The present review highlights some of the very important contributions to non-alignment ways of comparing biological sequences, which may be genome sequences of nucleotides, protein sequences of amino acids, or sequences of protein secondary structures. The discussion centers around specific methods applicable to the comparison of three types of sequences. The methods of comparison of genome sequences are based on three pairs of biological groups of nucleotides; the same for protein sequences are based on either physio-chemical property values of amino acids or on classified groups of amino acids of different cardinalities obtained from the physio-chemical properties; the same for sequences of secondary structures of proteins are based on their sequential expressions of structure elements of cardinality three and four. Comparison is made in the time domain and also in the frequency domain. Different taxa of known phylogeny are considered for comparison. It tries to find out the specific method of comparison, which can show the exact phylogeny of the taxa. If a new sequence appears in the database, it becomes essential to know its phylogeny. For this purpose, a phylogenetic tree is drawn on the sequences of the known taxa together with this new sequence using the best possible method. If the species having this new sequence belongs to the old taxa, there is nothing to worry about. Otherwise, the species with the new sequence has to be studied separately. This is the general reason for the construction of a phylogenetic tree in any form of biological sequence comparison.
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