Cladism is all about branching: structures like evolutionary history, the folders on your computer, and family trees have properties in common that can be measured in interesting ways.
One advantage to evolution is that it has restrictions on the branching. Fruit trees can be grafted and I won't even go into the complexities that can develop in some family trees! Bacteria–and even more complex species that have not been isolated so long that they can no longer breed–can complicated things if you are trying to measure relatedness or inheritance. BUT there are no jackelopes, not even batmen.
Compare natural evolution to cultural evolution and this difference is obvious. In culture we have an abundance of batmen! Branches combine and recombine, in a flagrant promiscuity that puts rhizomes and spores and algae to shame. Nonetheless there is a long history of efforts to determine inheritance. We care where things originated. Just think of your English teacher reminding you that Shakespeare said it first or your friend insisting "that wasn't Rod Stewart but Tom Waits' song" and you counter "that wasn't Tom Waits but a Louisiana funeral march" and another "that wasn't a Louisiana funeral march but an 18th C French folktale..."
For this reason its hard to know what cultural evolution even means. Dawkins' coined the word memes to refer to reproducible cultural units, on the analogy to genes, but because of the aforementioned restrictions that obtain in natural evolution, its a pretty sloppy concept. Lets take another cultural example. (I may get this wrong at one point but) the word Buxom originally came from a Scottish word for wheat, and was already a metaphor in its common usage. To say you were buxom, was to say that you bent easily, like wheat in the wind, to moral temptation. The word was frequently applied to women deemed loose in their morals. With time it became more associated with these women than the wheat of the metaphor, and eventually settled on the anatomy these allegedly loose women were famous for...What a rate of mutation!
So: in order to think about cultural evolution I think it is useful to go back to one of the historical questions about evolution: Use and Disuse. Charles Darwin did not completely dismiss this "Lamarckian" factor in a few of his works, and it was the backbone of his grandfather Erasmus Darwin's earlier evolutionary theory.
How would species branch differently if they evolved by passing on to their offspring the traits (muscles, minds, etc.) that were developed by use and disuse during their lifetime?
Here are some links to sites which attempt to map evolving systems, both natural and cultural (and perhaps some in between) Have a look if you see this before I come to class tonight (Wednesday 18 at 8:00):