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@array = sort { 0.5 <=> rand } @array;

#!/usr/bin/perl

...
    my $rx_every_second = join '|', grep $k ++ % 2 == 0, @{ $ref_array
+ };
    s/\b(?:$rx_every_second)\b/./g for @{ $ref_distribution };
    }

1)
A A A . . . C C C . . . E E E E E . . . . . G G G G G . . . . . I I I 
+I I I I I I I
...
A A A A . . . . C C C C . . . . . E E E E . . . . . G G G G . . . . . 
+I I I I
A A A A . . . . . C C C C . . . . . E E E E . . . . G G G G G . . . . 
+I I I I
A A A A . . . . . C C C C . . . . E E E E . . . . . G G G G G . . . . 
+. I I I I