Ducks in a Row

We open the chapter with the observation that the quantity of DNA sequence data available for biologists to analyze has been growing very rapidly in the past decades. We then consider what our simulations of genetic drift tell us about how DNA sequences should change over longer periods of time. We realize that many species will have similar but not identical sequences that they have inherited from their common ancestor, and that it would be useful to line these sequences up to compare them. To do so, we first formally define the concept of homology: structures shared by organisms due to common ancestry, using examples such as skeletal structures. We then define an alignment of a pair of sequences and a set of scores that reward placing identical bases together in those alignments and that penalize mismatched bases and gaps. We ask if there is an approach that can guarantee that we have found the alignment of the highest score, developing an inductive approach for doing so. The resulting algorithm gives us the alignment of highest score and takes time proportional to the square of the length of the sequences to compute. We note that this idea of computation complexity will be useful later in the book and close with some examples of applications of sequence alignment.