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Minimal mutation trees, and almost minimal trees, are constructed from two data sets, one of phenylalanine tRNA sequences, and the other of 5S RNA sequences, from a diverse range of organisms. The two sets of results are mutually consistent. Trees representing previous evolutionary hypotheses are compared using a total weighted mutational distance criterion. The importance of sequence data from relatively little-studed phylogenetic lines is stressed. A procedure is illustrated which circumvents the computational difficulty of evaluating the astronomically large number of possible trees, without resorting to suboptimal methods.

Branching rules for the second lowest dimensional representation of the exceptional simple Lie algebra of type E8 are given with repsect to all its 14 maximal semisimple subalgebras. This representation of E8 is of dimension 3875, the maximal subalgebras are of types A8, D8, A1-A7, A1-E7, A2-E6, A3-D5, A4-A4, A1-A2-A5, G2-F4, A1-A2, C2, and three nonconjugate subalgebras all of type A1. The Clebsch–Gordan series, necessary for decomposition of the direct product of three representations of dimension 248, are given.

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