Inequality and Heterogeneity Strike Again

September 30, 2010

One of the important characteristics of mathematical sociology is that it can allow us to make predictions about how the world should work without a lot of detailed substantive knowledge. Obviously, this advantage seems like a handicap to some scholars, but I think otherwise and a recent study suggests that I may be correct. I refer, of course, to a recent survey conducted by the Pew Research Center that has been getting a lot of attention. It finds that Atheists and Agnostics have more religious knowledge than any other group in the U.S.:

Atheists and agnostics, Jews and Mormons are among the highest-scoring groups on a new survey of religious knowledge, outperforming evangelical Protestants, mainline Protestants and Catholics on questions about the core teachings, history and leading figures of major world religions.

On average, Americans correctly answer 16 of the 32 religious knowledge questions on the survey by the Pew Research Center’s Forum on Religion & Public Life. Atheists and agnostics average 20.9 correct answers. Jews and Mormons do about as well, averaging 20.5 and 20.3 correct answers, respectively.

Protestants as a whole average 16 correct answers; Catholics as a whole, 14.7. Atheists and agnostics, Jews and Mormons perform better than other groups on the survey even after controlling for differing levels of education.

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Positive and Negative Networks: Lessons from Ecology?

September 8, 2010

Let me pose a puzzle.  Mathematical sociologists like puzzles!

Jordi Bascompte recently published an article in Science (vol. 329, 13 August, 2010, p. 765-6) titled “Structure and Dynamics of Ecological Networks.”  The piece is in the “Perspectives” section — which are commentaries and explanations of the “real” articles (which are often a bit too discipline-specific to be accessible to the average reader).  Basecompte’s article is an explanation and appreciation of the piece by Elisa Thebault and Colin Fontaine (also vol. 329, 13 August 2020 p. 853-6) titled “Stability of Ecological Communities and the Architecture of Mutualistic and Trophic Networks.”

A thanks to Peter Burke of the SPYRL social psych lab, and Department of Sociology at UCR for passing these along to me. 

A very common use of graphs and networks in ecology is as a representation of web of relations among species.  A “food web” for example, is composed of nodes (species) and directed relations (e.g. “eats”) as in Bear -> Salmon.

The food web is an “antagonistic” relation:  one species feeds on the other (occasionally, such relations are reciprocated).  The relation results in a “gain” for one node and a “loss” for the other.

Ecologists also focus on “mutualistic” relations where two species interact, but both benefit.  Bees and flowers, for example are mutualistic — bees pollinate flowers, flowers provide food for bees.  These kinds of networks can be thought of as undirected (though maybe they would better be regarded as multiplex and directed).  Generally, mutualistic ecological relations form bi-partite networks.

Bear with me just a moment more…

The interesting results in the Science article are that networks of “antagonistic” relations in ecology tend to have a characteristic form of largely separated and rather densely connected clusters – something akin to “communities”.  Mutualistic networks, on the other hand have a characteristic form composed of “generalists” (nodes with high degree) and “specialists” (nodes with low degree) of the species in each mode, in a nested “hierarchy”.

Networks of individual humans, groups, roles, organizations, or populations often have “antagonistic” relations — “A” dominates “B”.  But, human networks are also connected by mutually beneficial ties (e.g. emotional support and identity confirmation).

In sociology, we tend to think of “antagonistic” networks as, perhaps, having an equilibrium tendency toward hierarchy.  “Mutualistic” human relations, we tend to see as likely to be organized as communities — often largely separated from one another.

Are these patterns of findings really contradictory?  They would seem to suggest that structures of inter-species networks follow rather different rules than the structures that emerge in relations among heterogeneous human agents (individuals, groups, organizations, communities, societies).