It may not even be acyclic. For example it appears fetal DNA is permanently detectable in mothers and may even have health benefits that conceivably increase the mother’s evolutionary fitness.
Yup. Genetic recombination means some genotypes are the result of crossover of two parents. Horizontal gene transfer has a similar implication. This means the true structure is a directed hypergraph.
How can it be acyclic? A phylogenetic tree is a DAG. Organisms sharing DNA? That's definitely a cyclic graph.
If there were Schema.org/Animal and/or schema:AnimalInstance classes, what do you list under a :breed property to indicate that e.g. one parent is breed X and another is breed Y?! That's definitely not a DAG; that looks like a feature clustering dendrogram.
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.
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.
And who even knows how many different times high level intelligence has evolved. I think octopi, birds, and mammals are all good examples of separate intelligence tracks with similar results.
I believe Darwin envisioned that, and the Tree of Evolution was just an introductory notion (I never read his book) before going into subtler reasons for new traits.