Three representations of a multiple sequence alignment comprised of <i>M</i> sequences and <i>L</i> positions.

<p><b>A</b>, ascii text. <b>B</b>, a three-dimensional binary array , in which if sequence <i>s</i> has amino acid <i>a</i> at position <i>i</i>, and 0 otherwise; gaps are always set to 0. In this representation, the frequencies of amino acids at individual positions are , where <i>w</i>_<i>s</i> is the weight for each sequence <i>s</i> and <i>M</i>′ = ∑_<i>s</i> <i>w</i>_<i>s</i> represents the effective number of sequences in the alignment. Joint frequencies of amino acids between pairs of positions are defined by . <b>C</b>, a two-dimensional alignment matrix <i>X</i>_<i>sn</i>, in which the index <i>s</i> (along rows) represents sequences and the index <i>n</i> (along columns) represents the combination of amino acid and position dimensions in one, such that <i>n</i> = 20(<i>i</i> − 1) + <i>a</i>. This representation is useful in explaining the relationship between patterns of coevolution between amino acids and patterns of sequence divergence in the protein family (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004817#pcbi.1004817.e086" target="_blank">Eq (12)</a>).