The problem of the directionality of genome evolution is studied from the information-theoretic view. We propose that the function-coding information quantity of a genome always grows in the course of evolution through sequence duplication, expansion of code, and gene transfer between genomes. The function-coding information quantity of a genome consists of two parts, p-coding information quantity which encodes functional protein and n-coding information quantity which encodes other functional elements except amino acid sequence. The relation of the proposed law to the thermodynamic laws is indicated. The evolutionary trends of DNA sequences revealed by bioinformatics are investigated which afford further evidences on the evolutionary law. It is argued that the directionality of genome evolution comes from species competition adaptive to environment. An expression on the evolutionary rate of genome is proposed that the rate is a function of Darwin temperature (describing species competition) and fitness slope (describing adaptive landscape). Finally, the problem of directly experimental test on the evolutionary directionality is discussed briefly.
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