  Winner-take-all phenomena are observed in various competitive systems. We
find similar phenomena in replicator models with randomly fluctuating growth
rates. The disparity between winners and losers increases indefinitely, even if
all elements are statistically equivalent. A lognormal distribution describes
well the nonstationary time evolution. If a nonlinear load corresponding to
progressive taxation is introduced, a stationary distribution is obtained and
disparity widening is suppressed.
