December 23, 2008

Evolution as an Inverse Problem, Part I

A few years back, I was at a conference (SwarmFest '04, if you must know) at which I heard Marco Dorigo (from the Swarm Intelligence community) characterize the collective behavior of social insects (nest building in this case) as an "inverse problem". For those of you unfamiliar, inverse problems are complex problems where the data is well-known, but the model parameters are not.

Definition of an Inverse Problem (Wolfram Mathworld)

Take the construction of Dorigo's anthill problem as an example. We can easily observe the actions of each ant and the interactions between them. This can even be extrapolated to a description of the anthill structure. However, this description is not generalizable to all instances of anthill. The reason for this is that because the structure is emergent, an anthill of a particular morphology can be had using any number of equally-suitable sequences of interactions. In other words, there are many different equally-suitable ways to produce to the observed structure. If we were to attempt a reconstruction of the anthill without our a priori observations, we would fail: for this reason, inverse problems such as these are called ill-posed problems. Other behaviors (such as arm movements) have also been called ill-posed problems.

Why is this relevant to the post?

If the obvious parallels to evolution weren't obvious with the word "reconstruction", consider the following: there are many possible ways
to get to a coherent anthill, just as there are many ways to get to a fit phenotype. A form of convergent evolution called neutral networks, where selection is not extreme and many genotypes are fit enough to provide an adaptive solution, comes to mind here.

Definition of Neutral Networks

In addition, the concept (if not the analytical techniques) of inverse problems could be useful for a better understanding of parameters such as transcriptional regulation, gene action, selection, and even fitness. This is especially important for understanding how these parameters assemble a complex phenotype from a genotype.

In the next installment, I will consider the basic combinatorics of anthills and gene action, and how thismight produce emergent structures with and without "selection".

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