Evolution and analysis of model CPGs for walking: II. General principles and individual variability.
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.
Beer
R D
RD
Department of Computer Engineering and Science, Case Western Reserve University, Cleveland, OH 44106, USA. beer@alpha.ces.cwru.edu
Chiel
H J
HJ
Gallagher
J C
JC
D000465:Algorithms; D000818:Animals; D001522:Behavior, Animal / Q000502:physiology; D001696:Biomechanical Phenomena; D005684:Gait / Q000502:physiology*; D007395:Interneurons / Q000502:physiology*; D008124:Locomotion / Q000502:physiology; D008959:Models, Neurological; D009046:Motor Neurons / Q000502:physiology*; D016571:Neural Networks, Computer; D013569:Synapses / Q000502:physiology; D013997:Time Factors