Where Methods Disagree

NOTE: in the following, in almost all datasets, base compositions are identical and there are no transversions - as such the Jukes Cantor model is the only appropriate model

The first eight characters are all autapomorphies in the cladistic sense

one   AGGACTTC
two   GAAGTCCT
three GGAATTCC
four  GGAATTCC

parsimony prefers no tree
ML prefers no tree
one   AGGACTTC C
two   GAAGTCCT T
three GGAATTCC C
four  GGAATTCC T

parsimony prefers tree II
ML prefers tree II 
one   AGGACTTC A
two   GAAGTCCT A
three GGAATTCC G
four  GGAATTCC G

parsimony prefers tree III
ML prefers no tree (or tree II if F81)
one   AGGACTTC A C
two   GAAGTCCT A T
three GGAATTCC G C
four  GGAATTCC G T

parsimony prefers trees II and III
ML prefers tree II 
one   AGGACTTC AT CA
two   GAAGTCCT AT TG
three GGAATTCC GC CG
four  GGAATTCC GC TA

parsimony prefers tree III
ML prefers trees I and II


Here, transversions are possible, but everyone is different at all sites
one   ACGT
two   CGTA
three GTAC
four  TACG
parsimony prefers no tree
ML (K2P estimating ti:tv) prefers tree II


Here, there are unequal base compositions but all characters 
are autapomorphic or constant 

one   AGAGAGAGGGGGGGGGAAAAAAAAAAAA
two   GAGAGAGAGGGGGGGGAAAAAAAAAAAA
three TTTTTTTTGGGGGGGGAAAAAAAAAAAA
four  CCCCCCCCGGGGGGGGAAAAAAAAAAAA
parsimony prefers no tree
ML (F81 estimating base comps) prefers tree II