In this paper, the authors are interested in the problem of lossless compression of unlabeled semiordered
trees. Semi-ordered trees are a class of trees that present an order between some sibling
while some other siblings are unordered. They offer a wide possibility of applications especially
for the representation of plants architecture. The authors show that these trees present remarkable
compression properties covering those of ordered and unordered trees. To illustrate this approach,
the authors apply these notions to a particular class of semi-ordered trees, which is the most studied
branching structure particularly for a botanical motivation, namely axial trees.