Spontaneous symmetry breaking in directed percolation with many colors: Differentiation of species in the Gribov process

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well-known exponents of Reggeon field theory. In addition, this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.