Modeling for peace with Peter Turchin

May 2012


Nineteenth-century philosopher Herbert Spencer (1820-1903) was the first to discuss in detail the simultaneous existence of two levels, individual and group, in the development of human societies, and to define a role for Lamarckism—a word usually reserved to describe the heritability of acquired characteristics in biological organisms—in the human social evolution process. Thus an idea came to flourish that one equation, if slightly altered, could yield information regarding the effects of gene transmission and natural selection on the proportion of genes within each new generation of a population as well as it could yield information regarding conditions on the cultural variations and selective pressures that promote (for instance) the evolution of larger-scale human societies. Such an equation is George R. Price's (1922-1975), a covariance equation which provides a mathematical description of evolution and natural selection within various theoretical multilevel selection models. In his Principles of Biology (1864), Herbert Spencer formally introduced the survival of the fittest concept. One could have guessed that this underpinning would some day spin a bloody tale.

A recent mathematics colloquium speaker at Washington University in St. Louis, ecologist and mathematician Peter Turchin from the University of Connecticut applies multilevel selection theory in his study of the evolution of complex societies.  The Peter Turchin model under discussion [1], a creative jump that brings together factors as diverse as altruism, warfare, religion, geographical terrain, hierarchical networks, and the technological advances that influenced emerging human empires between 1500 BCE and 1500 CE at the boundary of the Eurasian steppe, indicates that the largest pre-industrial, territorial states should arise in regions where culturally diverse people are in contact and where warfare is particularly intense. "We started at a very abstract level," Turchin says of his model, "multilevel selection theory that explains not only evolution of social complexity, but also other major evolutionary transitions. The theory was made more concrete by focusing on cultural variation and warfare as the chief selection force."

Turchin sees large-scale sociality and large-scale warfare as being intimately connected. "Warfare is not in our genes, and evolutionary history is not destiny. However, current attempts to find other bases for cooperation at the scale of the whole humanity have, so far, proved inadequate," Turchin writes. "What are the social forces that held together, across history, huge societies that control millions of square kilometers and populations of ten or higher, in the hundred million people?" he asks us. Can general principles be identified? "What causes just states and cohesive societies?"  he asked his 2008 Candles in the Dark conference audience [2].  What can stop wars? Shift video camera to one pondering, concerned listener:  I too want to know.

In Turchin's version of the Price equation [1], units and entities are social groups at different levels of hierarchical complexity. In order for a society to grow in size, it has to make repeated transitions from i-th to (i + 1)-th level. The success of each transition depends on the balance of forces favoring integration versus those favoring fission. Cultural practices promoting unity at the i + 1 level will spread if:

PriceTurchin .

Like an organism, a society appears to be most successful when its activities are carried out with maximum productivity at the group level, which comes at a price for each individual, including patriotic bloodshed. Humans constantly have to work around issues of self-interest that would otherwise impede the emergence of social constructs. However, "prosocial behavior increases the fitness of the [human] group—its probability of surviving, growing, and perhaps reproducing," and this "increased group fitness comes at the expense of individual altruists having lower fitness than non-altruists," Peter Turchin states.

Although Turchin applies Price's equation to cultural rather than genetic traits, the broad implications of the equation are unchanged. Evolution of traits promoting integration at the i + 1 (metacommunity) level is favored (1) by increasing cultural variation among metacommunities and decreasing variation among communities and (2) by increasing the effect of the trait on the fitness of metacommunities, and reducing the effect at the community level.

The next step is to identify conditions under which the ratio on the left-hand side of the equation increases, while the ratio on the right-hand side declines, and testing. "Ideally, we would like to measure directly the relevant quantities, but the historical record, unfortunately, is not detailed enough to enable us to do so," Turchin admits. "The alternative approach is to rely on proxies, which requires making assumptions about which observable variables are best correlated with the quantities of theoretical interest (cultural variation and selection coefficients)." Here Turchin invokes philosopher of mathematics Imre Lakatos (1922-1974) and then goes on to construct the protective belt of auxiliary hypotheses that will make an empirical test of the model possible.

"Finding proxies for cultural variation and warfare intensity makes the theory more concrete and testable," Peter Turchin concludes with regard to the model. "However, should the empirical tests fail, we would not immediately know whether the reason for failure was an incorrect theoretical core or faulty assumptions involved in constructing auxiliary hypotheses. This is a normal situation in science, and should not inhibit us from proceeding with this research program."

From the slides displayed at the colloquium, it was apparent that calculations based on Peter Turchin's model did yield results consistent with empirical observations that large empires preferentially arose on the culturally diverse and bloody steppes frontier.  As for my part, I was left hoping that future generations may discover a more peaceful story about a superorganism we might call humans.

Read more about Peter Turchin and the new field of cliodynamics»
Discuss this story: Visit Peter Turchin's blog»
Read-up on efforts towards peaceful nation building at The Evolution Institute site»

—Math news, stories, videos, and interviews by Marie Taris,»

Enjoyed this story? See also April 2012 News story  Lopata Lamps Challenge meets Bob Bosch»

[1] Turchin, P., 2011, Warfare and the Evolution of Social Complexity: A Multilevel-Selection Approach.
[2] 2008 Candles in the Dark conference video.