  A quantitative theory on the construction and the evolution of the genetic
code is proposed. Through introducing the concept of mutational deterioration
(MD) and developing a theoretical formalism on MD minimization we have proved:
1, the redundancy distribution of codons in the genetic code obeys MD
minimization principle; 2, the hydrophilic-hydrophobic distribution of amino
acids on the code table is global MD (GMD) minimal; 3, the standard genetic
code can be deduced from the adaptive minimization of GMD; 4, the variants of
the standard genetic code can be explained quantitatively by use of GMD
formalism and the general trend of the evolution is GMD non-increasing which
reflects the selection on the code. We have demonstrated that the redundancy
distribution of codons and the hydrophobic-hydrophilic (H-P) distribution of
amino acids are robust in the code relative to the mutational parameter, and
indicated that the GMD can be looked as a non-fitness function on the adaptive
landscape. Finally, an important aspect on the symmetry of the code
construction, the Yin-Yang duality is investigated. The Yin-Yang duality among
codons affords a sound basis for understanding the H-P structure in the genetic
code.
