retention among church members, hardening rates etc. There is no information about these values for the FIEC. The reversion model has only five parameters:

  1. Reproduction Potential
  2. Duration Enthusiastic
  3. Loss Rate
  4. Fraction of Converts who Become Enthusiasts
  5. Initial Fraction of Enthusiasts in the Church

The key parameter is the reproduction potential. Its value will determine if the FIEC has revival growth.

Calibration Strategy

The best fit between data and model is found using least squares. To help find the most suitable parameter values, I vary parameters 3-5 above and optimise for 1-2, the reproduction potential and duration enthusiastic. Out of this optimisation set, I determined optimistic scenarios – those with moderate growth, and pessimistic scenarios – those with lower growth. I chose a representative of each optimisation close to the group’s average. I excluded extreme values of the parameters as they are unlikely to be correct.

Attendance 1950–2015

I took the data from Brierley’s church statistics that use the FIEC’s estimates of church attendance. Membership is often stricter in these types of churches and is often an underestimate of church activity.

I found it impossible to get a good fit for data from 2000, which could be caused to the church’s estimation methods. Alternatively, a small denomination with many growing churches may experience more irregular changes in attendance over short periods.

As an alternative, I used attendance figures from 1950, reducing the data in the post-2000 period to avoid it being overly weighted in its favour. The result gives average figures for the parameters over 65 years.

Every optimisation indicates that the Federation of Evangelical Churches is experiencing revival growth with no sign of slowing down.

One such optimisation is given in figure 1. The reproduction potential chosen was an average of the optimistic scenarios, a value of 1.023. The optimisation averages the rather lumpy changes in attendance figures over the entire period. In some decades, the reproduction potential may have been higher. In others, it would have been lower.

Data fit for the FIEC to the Limited Enthusiasm Model of church growth
Figure 1: Data Fit for FIEC Attendance and the Limited Enthusiasm with Reversion Model

Whatever data fit is used, the FIEC should continue to have revival growth for the foreseeable future, provided it keeps the same reproduction potential. “Revival growth” is where church and enthusiast numbers have accelerated growth. For example, figure 2 shows this rise in enthusiasts and church attendance for the FIEC. Even by the end of the century, the number of enthusiasts is increasing. However, it is only matching the growth of the church. The proportion of enthusiasts in the church is not changing much, which helps explain why the revival growth is so modest.

Figure 2: Growth of Enthusiasts in the FIEC

Range of Optimised Parameters

The optimisations indicate a range of possible parameter values:

Reproduction Potential1.006-1.167
Duration Enthusiastic0.2–5 years
Loss Rate
(Reversion and Deaths)
Fraction of Converts who Become Enthusiasts10%–50%
Initial Fraction of Enthusiasts in the Church0.5%–5%
Model Parameters for the FIEC

Although there is a wide range of parameter values above, these do not affect the revival growth status of the church.

Possible Reasons for Growth of the FIEC

Several mechanisms may explain the growth of the FIEC:

  1. Many churches are actively engaged in evangelism. As a result, people come to faith and added to the church through the action of church members and ministers. These people represent the enthusiasts of the model
  2. The FIEC plants about 10 new churches each year. This action widens the pool of potential converts and enables enthusiasts to be effective for longer as they make new connections in new areas.
  3. Individual Christians transfer from non-FIEC churches, often due to compromises of faith in denominational churches. Although these people are not new converts, their recruitment to the FIEC fits the limited enthusiasm narrative.
  4. Sometimes a whole congregation leaves a parent denomination and becomes a member church of the FIEC. This mechanism is not strictly part of the limited enthusiasm principle, but in the above simulations it would be treated as a word-of-mouth recruitment of all in the congregation.

I have not discovered any estimates for the proportions of the four mechanisms in the growth of the FIEC.

Future Projections

In Figure 3, I have extended simulations to the year 2100. Although these simulations are not predictions, the graph indicates possible futures, a range of forecasts, assuming the church reproduces enthusiasts at the same rate.

Figure 3: Projected Future Attendance for the FIEC

There is little to choose between the simulations up to 2040. After that, the most pessimistic estimates have the church’s growth slowing after 2060. By contrast, the most optimistic simulations indicate the FIEC’s continued growth at the end of the century. They could increase to over three times their current attendance.