  In this article we obtain a skew-product decomposition of a Brownian motion
on an ellipsoid of dimension $n$ in a Euclidean space of dimension $n+1$. We
only consider such ellipsoid whose restriction to first $n$ dimensions is a
sphere and its last coordinate depends on a variable parameter. We prove that
the projection of this Brownian motion on to the last coordinate is, after a
suitable transformation, a Wright-Fisher diffusion process with atypical
selection coefficient.
