  The competition graph of a doubly partial order is known to be an interval
graph. The CCE graph and the niche graph of a doubly partial order are also
known to be interval graphs if the graphs do not contain a cycle of length four
and three as an induced subgraph, respectively. Phylogeny graphs are variant of
competition graphs. The phylogeny graph $P(D)$ of a digraph $D$ is the (simple
undirected) graph defined by $V(P(D)):=V(D)$ and $E(P(D)):=\{xy \mid N^+_D(x)
\cap N^+_D(y) \neq \emptyset \} \cup \{xy \mid (x,y) \in A(D) \}$, where
$N^+_D(x):=\{v \in V(D) \mid (x,v) \in A(D)\}$.
  In this note, we show that the phylogeny graph of a doubly partial order is
an interval graph. We also show that, for any interval graph $G$, there exists
an interval graph $\tilde{G}$ such that $\tilde{G}$ contains the graph $G$ as
an induced subgraph and that $\tilde{G}$ is the phylogeny graph of a doubly
partial order.
