The application of the Institutional Model to denominations in the UK requires several model extensions to enable calibration. The model extensions are illustrated using the model details and calibration of the GB Methodist Church are given here. See the results of the GB Methodists for the background.

Calibration requires membership data for the Methodist Church, as well as population data, including births and deaths. Model extensions include: Growing population; Church births and deaths; Delays; Internal pressure to increase institutionalism.

Methodist Data

Membership data was taken for England, Scotland and Wales from 1767, the earliest available date, to 2014. Ireland was excluded due to insufficient population data in the early period, and the later political division of the country. The earliest Methodist membership figures are taken from Currie et al. (1977), table A3, pp. 139-144. Numbers for the various Methodist church divisions are combined so that they can be compared with the later united church. Later data is taken from publications by Brierley and figures released by the Methodist church.

Growing Population

A standard population model, figure 1, is calibrated over time with the total population data for Great Britain, figure 2, together with births and deaths, figure 3. Data is taken from the Office of National Statistics, with earlier data taken from a number of texts including British Historical Statistics by BR Mitchell. Inevitably, there is some discrepancy between the population figures and the published birth and death rates as all these figures have a degree of estimation. Thus a corrective flow is added to the model, figure 1. It follows that the population stock matches the population data exactly using the correct birth and death rates.

Figure 1: Population Model with Correction for Anomalies with Published Births and Deaths
Figure 2: Population Figures for Great Britain: England, Wales and Scotland
Figure 3: Birth and Death Rates for Great Britain

Extended Institutional Model

The extended model is given in figure 4. The processes of the basic model are preserved. R1 governs additions to the church through conversion in proportion to the size of the church. However, the additions are reduced according to institutionalism, B2B1 controls those who leave the church. As institutionalism grows, it becomes harder to increase further, B3. There may be a naturally declining institutionalism if it is no longer generated, B4. The extensions are described below.

Figure 4: Extended Institutional Model of Church Growth

Church Births & Deaths

Additions to the church from children of church members are given by the flow Biological addition to the church. This addition is a fraction of the birth rate of the population, assuming that average family size for church members was the same as the population. Information from church figures across denominations indicates that this fraction is around 50%. However, evidence from the Welsh Methodists suggests the age profile of churches up to 1900 was younger than the population. Thus a correction, actual birth ratio, is used to adjust the biological addition, curve 1, figure 5. This boosts church births due to the greater proportion of adults in the child-bearing range. After 1900, this ratio falls as the population ages. By 2014, there are few children being born into the church as many members are past child-bearing age.

Figure 5: Adjustment to Church Birth and Death Rates for Church Age Profile

Likewise a death ratio is used to adjust the church death rate for differing church age distributions over the date range. By 2014 this ratio is high as a large proportion of the church is elderly.


A delay is added between the church size and institutionalism. This is because it takes time for organisational structures to be decided on and constructed to manage size and complexity. Also, it takes time for an institutional mentality to be adopted by the organisation.

There is a further delay from institutionalism to recruitment as it takes time for institutional structure and mentality to affect behaviour.

There is a physical delay in the addition of the children of church members into membership as most churches have 16-18 as a minimum age for membership.

Internal Institutional Pressure

An additional loop R2 representing the desire of, and pressure from, people working for the church to adopt more institutionalism, figure 4. They do this because more institutionalism creates job and promotion prospects, gives them status in society, and also, crucially, because a stronger institution is seen as a better, more effective and professional church. It is easy to dismiss the desire for more institutionalism as self-interest, but that misses an important dynamic that churches genuinely see professionalism and status as a means to glorify God and better spread the message.

Thus there are two positive forces causing institutionalism to increase: internal pressure; and the requirements of size. These two influences are combined in such a way that the one enhances the other, i.e. they are added. To preserve model validity, they are added using the logical “or” method. That is, if the two influences are X and Y then the combination is X + Y – XY. Figure 6 shows the two causes, blue and red, and their combination, the green curve. Each cause enhances the other. This modelling method was developed in Hayward, Jeffs, Howells & Evans (2014).

Figure 6: Effects of Internal Pressure and Church Size on Institutionalism and Combination


The model was run in the software Vensim, which allows optimization to parameters, seeking the sum of least square error between data and model. With the number of parameters in the model, then there are several suitable optimum fits. Leaving rate was fixed at 2%, typical of most denominations and reflecting average Methodist data, figure 7. Delays were set pragmatically, 20 years for the biological addition and 30-50 years for the others. The initial institutionalism was set at 0.2, i.e. 20%, reflecting that some structure was in place by the 1760s, but that it was quite low compared to what would be achieved a century later when the Methodists became a respectable large denomination.

Figure 7: Model Parameters for Data Fit of Institutional Model to CB Methodist Membership

Some optimized runs were compared with the parameters for the internal pressure and church size effects on institutionalism. These were then set, figure 7, to give a balance between the two causes so that internal pressure was stronger in the early years, whereas the response to size was stronger in the later years, as the denomination became very large, figure 6. Likewise, response time and the sensitivity of the effect on institutionalism were set based on the different runs, figure 7.

Finally, an optimized run was performed for church recruitment rate and the institutional removal rate, with all other parameters set as above, figure 7.