The Connection between Adaptability and Dynamics

Abstract

I originally wrote down symbols such as ω̂ to express the dynamics of biological systems notationally. But the analysis has been in terms of the statistical quantity, H(ω̂). Now it is necessary to investigate the connection between these two objects. One important question is, what is the connection between the predictability of biological systems and the global structure of adaptability? I employ the answer to establish a correspondence between components of adaptability and the various notions of stability and instability used in dynamical descriptions of biological systems. This correspondence provides a natural interpretation of the functional significance of stability and instability in terms of the adaptability theory framework. An important implication is that the evolutionary tendency to economize adaptability implies a corresponding economics of stability and instability. A deep question is, does the structure of ω̂ along with the actual history of the environment impose evolutionary tendencies on H(ω̂) or do evolutionary tendencies of H(ω̂) impose structure on ω̂?