Dtjytyk

Beside it (maximum parsimony) being compuationally cheap what other good arguments are there for it? Is there any model behind this principle ? Why would one expect this principle to provide right phylogeny in any situation at all ?

I'd say maximum parsimony approaches assume genetic similarity is unlikely to occur by convergence, but likely a result of divergence. If this assumptions holds, finding the tree configuration that minimizes the number of unlikely events makes sense.

The principle of parsimony states that the simplest explanation consistent with a data set should be chosen over more complex explanations... (Stewart 1993)

Sometimes independent events in different lineages cause similarities in molecular sequences (or morphology or behavior or whatever characteristics one happens to be studying). These events are not true evidence of recently shared ancestry, but it is easy to mistake them as such evidence.

The principle of parsimony asserts that we will be better off assuming the simplest case--that is, that identical characters are evidence of recent shared ancestry, since the simple explanation should be true more frequently than alternative explanations. There are cases for which the maximum parsimony model works very well, and there are cases for which maximum likelihood, distance matrix, Bayesian, or other models perform better.

Stewart CB (1993) The powers and pitfalls of parsimony. Nature 361, 603-607, doi:10.1038/361603a0.

Parsimony was a nice idea and developed the algorithms and tree methods towards its successors, maximum likelihood and Bayesian. The fundamental assumption of mutational independence at each alignment position was founded via parsimony. Just the recursion algorithm involved in reading a tree isn't trivial coding. Also Walter Fitch (Fitch Marigold method) was a nice guy.

Weighted parsimony has performed well in simulation studies to prevent 'long branch attraction' artefacts. The key issue that was never resolved was how to objectively weight an MP analysis. It could be resurrected however, because machine learning ML could independently provide the weights in specific contexts. That a lot of "coulds" though.