  In order to make a case for or against a trend in the evolution of complexity
in biological evolution, complexity needs to be both rigorously defined and
measurable. A recent information-theoretic (but intuitively evident) definition
identifies genomic complexity with the amount of information a sequence stores
about its environment. We investigate the evolution of genomic complexity in
populations of digital organisms and monitor in detail the evolutionary
transitions that increase complexity. We show that because natural selection
forces genomes to behave as a natural ``Maxwell Demon'', within a fixed
environment genomic complexity is forced to increase.
