Spherical tropicalization and Berkovich analytification

Let X be a spherical variety. We show that Tevelev and Vogiannou's tropicalization map from X to its tropicalization factors through the Berkovich analytification X-an, as in the case for toric varieties. Furthermore we show that the tropicalization is a strong deformation retraction of X-an. We also give a strong deformation retraction of Thuillier's analytification X-? onto a subspace described using the colored fan of X.