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
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-
C
opyright © 2012 SciRes. OJS

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

1
010 2030 4050 60 708090 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
V
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-
sc
ility
ov
creasing values of time (t1, ···, t3) show
ch
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
V
P (V)
t
3
t
2
t
1
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
on
r
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
n
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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