  We study the simple evolutionary process in which we repeatedly find the
least fit agent in a population of agents and give it a new fitness which is
chosen independently at random from a specified distribution. We show that many
of the average properties of this process can be calculated exactly using
analytic methods. In particular we find the distribution of fitnesses at
arbitrary time, and the distribution of the lengths of runs of hits on the same
agent, the latter being found to follow a power law with exponent -1, similar
to the distribution of times between evolutionary events in the Bak-Sneppen
model and models based on the so-called record dynamics. We confirm our
analytic results with extensive numerical simulations.
