Selective Breeding Analysed as a Communication Channel: Channel Capacity as a Fundamental Limit on Adaptive Complexity

Abstract-Selective breeding is considered as a communication channel, in a novel way. The Shannon informational capacity of this channel is an upper limit on the amount of information that can be put into the genome by selection: this is a meaningful upper limit to the adaptive complexity of evolved organisms. We calculate the maximum adaptive complexity achievable for a given mutation rate for simple models of sexual and asexual reproduction. A new and surprising result is that, with sexual reproduction, the greatest adaptive complexity can be achieved with very long genomes, so long that genetic drift ensures that individual genetic elements are only weakly determined. Put another way, with sexual reproduction, the greatest adaptive complexity can in principle be obtained with genetic architectures that are, in a sense, error correcting codes. For asexual reproduction, for a given mutation rate, the achievable adaptive complexity is much less than for sexual reproduction, and depends only weakly on genome length. A possible implication of this result for genetic algorithms is that the greatest adaptive complexity is in principle achievable when genomes are so long that mutation prevents the population coming close to convergence.