Evolution and Analysis of Model CPGs for Walking: II. General Principles and Individual Variability Beer Chiel Gallagher 1999

This paper does an analysis of the legs, using some work from the companion paper on dynamical modules.  This paper gets into degeneracy and its conceptual utility in this context.  he frames the issues of characterizing general principles of pattern generation in terms of degeneracies.

Important:
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Actually, I was about to retype the abstract, Ill just cut and paste it (i guess thats a good abstract, the end in particular):
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Abstract: Are there general principles for pattern generation? We examined this question by analyzing the operation of large populations of evolved model central pattern generators (CPGs) for walking. Three populations of model CPGs were evolved, containing three, four, or five neurons. We identified six general principles. First, locomotion performance increased with the number of interneurons. Second, the top 10 three-, four-, and five-neuron CPGs could be decomposed into dynamical modules, an abstract description developed in a companion article. Third, these dynamical modules were multistable: they could be switched between multiple stable output configurations. Fourth, the rhythmic pattern generated by a CPG could be understood as a closed chain of successive destabilizations of one dynamical module by another. A combinatorial analysis enumerated the possible dynamical modular structures. Fifth, one-dimensional modules were frequently observed and, in some cases, could be assigned specific functional roles. Finally, dynamic dynamical modules, in which the modular structure itself changed over one cycle, were frequently observed. The existence of these general principles despite significant variability in both patterns of connectivity and neural parameters was explained by degeneracy in the maps from neural parameters to neural dynamics to behavior to fitness. An analysis of the biomechanical properties of the model body was essential for relating neural activity to behavior. Our studies of evolved model circuits suggest that, in the absence of other constraints, there is no compelling reason to expect neural circuits to be functionally decomposable as the number of interneurons increase. Analyzing idealized model pattern generators may be an effective methodology for gaining insights into the operation of biological pattern generators.
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Paper starts off with a big list showing the variability of pattern generators in nature.

it describes the model and the network and the evolution.  I read it while brain storming an outline and figuring out major problems with my research proposal to the lab.  lots of notes on the paper about what i was first thinking.

The argument for GAs to biologists:
"While genetic algorithms are obviously highly simplified compared to biological evolution, they do capture the two key features of Darwinian evolution-namely, heritable variation and differential reproduction (natural selection)."

"The biomechanical properties of the body give rise to a ''biomechanical degeneracy'' because different motor patterns can give tise to the same motion."
"Notice that the leg can be moded in many different ways and still generate the same average velopcity, leading to a ''fitness degeneracy'' in the performance evaluation"

"A dynamical module is a colection of one or more neruons that makes a transition between one quasistable output confiuration and anaother while the outputs of the remaining neruons are effectiely constant"

I think most of the most interesting stuff in this article is in the analysis of the 5 celled legs, which I skipped.

===Discussion:===
Good words:"
Interestingly, it was only be examinging these model CPGs at a fairly high level of abstraction that we were able to identify any general principles; at lower levels of abstraction one observes only remendous variability.  By a general principle, we main a recurring pattern that can be observed at a particular spatiotemporal scale with an accompanying quantitative theoretical framework that has both explanatory and prdictive power."
Than he lists six general principles for the operation of evolved model pattern generators.
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"For general patterns to exist at one level despite variability at a lower level, there must be some ''degeneracy'' in the relationship between the levels. By degeneracy, we mean that multiple confiucrations of the lower level can give rise to equivalent funcation at the upper level."