Jason Cawley
Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Posts: 712 
Nature paper  Evolutionary Dynamics on Graphs
There is an excellent article in the most recent Nature (Jan. 20) by a team including Martin Nowak, entitled "evolutionary dynamics on graphs". Truly useful work, fun, very clear, with broad areas of application. Many easily stated, useful theorems (including e.g. that invasion stability for general games on arbitary directed graphs is an NP hard problem; examples of graphs that amplify or suppress selection, etc).
The team is Erez Lieberman, Christoph Hauert, and Martin A. Nowak.
(For Nowak's homepage and some of his other articles, see http://www.ped.fas.harvard.edu/nowak.htm )
The abstract reads 
Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scalefree networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequencydependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multicellular organization and economics.
A link to the full PDF for those with Nature subscriptions can be found here 
http://www.nature.com/cgitaf/dynap...ex.html#letters
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