Biological adaptation and the mathematical theory of information (Q1122541)

The authors study the Shannon entropy in biological systems defined by a triple \(<B,E,\Omega >\) where the sets of biota probabilities, environmental state probabilities and the joint probabilities of the biota and environmental states are given by, respectively, \[ B=\{p(\beta_ i)\},\quad i=1,2,...,n,\quad E=\{p(\epsilon_ j)\},\quad j=1,2,...,m,\quad \Omega =\{p(\beta_ i,\epsilon_ j)\}. \] Using these probabilities, the Shannon measures of information H(B), H(E) and \(H(B| E=\epsilon_ j)\) are interpreted, respectively, as the measure of richness of the biota alternatives, the uncertainty of the environment and the entropy of the biota for a given state \(\epsilon_ j\) of the environment. Furthermore, I(B,E) is interpreted as the average information transmitted through an eventual channel from the biota to the environment and H(B,E) as the complexity of the joint events of the biota and its environment. Employing these concepts, various interesting results of information theory have been interpreted for biological systems. These results have also been verified numerically.