[Editor's note: this article previously appeared on Bradly's excellent blog Synthetic Daisies]
Figure 2. LEFT: Internal representations for automata in the CGS paper. RIGHT: Internal representations for automata in the LCS-paper.
In my application, some of the equations and data structures are borrowed, and some are uniquely "evolutionary". This allows me flexbility in terms of applying the model to many different kinds of evolutionary scenarios. One of these (identified in the LCS-like paper) is biogeography, particularly island biogegraphy. For the uninitiated, biogeography  is the study of population processes in a geographic context. As organisms migrate and geomorphology changes, population genetics and demography are affected in corresponding fashion.
In my LCS-inspired evolutionary model, recall that the environment consists of a generic flow field (and in CGS paper, this is already exploited as a quasi-geography). If this substrate could be replaced by a dynamic topology (e.g. a more explicit geography), the LCS-inspired model might provide insights into evolutionary "deep" time. When I say deep time, I mean a period of time long enough for uplift, continental drift, and seafloor spreading to occur and effect the distribution of populations and species.
How do we go about establishing this dynamic topology? There are a number of options here, two of which I will discuss in detail. The first is the terraforming engine used in virtual worlds such as SimCity, Spore, and Second Life . The second involves using a mathematical tool called plate motion vectors to predict tectonic drift . Figure 3 shown examples of each. While this has not been formally worked out, the basic goal is to create kinematics (underlying movements that govern environmental constraints) much as the quasi-flow regimes provide in the CGS and LCS-like models.
Once the kinematics of geomorphology have been established as an evolutionary field, the kinetics (e.g. how these movements unfold in time) must then be accounted for. A model of plate tectonics (the Burridge-Knopoff model, ) can be used to approximate tectonic activity as a series of sliding blocks that interact according to local rules. A simpler method might be to represent the buildup and release of stresses between tectonic units as a non-uniform probability density function (PDF). In any case, examples of the concept on a three-dimensional space can be seen in Figure 4.
Figure 4. Single generation examples of organisms (automata, black balls) and populations (clusters of black balls) on a dynamic topology. LEFT: Two separate landmasses, one with mountains. UPPER RIGHT: Newly-uplifted mountains and an isthmus (land bridge). LOWER RIGHT: Pre-uplifted mountains and continental drift. Simulated using pseudo-data.
What I am describing, then, is a three-level hybrid model (see Figure 5): a geomorphological model to partition and add dimensionality to the underlying substrate of evolution, a general model of particle diffusion (genetic drift), and a genomic representation that provide diversity and relatedness to the automata population. This is only a quick sketch from the Fluid Models of Evolutionary Dynamics project -- if you interested in collaborating or otherwise helping develop this model, let it be known. Other comments are also welcome.
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