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HEARING DISTANT ECHOES: USING EXTREMAL STATISTICS TO PROBE EVOLUTIONARY ORIGINS 95 or where in the first case there are three identities, two substitutions, and one insertion/deletion (indel) and in the second case there are two identities, three substitutions, and one indel. An alignment can be obtained by inserting gaps ("â") into the sequences so that and Here the subsequence of all is identical to A1A2. . . An. Then, since the *-sequences have equal length, is aligned with . In Chapter 3, algorithms to achieve optimal alignments are discussed. Here we are interested in the statistical distribution of these scores, not in how they are obtained. Global alignments refer to the situation where all the letters of each sequence must be accounted for in the alignments. There are two types of global alignments, alignments where the pairing is given and alignments where the pairing is not given. Alignment Given In this section, we assume the alignment is given with the sequences: A1A2. . . An B1B2. . . Bn (Gaps "â" have been added so that these sequences both have the same lengthâL in the previous section, n hereâand the stars have been omitted to simplify the notation.) In this case the alignment is given and
