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

The Church of England (C of E) is the established church in England with an extensive network of parishes covering the country. Most of the English population are close to one of its churches. Consequently, the C of E has the largest membership and attendance of all the protestant churches in the UK and contains a variety of churchmanships. Its evangelical wing is a significant part of British evangelical Christianity.

I have studied the Church of England’s decline on two previous occasions, 2001-2011, 1979-1998.

### Estimating Model Parameters

I will use the Church of England’s attendance data to estimate the parameters of the Limited Enthusiasm Model with Reversion. The C of E does not have a membership system as such. Its equivalent is the electoral roll, which is not independently compiled each year.

Using the Reversion Model rather than the full Demographics Model avoids estimating values for child retention among church members, hardening rates etc. There is no information about these values for the C of E. 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. If this potential is less than one, the C of E’s decline leads to extinction.

### Calibration Strategy

The best fit between data and model is found using least squares. Avoiding systematic deviations from the data can help reduce the number of best fits. 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 count how many indicate the church will become extinct. Although these parameter values cannot be determined with certainty, deciding the likelihood of extinction is more robust.

### Attendance 2001-2019

I took the attendance figures from the Church of England’s annual statistical publications, confirmed by Brierley (2008-2020).

88% of the optimisations indicate that the Church of England will become extinct. Its current decline will likely lead to future extinction.

The data suggests that the reproduction potential could just get to 1 and save the church from extinction. However, this value is an outlier and is not reliable.

One optimisation is given in figure 1. The reproduction potential chosen was an average figure of 0.94, under the extinction threshold of 1, but not by much.

### Range of Optimised Parameters

The optimisations indicate a range of possible parameter values:

I have given a higher value to converts who become enthusiasts compared with other churches, 50%. The C of E makes extensive use of the Alpha and Christianity Explored courses, which are designed to generate enthusiasts.

I repeated this optimisation strategy for different total population values, starting with the full England value and then lower values. It is possible the C of E has a restricted influence in society and has contact with only part of the population. The model might give a more optimistic reproduction potential with a lower population. If the C of E only had contact with 20% of the English population, extinction occurred in 60% of optimisations. As the national church, it is unlikely that it had such limited contact with the population.

### Possible Extinction Date

Although the model forecasts extinction, it does not indicate an extinction date. This model contains exponential decline because it does not capture the effects of ageing. By 2062, it predicts the C of E with a total attendance of 160,000. This result is probably too optimistic.

Fitting a straight line to the data gives a more realistic estimate of the extinction date, as decline through ageing is a linear process. The Church of England is forecast to be extinct by 2062, figure 2. Its future will likely lie somewhere between linear and exponential decline due to the presence of some city-based strong congregations. By 2030 some slowing down of its decline may be seen, perhaps delaying extinction to near the end of the century.

### Long–Term View

The electoral roll of the Church of England from 1800 to the present day shows the classic institutional lifecycle, figure 3. The Anglicans benefitted from the revivals of the 19th century and only fit setbacks after each of the two world wars. This second post-war decline temporarily halted during the 1950s, like many UK denominations. Some people believe this was a post-war baby boom effect.

From the 1960s, the decline is steep but slows from the 1980s onwards. This reduction in the rate of decline may be due to the use of more realistic electoral rolls. Alternatively, the reduction may be due to the effects of Charismatic renewal on some of their parishes. Nevertheless, the C of E’s electoral roll is now only 1.7% of the English population, compared with 17% in 1800, showing a considerable loss of significance of the church.