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

The Methodist Church of Great Britain^[1] is a protestant church founded through the work of John Wesley and others. It originated in the 18th-century evangelical revivals within the Church of England, from which it eventually broke away. It has a wide variety of churchmanships. In common with most historic UK Christian denominations, it has been steadily declining since 1960. This analysis investigates the likelihood of decline leading to denominational extinction.

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Estimating Model Parameters

I will use the Methodist Church’s membership 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 Methodist Church. 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, then the Methodist Church’s decline is to extinction.

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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, the likelihood of extinction is more robust.

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Membership 2000-2020

I took the membership data from the Methodist Church’s website for recent values and Brierley (2008-2020). The year 2017 brought a considerable drop in members. By contrast, the 2019 figures are almost unchanged from 2018 and 2020 is also higher than expected. The latter is possibly COVID related.

Every optimisation indicates that the Methodist Church will end up extinct.

One such optimisation is given in figure 1. The reproduction potential chosen was an average figure of 0.84, well under the extinction threshold of 1.

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Range of Optimised Parameters

The optimisations indicate a range of possible parameter values:

Reproduction Potential	0.62-0.96
Duration Enthusiastic	1.2–7.8 years
Loss Rate (Reversion and Deaths)	5%–8%
Fraction of Converts who Become Enthusiasts	about 10%
Initial Fraction of Enthusiasts in the Church	0.5%–3%

The low value of converts who become enthusiasts is consistent with the view I hear from those engaged in evangelism. Similarly, with the fraction of the church who are enthusiasts. The loss rate is high as it includes the deaths, which are high due to the church’s age profile.

I repeated this optimisation strategy for different total population values, starting with the full England/Wales value and then using lower values. It is possible the Methodist Church 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. Extinction occurred in all such optimisations.

David Flavell has estimated the evolution of the Methodist church’s reproduction number from the 1930s to the present^[2]. He showed it had declined from 1 to a current value of just under 0.7. My data fitting here supports this figure.

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Possible Extinction Date

Although the model predicts extinction, it does not indicate an extinction date. The model contains exponential decline because it does not capture the effects of ageing. By 2060 it forecasts a church of 30,000 members. 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 Methodist Church is forecast to be extinct by 2036, figure 2. Ignoring the aberrant 2017 and 2018 figures and just using 2016 with 2019-20 extends the extinction date to 2045^[3].

The church’s future will likely lie somewhere between linear and exponential decline due to the presence of some city-based strong congregations. It is too early to tell whether the most recent data indicates a slowing of decline.

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Long–Term View

The membership of the Methodist Church from 1760 to the present day shows the classic institutional lifecycle, figure 3^[4,5]. The church saw phenomenal growth for over a hundred years until 1900. Later, it fell back after each of the world wars. This decline temporarily halted during the 1950s, like many UK denominations. Some people believe this was a post-war baby boom effect. Since the 1960s, the decline has been relentless.

Viewing the membership data as a proportion of the population shows that the real peak in the church’s effectiveness was the middle of the 19th century, figure 4. The remaining 50 years of growth benefitted from population growth. The 2020 proportion has fallen to that of 1760. The church’s current situation is very different compared with the 18th century. It is older, less evangelical and more institutionalised. Nevertheless, if they experienced a similar outpouring of the Holy Spirit to that of John Wesley’s day, recovery would take place.

Notes

1. The church covers Great Britain: England, Scotland and Wales. Methodists in Northern Ireland come under the Methodist Church of Ireland.
2. The Church R Number, and Part 2. David E Flavell, August 2020.
3. In 2014, David Flavell estimated an extinction date of 2033 for the Methodist church. In Pyramid Schemes, he compares the straight-line decline through ageing with the negative exponential of an epidemic model.
4. The Methodists had various splits in the 19th century. I added together their memberships during the period of the split. They reunited at a later date. Data was obtained from Currie 1977 and Brierley 1991-2020.
5. I have previously discussed the effects of institutionalism on the Methodist’s growth and decline. See:
   • The Rise and Fall of British Methodism
   • The Rise and Decline of British Methodism