  For a function $f : V(G ) \rightarrow \{0, 1, 2\}$ we denote by $V_i$ the set
of vertices to which the value $i$ is assigned by $f$, i.e. $V_i = \{ x \in V
(G ) : f(x ) = i \}$. If a function $f: V(G) \rightarrow \{0,1,2\}$ satisfying
the condition that $V_i$ is independent for $i \in \{1,2\}$ and every vertex
$u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v)
= i$ for each $i \in \{1,2\}$, then $f$ is called a 2-rainbow independent
dominating function (2RiDF). The weight $w(f)$ of a 2RiDF $f$ is the value
$w(f) = |V_1|+|V_2|$. The minimum weight of a 2RiDF on a graph $G$ is called
the \emph{2-rainbow independent domination number} of $G$. A graph $G$ is
2-rainbow independent domination stable if the 2-rainbow independent domination
number of $G$ remains unchanged under removal of any vertex. In this paper, we
characterize 2-rainbow independent domination stable trees and we study the
effect of edge removal on 2-rainbow independent domination number in trees.
