  We study the Ricci flow of the four-parameter family of Sp(n+1)-invariant
metrics on spheres. We determine their forward behaviour and also classify
ancient solutions. In doing so, we exhibit a new one-parameter family of
ancient solutions on spheres. These (non-isometric) ancient solutions all have
a larger isometry group, namely Sp(n+1)Sp(1), Sp(n+1)U(1), or U(2n+2). Two
ancient solutions are non-collapsed and converge, under the backwards flow, to
Jensen's second Einstein metric. One solution parametrizes the well known
Berger metrics. The rest are new and collapse, under a rescaling of the
backwards flow, to Ziller's second homogeneous Einstein metric on complex
projective space.
