Universal features in the growth dynamics of religious activities

S. Picoli, Jr. and R. S. Mendes

Phys. Rev. E 77, 036105 – Published 5 March 2008

Abstract

We quantify and analyze the growth dynamics of a religious group in 140 countries for a 47-year period (1959–2005). We find that (i) the distribution of annual logarithmic growth rates exhibits the same functional form for distinct size scales and (ii) the standard deviation of growth rates scales with size as a power law. Both findings hold for distinct measures of religious activity. These results are in surprising agreement with those found in the study of economic activities and scientific research, suggesting that religious activities are governed by universal growth mechanisms. We also compare the empirical findings on religious activities with the predictions of general models recently proposed in the context of complex organizations. Our findings should provide useful information for a better understanding of the mechanisms governing the growth of religion.

Received 24 August 2007

DOI:https://doi.org/10.1103/PhysRevE.77.036105

Authors & Affiliations

S. Picoli, Jr. and R. S. Mendes

Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá, PR, Brazil

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Vol. 77, Iss. 3 — March 2008

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Figure 1
Temporal evolution of growth rates $R (t)$ , given by Eq. (1), for some countries in the period 1959–2005. $\bar{S}$ is the average number of publishers in the period considered. (a) Britain $(\bar{S} = 92,006)$ and Cayman Islands $(\bar{S} = 67)$ , (b) Brazil $(\bar{S} = 226,682)$ and Niue $(\bar{S} = 20)$ , (c) United States $(\bar{S} = 655,607)$ and Montserrat $(\bar{S} = 24)$ , (d) Italy $(\bar{S} = 112,660)$ and Falkland Islands $(\bar{S} = 6)$ , (e) Zambia $(\bar{S} = 66,554)$ and Gambia $(\bar{S} = 42)$ , (f) Japan $(\bar{S} = 96,937)$ and Nevis $(\bar{S} = 40)$ . Observe that fluctuations in $R$ are larger in countries with small $S$ .Reuse & Permissions
Figure 2
Distribution of publishers. (a) Probability density of the logarithm of the number of publishers $p (\log_{10} S)$ for 207 countries in 2005. The solid line is a Gaussian fit to the data. (b) Cumulative distribution of the logarithm of the number of publishers $p_{c} (\log_{10} S)$ for the same data defined in (a). The solid line represents the cumulative distribution of a Gaussian variable with mean and standard deviation identical to the empirical data.Reuse & Permissions
Figure 3
(Color online) Growth dynamics of publishers. Panels (a), (b), and (c) refer to the following groups of countries selected by their average number of publishers: $6 < \bar{S} < 105$ (triangles), $105 < \bar{S} < 425$ (circles), and $980 < \bar{S} < 2,160$ (squares). We also consider the group $76,638 < \bar{S} < 655,607$ but, for clarity, we show data only for the three first groups. (a) Conditional probability density $p (R ∣ S)$ of the growth rates $R$ . The solid lines are given by Eq. (2) using $μ$ and $σ$ obtained directly from the data. (b) Cumulative distribution $p_{c} (∣ R ∣)$ of the absolute value of $R$ . The solid lines are linear fits to the data (on monolog scale), representing exponential decay. (c) Conditional probability density $p (r ∣ S)$ of the normalized growth rates $r$ . All data collapse onto a single curve (solid line) given by Eq. (4). (d) Standard deviation $σ$ of the growth rates $R$ as a function of $S$ . The solid line is a linear fit to the data (on log-log scale), giving a scaling exponent $β ≃ 0.16$ .Reuse & Permissions
Figure 4
Growth dynamics of other measures of religious activity. (a) Standard deviation $σ$ of growth rates as a function of the following measures of size $(X)$ : hours $H$ (squares), courses $C$ (circles), and pioneers $N$ (triangles). The solid lines are linear fits to the data (on log-log scale) giving $β ≃ 0.16$ for hours, $β ≃ 0.13$ for courses, and $β ≃ 0.10$ for pioneers. The curve for pioneers was vertically shifted for better visualization. (b) Conditional probability density functions $p (r ∣ S)$ , $p (r ∣ H)$ , $p (r ∣ C)$ , and $p (r ∣ N)$ . These distributions were obtained, respectively, from the following groups of countries: $979 < \bar{S} < 2157$ and $123 < \bar{S} < 424$ ; $230,508 < \bar{H} < 596,327$ and $26,431 < \bar{H} < 79,627$ ; $1,014 < \bar{C} < 2,664$ and $122 < \bar{C} < 390$ ; $113 < \bar{N} < 328$ and $15 < \bar{N} < 44$ . The solid line is given by Eq. (4). (c) Probability density $p (r)$ of normalized growth rates $r$ , calculated for 140 countries, for the following variables: $C ∕ S$ (squares), $N ∕ S$ (triangles), and $H ∕ S$ (circles). The solid line is given by Eq. (4).Reuse & Permissions
Figure 5
Temporal evolution of growth rates: comparison between empirical data and simulations. (a) and (b) Temporal evolution of the empirical growth rates defined in Eq. (1) for selected countries in the 47-year period considered. (c) and (d) Temporal evolution of growth rates obtained by a typical realization of the model given by Eqs. (6, 7) for 47 time steps. We use the empirical initial number of publishers as initial condition and choose $a_{0} = 0.18$ , $a_{1} = 0.50$ and $q = 0.85$ . In order to avoid negative values of $S$ we introduce a lower cutoff so that $S \geq 1$ .Reuse & Permissions
Figure 6
(Color online) Statistical properties of growth rates: predictions of the model. Panels (a) and (b) refer to a typical realization of the model given by Eqs. (6, 7), with $a_{0} = 0.18$ , $a_{1} = 0.50$ , $q = 0.85$ , and a cutoff $S \geq 1$ . (a) Conditional probability density of growth rates $p (R ∣ S)$ for three distinct groups of countries selected by their average value of $S$ : small $\bar{S}$ (triangles), medium $\bar{S}$ (circles), and large $\bar{S}$ (squares). The solid lines are given by Eq. (2) using $μ$ and $σ$ obtained directly from the simulated data. Compare with Fig. 3a. (b) Standard deviation $σ$ of the growth rates $R$ as a function of $S$ . The solid line is a linear fit to the simulated data (on log-log scale), giving a scaling exponent $β ≃ 0.15$ . Compare with Fig. 3d.Reuse & Permissions

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