A General Framework For Determining the Temporal and Evolutionary Dynamics of Religion-Based Website Popularity on the Internet

doi:10.4236/ojs.2012.24052

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Open Journal of Statistics, 2012, 2, 424-428

http://dx.doi.org/10.4236/ojs.2012.24052 Published Online October 2012 (http://www.SciRP.org/journal/ojs)

A General Framework for Determining the Temporal and

Evolutionary Dynamics of Religion-Based Website

Popularity on the Internet

Michael R. Golinski1, Connie Petersen2

1Energy Research Laboratory, New Mexico State University, Las Cruces, USA

2Department of Sociology, New Mexico State University, Las Cruces, USA

Email: mgolinsk@nmsu.edu, [email protected]

Received June 29, 2012; revised July 30, 2012; accepted August 12, 2012

ABSTRACT

Religion-based websites are fast becoming a major pipeline for disseminating religious information to broad popula-

tions of individuals in the United States. Both mainstream religions and fringe religions are easily accessible to a large

population of internet users. The purpose of this review is to develop and examine a general framework that uses simple

mathematical and statistical models to interpret and measure temporal “snap shots” in the popularity of religious web-

sites. We extend this framework to include an evolutionary model that has the potential to predict long-term shifts or

changes in the popularity of relig ious websites over time. Ultimately, the goal of th is review is to introduce a new mod-

eling framework for research into how the internet is changing the accessibility and views of populations of individuals

who follow various religions on the internet and how this may in-turn affect the distribution of religion in the “real

world”.

Keywords: Communities; Drift; Evolution; Fringe Religion; Internet; Mainstream Religion; Powerlaw; Selection;

Website

1. Introduction

The aims of this paper are to propose a general frame-

work for using statistical and mathematical models to

determine if increases over time in the popularity of

religion-based websites in the United States results in the

emergence of relatively large scale internet “communities”

composed of individuals who follow “fringe” religions.

Based on the aims of this general study, we define

popularity as a measure of the website’s visibility to an

individual searching the internet. Within the context of

this general overview, an internet-based community is

defined as a social network of individuals who interact

through specific websites [1]. We define “mainstream”

religion practiced in the United States and promoted by

the internet as Islam, Judaism, Buddhism, Spiritism,

Christianity and Hinduism [2]. “Fringe” religions as prac-

ticed in the United States and promoted by the internet

include but are not limited to Neo-Paganism, Rasta-

farianism, Scientology, New Age, Christian Scientist and

a large number of so-called “cult” religions [3]. This

general overview also considers changes over time in the

popularity of non-mainstream web-based religion s whose

visibility to individual internet users falls somewhere

between the visibility of websites that promote main-

stream and fringe religions. Ultimately, the long-term

aim of this paper described herein is to develop a general

framework that can be used to describe short-term pat-

terns in the popularity of religion-based websites and to

determine if these patterns manifest themselves as long-

term evolutionary shifts in the popularity in internet

based religions. We believe that such a shift could result

in the redistribution of religious websites on th e internet,

with less popular non-mainstream and fringe religion-

based websites becoming as popular as mainstream

websites over time.

Just as with non-internet based religious communities,

we assume that generally speaking, religion-based in-

ternet communities are composed of individuals that

follow different internet-based religions that are moti va te d

by several factors, including: 1) The ability of the com-

munity to provide a source of group identity, individual

identity, and impersonal social interaction; 2) The ab ility

of the community to provide a philosophical and ethical

framework, and the language through which philosophy,

ethics and community issues can be discussed; 3) The

ability of the community to provide a source of unity

necessary for defense of the community and its ideals; 4)

The ability of the community to address universal ex-

M. R. GOLINSKI, C. PETERSEN 425

periences such as death, sexu ality, and family life.

Though sparse, there have been studies that show that

the numbers of individuals that follow websites devoted

to non-mainstream and fringe religion are small relative

to the number of individuals that follow websites devo ted

to mainstream religion [4]. The relative acceptance of an

ideology promoted by a religion-based website, as meas-

ured by the number of web hits the website receives over

relatively short periods of time, may become main-

stream, non-mainstream or fringe on a larger-scale with

respect to the internet based community. There have been

multiple studies that show that diverse cultural pheno-

mena, including change in the frequency of archaeolo-

gical pottery motifs over time [5] change in the freq uen cy

of baby names in the United States during the twentieth

century [6] and change in the frequency of the number of

times United States patents have been cited since 1963

exhibit a “long-tailed” distribution [7].

2. Snap Shot Models

Within the context of this paper, the long-tail distribution

suggests that rather than one dominant religious website

giving way to another over time, there may be many dif-

ferent choices of religion-based websites at all times.

Mathematically, the highly skewed long-tail distribution

is described by a simple power-law equation:



PV CV



(1)

where α and C are constants and V > 0. In Equation (1),

P(V) is the proportion of web hits (out of all hits for all

religion-based websites) that a religion-based website

receives over time and V is the number of religion-based

websites (variants) in order of decreasing popularity. The

power-law distribution described by Equation (1) and

illustrated in Figure 1 is called the Pareto power-law [8],

and it has been used in many scientific and sociological

fields to describe temporal changes in the frequency of

natural and sociological phenomena [9].

In one of the few studies of temporal changes in e-

commerce patterns on the web [10], used the long-tail

distribution to describe how most internet purchases in

the United States congregate under the left side or nor-

mally distributed “buldge”, while a large group of inter-

net purchases for unpopu lar products tends to congr egate

under the long-tail of the distribution. 5% of the total

number of web hits for all religion-based websites.

This type of pattern indicates that while there are many

more unpopular variants than popular variants, the very

few popular varian ts are thou san ds of times more popu lar

than the unpopular variants.

Of key importance for the purposes of constructing a

general framework, is that Anderson did not demonstrate

how temporal change in e-commerce patterns in the

United States is affected by website visibili ty . Specifically,

he did not demonstrate if temporal patterns in internet

purchases could change as more and more individuals

that buy less popular items (those in the right side of the



010 2030 4050 60 708090 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P (V)

Figure 1. Long-tail distribution generated by Equation (1). P(V) is the proportion of web hits (out all hits for all relig-

ion-based websites) that a religion-base d website receives over ti me as a function of the number of religion-based websites in

order of decreasing popularity V. In the figure, the 100th website receives approximately 1% of the total number of web hits

for all religion-based websites. In the figure, C = 2.2 and α = 1.15 in P(V).

M. R. GOLINSKI, C. PETERSEN

426

long-tail distribution) begin to purchase more and more

of a select number of unpopular produ cts, thus increasing

the proportion of those products being purchased over

time.

Therefore, we believe that future research should ad-

dress the following: 1) Does the distribution of the ob-

served proportion of web hits that religion-based web-

sites receive over time follow the power-law distribution

described by Equation (1). 2) Can simple mathematical

and statistical models be developed and used to extend

Anderson’s work to explore the hypothesis that increased

visibility of religion-based websites to individual in ternet

users facilitates an increase in the proportion of web hits

that those websites receive, resulting in a cultural shift in

internet-based religion over relatively long periods of

time. We hypothesize that such a shift could result in a

redistribution of religion-based websites on the internet,

with less popular non-mainstream and fringe religion-

based websites becoming as popular as mainstream re-

ligion-based websites over time.

To begin to test these hypotheses and accomplish the

goals laid out in this paper, we call upon researchers with

expertise in statistical and mathematical modeling to

communicate their work to experts in ethics and tech-

nology, whose work combines the fields of science and

technology studies, ethics and public policy. Integration

of work from these disciplines could lead to a better un-

derstanding of both the interconnected relationships be-

tween technology, society, and the forces that change

those relationships over time.

3. Modeling the Evolution of Religion-Based

Websites

While Equation (1) can be used to construct a temporal

“snap shot” of the phenomenon of religion-based website

usage, the casual mechanisms for change i.e. how this

phenomena manifests itself in over relatively long peri-

ods of time, can only be addressed with appropriate

mathematical and statistical models. In order to accom-

plish this would require future development of models

that can be used to predict mechanisms that shape the

short-term and long-term temporal dynamics of inter-

net-based religion.

There are many documented examples of cultural

change in situations where, rather than one dominant

cultural variant giving way to another over time, there

are many different choices available at all times [9]. This

pattern is analog ous to the pattern of gene tic drift through

random copying described by population genetics, and is

referred to as the neutral model [11] because the variants

are considered neutral with respect to the success of the

individual. The process of random genetic drift, which is

characterized by the long-tail power-law distribution de-

proportion of a cultural “type” as a function of the num-

ber of cultural variants in that population. The skewness

of the distribution indicates that the process of random

copying dominates temporal change in the diversity of

variants over time [9]. Deviation of cultural change from

the long-tail distribution may indicate selection for spe-

cific variants over time [5,6,12,13].

Within the context of this paper,

scribed by Equation (1), relates temporal change in the

Equation (1) de-

ility

creasing values of time (t1, ···, t3) show

4. Methods and Conclusion

ty of the hypotheses

content specific to the promotion of that religion. To

ribes a property that characterizes “neutral” evolution

of religion-based websites in the United States popula-

tion. Hence, the power-law equation predicts that there

are many uncommon religion-based websites and a very

few popular religion-based websites th at are thousands of

times more popular than the majority (long-tail of the

distribution). While information generated by the shape

of the powerlaw distribution is useful in describing short-

term trends in the popularity of religion-based websites

on the internet, it does not tell us how these short-term

patterns manifest themselves of longer time periods.

Under our proposed hypothesis, increased visib

er time of non-mainstream and fringe religion-based

websites to individual internet users could facilitate an

increase in the proportion of web hits (out all hits for all

religion-based websites) that the religion-based websites

receives, resulting in a cultural shift in internet-based re-

ligion. We propose that such a shift could result in a re-

distribution of religion-based websites on the internet,

with less popular religion-based websites becoming as

popular as mainstream websites over time (Figure 2).

Therefore, we make the claim that future mathematical

and statistical model(s) that are developed to address this

hypothesis must assume that the mechanism leading to

increases over time in the popularity of websites that

promote non-mainstream and fringe religion is selection,

not genetic dri f t .

In Figure 2, in

anges in the popularity of fringe religious websites i.e.

the area under the curve increases over time. While pop u-

lar websites remain popular over time, selection begins to

act on fringe websites, increasing their popularity over

time. For ever increasing time, selection should act to

continue to increase the popularity of fringe websites,

which may result in a cultural shift, where fringe web-

sites begin to become as popular as mainstream web-

sites.

In order to strengthen the testabili

outlined in this paper requires that future research focus

on religion-based websites whose sole purpose is to

promote their religious ideology. Therefore, data used in

future research should be based explicitly on religion-

based websites that are well organized and provide

M. R. GOLINSKI, C. PETERSEN 427

010 2030405060 708090100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P (V)

Figure 2. Prediction of a model if selection drives temporal change in the proportion P(V) of web hits (out all hits for all re-

ligion-based websites) that a religion-based website rece ives over time as a function of the number of eligion-based websites

in order of decreasing popularity (V). Increased visibility of unpopular religion-based w ebsites (non-mainstream and fringe)

umber of web hits that religion-based websites received er time. Based on the distribution of

College of Liberal Arts and Sciences.

Arizona State University) for his insight.

Johnson, “World

Christian Encyclopedia: A Comparative Survey of Churc hes

and Religions lume 1: The Wor ld

by Countries: inistries,” Oxford

to individual internet users could result in a cultural shift in internet-based religion over time (t1, ···, t3). As time increases

from t1 to t3, selection acts to increase the proportion of web hits initially unpopular religion-based websites receive. In the

figure, t1 is approximately 0.20, t2 is approximately 0.40, and t3 is approximately 0.70.

quantify increased visibility o f religion-based web sites in

the United States requires that these studies measure the time to show the number of web hits that religion-based

websites receive ov

over an extended period of time, and use this as a proxy

for quantifying popularity. With this information, future

research should focus on constructing a probability dis-

tribution that describes the relationship between the ob-

served proportions of web hits (out all hits for all

religion-based websites) that a religion-based website

receives over time as a function of the number of rel ig io n-

based websites in order of decreasing popularity. For

example, in order to quantify differences in the popu larit y

of different religion-based websites, future studies could

measure the proportion of web hits that each website

receives over a specified period of time (e.g. one year,

two years, etc.). If the proportion of web hits that a

website receives over time ranges from 20% to 100%, it

will be classified as a mainstream religion-based website,

if the proportion is less than 20% but greater th an 10%, it

will be classified as non-mainstream, and if the pro-

portion is less than 10% it be classified as fringe. If our

hypothesis is correct, the distribution will follow the

power-law distribution described by Equation (1). Pre-

sently, several statistical software packages exist for

analyzing the number of hits that websites receive over

time, including Flow AnalyticsTM and SolarwindsTM net-

work flow analyzer. These types of software packages

and others can be used to capture and analyze data in real

the number of web hits that religion-based websites

receive over time, future studies should construct mathe-

matical models to p red ict if neutral or selective forces are

more likely to drive the redistribution of religion-based

websites over time, and how this redistribution could

shape the demographics of religion among technology-

based societies.

5. Acknowledgements

The author’s would like to thank Dr. Jameson Wetmore

(Assistant Professor, School of Human Evolution and

Social Change,

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