We study tree languages that can be defined in
. These are tree languages definable by a first-order formula whose quantifier prefix is
, and simultaneously by a first-order formula whose quantifier prefix is
, both formulas over the signature with the descendant relation. We provide an effective characterization of tree languages definable in
. This characterization is in terms of algebraic equations. Over words, the class of word languages definable in
forms a robust class, which was given an effective algebraic characterization by Pin and Weil .