The fractal dimension of group selection

The concept of a fractal dimension is simple. A straight line or curved line (circle) has dimension 1. A surface or area has the dimension 2. In real life lines are rarely straight but often rugged and crumpled. A crumpled line like the coastline of Britain has a fractal dimension between 1 and 2, of about 1.21. It can be measured by the box-counting method. Basically this box-counting method measures the degree of “crumpleness”: how much the object we measure covers a different, higher dimension. In our one dimensional case of the coastline this means if the object is slightly crumpled and resembles a curved line then the dimension approaches 1. If the object is strongly crumpled and fills nearly a whole area like a space-filling curve then the dimension approaches 2.

We can apply this concept of a fractal dimension to evolutionary systems, because there is more than one inheritance system in evolution. Jablonka et al. [1] identify different dimensions of heredity and evolution: the genetic dimension, the epigenetic dimension, the behavioral dimension and the symbolic dimension. All of these would be different inheritance systems and contain different forms of inheritable informations. The epigenetic dimension is reset for new generations though, and the symbolic dimension can only be found in humans. Most anthropologists like William Durham [2] or  Peter J. Richerson and Robert Boyd [3] are in favor of gene – culture coevolution or Dual Inheritance Theory (DIT). For a start, let us assume we have between 1 and 2 dimensions.

To measure how many different evolutionary systems we have we need to count the number of “genetic codes” that produce recipes for organisms. The genetic code in turn contains recipes to create genetic organisms. And if we try to count the fractal dimension for a complex evolutionary system which exhibts high phenotypic plasticity, it turns out that group selection has a fractal dimension close to 2, about 1.875. This means that group selection is actually an approximation of a new evolutionary system in an old one. For kin selection we arrive at a lower dimension of 1.25.

– normal biological evolution (fractal dimension of 1)

• biological genes in encoded, inheritable form

– kin selection (fractal dimension of 1+2/8=1.25)

• recipes for recognizing kinship
• recipes for specific tribal attributes: slogans

– group selection among primitive tribes (fractal dimension 1+4/8=1.5)

• recipes for recognizing and creating ethnic markers
• recipes for tools like a new snare or weapon

– group selection among ethnic groups (fractal dimension 1+7/8=1.875)

• recipes for altruistic behavior
• recipes for conserving trust
• new replicators in spoken form

– dual-level evolution (fractal dimension 1+8/8=2)

• cultural genes in encoded, inheritable form

The system we have today is high dimensional where the number of different evolutionary systems is much larger than 2. We have religious organizations, political parties, economic companies that exist in many multiple subsystems and economic sectors like primary, secondary and tertiary, media, nonprofit sector, etc). At best we can describe it as a multi-dimensional evolutionary system with a high number of dimensions.

( The picture for the fractal dimension of the coast of britain is from Wikipedia user Prokofiev )

[1] Eva Jablonka, Marion J. Lamb, Anna Zeligowski, Evolution in Four Dimensions: Genetic, Epigenetic, Behavioral, and Symbolic Variation in the History of Life, MIT Press, 2006

[2] William H. Durham, Coevolution: Genes, Culture, and Human Diversity, Stanford University Press, 1991

[3] Peter J. Richerson and Robert Boyd, Not By Genes Alone: How Culture Transformed Human Evolution, University of Chicago Press, 2005