  Binary trees are fundamental objects in models of evolutionary biology and
population genetics. Here, we discuss some of their combinatorial and
structural properties as they depend on the tree class considered. Furthermore,
the process by which trees are generated determines the probability
distribution in tree space. Yule trees, for instance, are generated by a pure
birth process. When considered as unordered, they have neither a closed-form
enumeration nor a simple probability distribution. But their ordered siblings
have both. They present the object of choice when studying tree structure in
the framework of evolving genealogies.
