Revisiting the Evolution of Religious Forms Using the Dow-Eff Network
Autocorrelation Approach to the Comparative Method
Wesley W. Roberts
Abstract : Sanderson and Roberts (2008) advanced the quantitative, comparative study of religious by generating a new dependent variable and discovering new variables influencing the evolution of religion forms. This research is updated here using the Dow-
Eff network autocorrelation approach. Stage of religious evolution predictors from the usual SCCS variables include Writing and Records (v149), no hunting (v204), and wet climate (bio.8), supporting Sanderson and Roberts. Interactive variables SuperjhWriting and AnimXbwealth are added from the (White, et al. 2011) model and are significant predictors, emphasizing along with population pressure the role of natural and humancaused scarcities. This adds a new wrinkle to the Sanderson and Roberts research, though the original model gets very high grades.
Introduction
Recent research by Sanderson and Roberts (2008) did much to expand the crosscultural, quantitative study of the evolution of religious complexity. In particular, the research created a new dependent variable, Stage of Religious Evolution (SER) as an alternative to the standard High Gods (HG) variable originally devised by Swanson
(1960), more fully coded by Murdock (1967), and fully coded by Snarey (1996) for the
SCCS. Using SER, Sanderson and Roberts tested a number of hypotheses that attempt to explain the evolution of religious complexity from a cross-cultural perspective. The results led to new conclusions about variables impacting religious evolution, including a new finding, the influence of the variable Writing and Records.
Stage of Religious Evolution
Sanderson and Roberts’s dependent variable SER was inspired by the work of
Anthony Wallace (1966). Using data on Standard Cross Cultural Sample (SCCS) societies, the authors operationalized Wallace’s four-stage evolutionary typology of religious evolution: (1) Shamanic, (2) Communal, (3) Olympian, and (4) Monotheistic.
Sanderson and Roberts proposed that this dependent variable is superior to Swanson’s
HG variable—which operationalized high gods as (1) absent or unreported; (2) present but not active in human affairs; (3) present and active in human affairs but not concerned with human morality; and (4) present, active in human affairs, and concerned with human morality—because SER takes into account religious practice and practitioners as well as belief, and it focuses on a long-term evolutionary trajectory, which was never the intention of Swanson. The authors tested several hypotheses of religious evolution comparing HG and SER side-by-side.
Hypotheses Tested and Methods
Prior to Sanderson and Roberts several major works sought to quantitatively test the relationship between social structure and religious complexity using cross-cultural data. Swanson’s (1960) research developed the dependent variable HG and tested the

relationship between it and “sovereign groups,” or, essentially, societal complexity, and found a correlation between high gods and the number of sovereign groups composing a society. Davis (1971) was concerned with technological evolution and religious evolution, and found a correlation between level of technological development and the presence of high gods concerned with human morality. Economic development was the focus of Underhill (1975), who found a relationship between advanced economic complexity and Monotheism (a variable generated using Swanson’s HG). Relatedly,
Irons (1991) tested for and found a correlation between economic stratification and moral high gods. Finally, Roes and Raymond (2003) tested Richard Alexander’s (1987) societal size hypothesis and found a relationship between moral high gods and societal size.
Sanderson and Roberts retested each of these hypotheses using the dependent variables HG and SER, and seven major independent variables: Sovereign Groups;
Writing and Records; Technological Specialization; Subsistence Economy; Stage of
Political Evolution; Class Stratification; and Societal Size. Binary logistic regression (for
HG) and ordered logistic regression (for SER) were performed. Cross-tabulations were created as descriptive supplements.
Results
In the HG test, Sanderson and Roberts found that Swanson’s sovereign groups hypothesis received the most support of all the hypotheses, though weakly. Writing and
Records, too, was also significant in one regression analysis using HG.
SER provided much stronger results, and demonstrated the most support for the
Davis, Underhill, Irons, and Alexander hypotheses. Interestingly, Writing and Records emerged in this analysis as the strongest predictor of a society’s stage of religious evolution. Sanderson and Roberts interpret these results by explaining that religious complexity is generated and sustained by social complexity, in terms of a society’s technological and economic development, and also it’s population size. Complex and specialized priesthoods representative of polytheistic or monotheistic religions can only emerge when a society is economically complex enough to sustain them. The ability to write and keep records goes hand-in-hand with this new class, as the newly formed religious elite uses it to generate and promote religious beliefs, often to their economic and political benefit.
New Method: Dow-Eff Network Autocorrelation
A long-running concern with cross-cultural research like that described above is
Galton’s Problem, which suggests that cultural diffusion makes cross-cultural data unreliable because of the assumption of shared traits between two geographically or historically close cultures. This is otherwise known as autocorrelation, which may include spatial and other factors such as common language. Recently, Dow (2007) suggested a network autocorrelation model as a way to incorporate Galton’s Problem into cross-cultural analyses. In this model “the autocorrelated dependent variable is included as an endogenous predictor variable” (Dow and Eff, 2013:218). This method was employed here to reanalyze the influence of specific independent variables on the dependent variable SRE.

Data
Table 1 highlights the variables used in the network autocorrelation model.
Stage of Religious Evolution, or EvoGod, is included as the dependent variable. The bulk of independent variables are from the SCCS. SuperjhWriting, FxCmtyWages, and
AnimXbwealth are compound variables (White et al. 2011). SuperjhWriting includes
Superjurisdictional compounded with Writing and Records, and it measures the extent to which there is a potential for dynamically unstable exchange between government collecting taxes and citizens paying taxes.
FxCmtyWages measures the potential for income inequality in agricultural societies, and AnimXbwealth measures the potential for inequalities in herd sizes among pastoral societies that engage in bridewealth. These two variables are representative of moments of economic trouble that lead to moral crises requiring the intervention of a moral god (Alexander 1987, cited in White et al. 2011). Along with SuperjhWriting, they are also representative of population pressure, especially as it affects resources, in increasingly complex societies.
Table 1: Descriptive statistics of variables used as predictors of religious complexity
Variable Description Nobs Mean Min Max SD
EvoGod bio.1 bio.5 bio.6 bio.8 bio.10 bio.11 bio.15
Stage of religious evolution 168 2.333 1 4 1.013
Annual mean Temp 186 182.92 -129 292 98.153
Max temp of warmest month 186 297.93 95 433 64.859
Min temp of coldest month 186 69.261 -414 251.172 146.97
Mean temp of wettest quarter 186 199.76 -86 30 84.24
Mean temp of warmest quarter 186 231.8 41 335 335
Mean temp of coldest quarter 186 130.44 -362 276.172 142.75
Precipitation seasonality 186 60.499 0 161 33.449 bio.2 v2125 v204
Mean diurnal range
Importance of wage labor
186 109.07 43 182 31.17
156 1.974 1 3 0.908 inside the community or outside
Dependence on hunting 186 1.554 0 9 1.73
SuperjhWriting SuperjhWriting
FxCmtyWages FxCmtyWages
AnimXbwealth AnimXbwealth
No_rain_Dry No_rain_Dry
V149 Writing and Records
184 3.114 1 10 2.755
186 0.07 0 1 0.256
186
186
186
0.973 0 9 1.993
1.801 1 4 1.018
2.349 1 5 1.467
Notes : Variables of the form v# are given the name of their SCCS number. Sources: GIS data from Hijmans, et al. (2005), SuperjhWriting, FxCmtyWages, and AnimXbwealth from White et al. (2011).
Results
Table 2 reports the results of a 2SLS estimation of the network autocorrelation effects regression model. The top panel reports standardized regression coefficients and p-values for an unrestricted model including 12 SCCS variables and the compound variables AnimXbwealth, FxCmtyWages, and SuperjhWriting. Four coefficients are statistically significant at <.01 or <.05 including the network lag term Wy (.286),

AnimXbwealth (.136), v149 Writing and Records (.288 and the strongest predictor of the significant variables) and v204 Dependence on Hunting (-.145, and the expected sign).
Table 2:Comparison of network autocorrelation regression model
Variable Description Std coef p-value VIF
Unrestricted model standardized coefficients
Wy Network lag term
AnimXbwealth AnimXbwealth bio.1 bio.10
0.13637
Annual mean Temp
0.28624
0.69729
3.00E-05***
0.01608**
0.61345
Mean temp of warmest quarter -0.14715 0.83852
2.3501
1.6274
966.05
264.55 bio.11 bio.15 bio.2 bio.5 bio.6
Mean temp of coldest quarter -1.46682
Precipitation seasonality
Mean diurnal range
Max temp of warmest month
Min temp of coldest month
-0.01056
.02172
-0.12297
0.96192
0.29709
0.86734
0.22298
0.78307
0.2667
1003.8
2.0247
15.306
101.26
280.71 bio.8 v149 v204
FxCmtyWages FxCmtyWages
No_rain_Dry No_rain_Dry
SuperjhWriting SuperjhWriting v2125
R 2 = .704
Mean temp of wettest quarter
Writing and records
0.15121
0.01721
-0.08977
0.25445
0.28868
Dependence on hunting -0.14525
Importance of wage labor -0.01062
inside the community or outside
0.19703
0.7186
6.9726
1.1576
0.21525
0.3003
2.6636
30.588
0.00164 *** 4.2482
0.01462** 1.7931
0.83752 1.3542
Restricted model standardized coefficients
Diagnostics Null hypothesis
Std coef
Wy Network lag term
AnimXbwealth AnimXbwealth bio.8 Mean temp of wettest quarter
SuperjhWriting SuperjhWriting
0.25163
0.1179
0.12781
0.26779 v149 Writing and records v204 Dependence on Hunting
0.30652
-0.14801
R
2
= .696 p-value VIF
1.00E-05*** 1.6933
0.01214 ** 1.172
0.00658 *** 1.1734
0.00085*** 3.3773
0.00022*** 3.6192
0.00404*** 1.4038
F-stat df p-value
RESET
Wald test
H
0
: model has correct functional form
H
0
: appropriate variables dropped
Breusch-Pagan H
0
: residuals homoscedastic
Shapiro-Wilkes H
0
: residuals normal
0.4971 3775565 0.4808
0.0014 3.704E+09 0.9698
0.8379 3064137 0.3600
5.5675 92909 0.0183**
Hausman H
0:
Wy exogenous 0.1909 15093700 0.6622
Sargan Test H
0
: residuals uncorrelated with instruments 0.3126 9532912 0.5761
Notes : Dependent variable is EvoGod. “***” p-value <0.01, “**” p-value <0.05, “*” pvalue <0.10. N’s range from 156 to 186.
The middle panel of Table 2 reports the results of the final model. All coefficients are significant and of the expected sign. The standardized coefficients of SuperjhWriting
(.267) and v149 Writing and Records (.306) are by far the strongest predictors of a society’s stage of religious evolution, and are both significant at the <0.01 level. The
Network lag term Wy (.251), bio.8 Mean Temp. of Wettest Quarter (.127), and v204

Dependence on Hunting (-.148) are also significant at <0.01. Compound variable
AnimXbwealth (.117) is significant at <0.05.
All diagnostic tests report that the model is sound and robust.
Discussion
The 2SLS model results reported above demonstrate further support for
Sanderson and Roberts’s (2008) original research discussed in the Introduction. In particular, it shows the reverse influence that a dependence on hunting has on religious complexity, suggesting support for Sanderson and Roberts’s findings and assertion of the relationship between advanced subsistence methods and complex religions. Most interestingly, the influence of the development of writing and records is reestablished in this model with strong support for v149 Writing and Records, and also the compound variable SuperjhWriting. Taking SuperjhWriting into account with the new compound variable AnimXbwealth, the results from this updated methodology add an additional twist to the evolution of religion. Specifically, it suggests that the emergence of an established priesthood, complex religious practices, and belief in a single god—all elements of the SRE variable’s Monotheism—is related to “recurrent periods of propertybased inequality generated by certain forms of exchange in agricultural and pastoral societies that create a need for prosocial ethics” (White, et al 2011).
Figure 1 . This map shows 168 SCCS societies coded for the Stage of Religious
Evolution variable. Large circles represent Monotheistic religions, with subsequent smaller circles representing Olympian, Communal, and Shamanic religions, respectively. High autocorrelation regions are noted with a connecting line.

Support of Network lag term Wy suggests an influence of spatial diffusion on the evolution of religious complexity (Figure 1), which is not surprising in light of history’s demonstration of the spread of monotheism via conquest and missionization. White et al.
(2011, p.14) found a similar influence on the spread of moral gods, but otherwise found no missionization influence on “other significant variables and their Premissionization effects.” In light of the influence of spatial diffusion, it is important to consider White et al.’s (p. 2) recommendation of following Alexander’s (1987) admonishment that researchers “consider effects of different periods of evolutionary time, as for example, the independent invention of moral gods in earlier periods versus increasing cultural diffusion in later periods.” In the case of this paper the primary concern is finding variables that correlate with the evolutionary leap to monotheism in the earlier periods of evolutionary time. We believe the findings posited here are suggestive of independent leaps, and that the influence of spatial diffusion likely occurs most in later periods of evolutionary time, when monotheistic religions make the leap to fully established salvation religions, a complex narrative that must follow in later work.
The findings that suggest a relationship between the level of complexity between a society and its religious beliefs are useful if not fairly intuitive. Given a basic understanding of history, it is no surprise that polytheistic and, eventually, monotheistic religious practitioners, practices, and beliefs emerged in pastoral and agricultural societies. The emergence of the variable Writing and Records is no big surprise, either, if one considers that the practitioners of several of the first major monotheistic religions,
Judaism and Christianity, are often referred to as “the people of the book” by those of the
Muslim faith, referring to the fact that those religions stored their sacred beliefs and practices with the written word rather than orally, some of the first to do so in a comprehensive way.
However, one way we might interpret the emergence of Writing and Records as a strong variable along with SuperjhWriting and AnimXbwealth is that these variables represent a tipping point for the establishment of more advanced forms of religious belief.
This is an idea borrowed from the eminent sociologist Max Weber (1922[1991]), who was concerned with the “process of breakthrough,” the point at which a belief or practice is developed by an individual (often a “prophet”) and it is made part of the culture of the community. It is, indeed, the point at which a society makes a clean break with one evolutionary stage and emerges into another. In the context of this paper’s findings, it could be that the crises generated by property-based inequality also generate preferences for new religious forms involving a single, moralistic god, and, especially, the priesthoods and practices that go along with that god.
As for Writing and Records, Sanderson and Roberts suggest that newly formed priesthoods monopolize the control of writing and records, at first out of economic necessity, but later as a means of political and religious control, and as a means to spread their beliefs. This interpretation can remain within the current research, though it’s clear that this variable is entangled within the comparative study of religion in complicated ways that will need some more working out. It’s possible that writing is indicative of the complex societal structures that cause property-based inequality crises and thence the establishment of new religious forms. From there, newly established priesthoods gain their own control over writing and records, and use it as a means to establish their religions further. Robert Bellah’s (2011) suggestion that advanced religions emerge from

a kind of “mythospeculation” is supportive of the idea that the advent of writing and record keeping allows for deeper reflection about one’s religious ideas, hence deeper thinking and writing about religious practice, and increased religious complexity overall.
The idea, too, that writing and records is a means of transmission for religious ideas for the sake of the ideas is a Weberian notion that cannot be ignored. This is not contrary to a materialist evolutionary perspective if we consider it in the context of behavior that might influence individual—or perhaps group—inclusive fitness. This is especially relevant since the Stage of Religious Evolution variable focuses as much on religious practitioners as it does religious belief.
Further Research
At the time of writing a new network autocorrelation model is in development that improves on some of the results above. Specifically, it focuses on agriculture rather than absence of hunting; eliminates temperature variables; takes into account population size and external warfare; and removes v149 Writing and Records in favor of compound variable SuperjhWriting. A report on the results of that improved model will be forthcoming, but for now it is safe to say that improvement in the model does not change the fundamental quality of the model discussed here.
Aside from improved modeling of this research, the complex story being developed in the statistics needs to be unraveled further with more theoretical depth and understanding of the descriptive history of the emergence of polytheistic and monotheistic religions.
References
Alexander, Richard D. 1987. The Biology of Moral Systems, Aldine de Gruyter,
Hawthorn, N.Y.
Bellah, Robert. 2011. Religion in Human Evolution: From the Paleolithic to the Axial
Age. Belknap Press.
Davis, William. 1971. Societal Complexity and the Nature of Primitive Man’s
Conception of the Supernatural. Ph.D. dissertation, Department of Sociology, University of North Carolina at Chapel Hill.
Dow, Malcolm. M. 2007. Galton’s Problem as Multiple Network Autocorrelation Effects.
Cross-Cultural Research 41:336-363.
Dow Malcolm M. and E. Anthon Eff. 2013. When One Wife is Enough: A Cross-Cultural
Study of the Determinants of Monogamy. Journal of Social, Evolutionary, and Cultural
Psychology 7(3):211-238.
Hijmans, Robert J., Susan. E. Cameron, Juan. L. Parra, Peter G. Jones, and Andy Jarvis.
(2005). Very High Resolution Interpolated Climate Surfaces for Global Land Areas.
International Journal of Climatology 25:1965-1978.

Irons, William. How did Morality Evolve? Zygon 26:49-89.
Murdock, George P. 1967a/b. Ethnographic Atlas. Pittsburgh: University of Pittsburgh
Press.
Roes, Frans L. and Michel Raymond. 2003. Belief in Moralizing Gods. Evolution and
Human Behavior 24:126-135.
Sanderson, Stephen K. and Wesley W. Roberts. 2008. The Evolutionary Forms of the
Religious Life. American Anthropologist 110 (4):454-466.
Snarey, John R. 1996. The Natural Environment's Impact Upon Religious Ethics: A
Cross-Cultural Study. Journal for the Scientific Study of Religion 35(2):85-96.
Swanson, Guy. 1960. The birth of the Gods: The Origin of Primitive Beliefs. Ann Arbor:
University of Michigan Press.
Underhill, Ralph. 1975. Economic and Political Antecedents of Monotheism: A Cross-
Cultural Study. American Journal of Sociology 80:841-861.
Wallace, Anthony F. C. 1966. Religion: An Anthropological View. New York: Random
House.
Weber, Max. 1922[1991]. The Sociology of Religion. Ephraim Fischoff, trans. Boston:
Beacon Press.
White, Douglas R., B. Tolga Oztan, Giorgio Gosti, Elliott Wagner, and John Snarey.
2011. Discovery of Hidden Variables for the Evolution of Ethical Religions. (Submitted to Scientific American 2012, not accepted).