  In this letter, we investigate the population dynamics in a May-Leonard
formulation of the rock-paper-scissors game in which one or two species, which
we shall refer to as "weak", have a reduced predation or reproduction
probability. We show that in a nonspatial model the stationary solution where
all three species coexist is always unstable, while in a spatial stochastic
model coexistence is possible for a wide parameter space. We find, that a
reduced predation probability results in a significantly higher abundance of
"weak" species, in models with either one or two "weak" species, as long as the
simulation lattices are sufficiently large for coexistence to prevail. On the
other hand, we show that a reduced reproduction probability has a smaller
impact on the abundance of "weak" species, generally leading to a slight
decrease of its population size -- the increase of the population size of one
of the "weak" species being more than compensated by the reduction of the
other, in the two species case. We further show that the species abundances in
models where both predation and reproduction probabilities are simultaneously
reduced may be accurately estimated from the results obtained considering only
a reduction of either the predation or the reproduction probability.
