Short-time evolution in the adaptive immune system

We exploit a simple model to numerically and analytically investigate the effect of enforcing a time constraint for achieving a system-wide goal during an evolutionary dynamics. This situation is relevant to finding antibody specificities in the adaptive immune response as well as to artificial situations in which an evolutionary dynamics is used to generate a desired capability in a limited number of generations. When the likelihood of finding the target phenotype is low, we find that the optimal mutation rate can exceed the error threshold, in contrast to conventional evolutionary dynamics. We also show how a logarithmic correction to the usual inverse scaling of population size with mutation rate arises. Implications for natural and artificial evolutionary situations are discussed.