Dale's necessary and sufficient conditions for an array to contain the joint moments for some probability distribution on the unit simplex in ℝ2 are extended to the unit simplex in ℝd. These conditions are then used in a computational method, based on linear programming, to evaluate the stationary distribution for the diffusion approximation of the Wright–Fisher model in population genetics. The computational method uses a characterization of the diffusion through an adjoint relation between the diffusion operator and its stationary distribution. Application of this adjoint relation to a set of functions in the domain of the generator leads to one set of constraints for the linear program involving the moments of the stationary distribution. The extension of Dale's conditions on the moments adds another set of linear conditions and the linear program is solved to obtain bounds on numerical quantities of interest. Numerical illustrations are given to illustrate the accuracy of the method.
