  We investigate the problem of the predominance and survival of "weak" species
in the context of the simplest generalization of the spatial stochastic
rock-paper-scissors model to four species by considering models in which one,
two, or three species have a reduced predation probability. We show, using
lattice based spatial stochastic simulations with random initial conditions,
that if only one of the four species has its probability reduced then the most
abundant species is the prey of the "weakest" (assuming that the simulations
are large enough for coexistence to prevail). Also, among the remaining cases,
we present examples in which "weak" and "strong" species have similar average
abundances and others in which either of them dominates -- the most abundant
species being always a prey of a "weak" species with which it maintains a
unidirectional predator-prey interaction. However, in contrast to the
three-species model, we find no systematic difference in the global performance
of "weak" and "strong" species, and we conjecture that the same result will
hold if the number of species is further increased. We also determine the
probability of single species survival and coexistence as a function of the
lattice size, discussing its dependence on initial conditions and on the change
to the dynamics of the model which results from the extinction of one of the
species.
