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To study problems in community ecology I have been investigating mathematical models of species interactions which take the form of nonlinear multidimensional Markov processes in continuous space. The basic questions concern species coexistence, which means finding conditions under which no species density converges to zero with time. The particular mathematical techniques are invasion analysis and quadratic approximations of the model. The particular ecological problem studied is the effect of a common enemy (so-called apparent competition) on the coexistence of species that compete for common resources. Biodiversity and coexistence are well studied by many ecologists over the past century; however, this is the first study which consider both resource and apparent competition in a stochastic model.