I am searching various sources about phylogenetics. I saw some materials about perfect phylogeny and also phylogenies acquired from maximum parsimony constraint. They seem very similar to me. Are they the same?
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No. A perfect phylogeny is one such that all characters evolve on the tree with no homoplasy, i.e. for a binary character, changes occur once from 0 -> 1 but never from 1 -> 0. Maximum parsimony inference may produce a perfect phylogeny, but typically for real datasets some degree of homoplasy is required to explain character patterns.
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Long discussion that took many years to resolve.
MP doesn't account for back mutation, which is a HUGE problem for nucleotide data because in theory 1:4 mutations is a back mutation. Maximum likelihood has resumed is crown here, however Beast deployment of a Bayesian calculation is also very widely, particularly for molecular dating. ML uses a reversible matrix A <-> T, whilst Beast uses a directional matrix A->T and will score T->A separately.
Happy to discuss the approaches and modern interpretations at length.
The model which accounts for back-mutation is the Jukes-Cantor correction (JC correction), this is a basic model present in every phylogenetic algorithm except p-distances). Essentially JC extrapolates back-calculation for the true number of mutations against the observed number of mutations against divergence time. However, when the P-distance (uncorrected observed distance) exceeds 0.75 for nucleotides the model is not viable. Basically, nucleotide divergence >0.75 is saturated and the phylogenetic information is essentially random.
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$\begingroup$ Imo a general comment about phylogenetic methods is not particularly helpful for the distinction between most MP trees and one that mathematically fits the description of a perfect phylogeny. But to which models are you referring to for ML and BEAST? AFAIK they have consistent sets of CTMC models. $\endgroup$– NatWHCommented Feb 4, 2019 at 14:31