[sixstringtheory]

My assumption as someone not formally trained in advanced biology is that the phylogenetic tree has an implied arrow of time, and each node of the tree is a point where a mutation occurred that was sufficient to create a new and separate family/order/genus/etc afterwards, with leaf nodes representing species.

In this sense a cycle can’t occur because a branch would need to reach back in time and rejoin with an ancestral branch. It would be a different kind of grandfather paradox: who would be the ancestor and who the descendant in a cycle?

Maybe someone could help point out the flaws in this model.

[flobosg]

Your assumption is true, but only for rooted phylogenetic trees. In unrooted trees the node representing the most ancestral state is absent and thus no directionality can be determined.