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The existence of global nonnegative martingale solutions to a cross-diffusionsystem of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven.The model describes the segregation dynamics of populations with an arbitrarynumber of species. The diffusion matrix is generally neither symmetric norpositive semidefinite, which excludes standard methods. Instead, the existenceproof is based on the entropy structure of the model, approximated by aWong-Zakai argument, and on suitable higher moment estimates and fractionaltime regularity. In the case without self-diffusion, the lack of regularity isovercome by carefully exploiting the entropy production terms.

Global martingale solutions for a stochastic Shigesada-Kawasaki-Teramoto population model