  The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a
hypersphere is transformed into the diffusion for the Wright-Fisher model with
a particular mutation rate. We use the Ito calculus considering stochastic
differential equations. The expansion gives a simple interpretation of the
Griffiths eigenfunction expansion for the Wright-Fisher model. Our
representation is useful to simulate the Wright-Fisher model as well as
Brownian motion on a hypersphere.
