  The competition graph of a doubly partial order is known to be an interval
graph. The competition-common enemy graph of a doubly partial order is also
known to be an interval graph unless it contains a cycle of length 4 as an
induced subgraph. In this paper, we show that the niche graph of a doubly
partial order is not necessarily an interval graph. In fact, we prove that, for
each integer n at least 4, there exists a doubly partial order whose niche
graph contains an induced subgraph isomorphic to a cycle of length n. We also
show that if the niche graph of a doubly partial order is triangle-free, then
it is an interval graph.
