Two dimensional sequence alignment shows that replication slippage may generate a significant proportion of all transversion substitutions.

Homologous sequences diverge in length via insertions and deletions (indels). Consequently, evolutionary genetic analyses routinely use methods to produce gapped alignment (GA). In GA, artificial null characters (gaps) are inserted into sequences so that nucleotide characters may be placed into homological correspondence within an alignment column. However, this approach sacrifices the homological correspondence of nucleotides diverging via tandem repeats (TRs). To address this deficit, we generalize GA with micro-paralogical gapped alignment (MPGA). While GA operates under a strict two-state homology model of one-to-one and one-to-none (i.e. one-to-gap) relationships, MPGA adds one-to-many, many-to-many, and many-to-none relationships. This expanded, multi-state homology model is motivated by DNA replication slippage (RS). RS produces short tandem repeats, constituting interrelated micro-paralogous sequences. Together, RS and TR-associated instability have a synergistic effect in the production of indels, which generate the need for gap insertions. MPGA reduces the computational cost of determining optimal gap insertions by reducing the number of gaps required by two-dimensional (2D) representations of sequence. A 2D representation of one sequence is achieved when tandem repeats are contracted into the same columns (dimension one) by occupying multiple rows (dimension two), an internal micro-paralogical dimension. To demonstrate the benefits and challenges of 2D representation, we develop a program called LINEUP and identify a pervasive fractal dimension in evolving sequences. We then demonstrate how LINEUP-generated 2D representations provide improved measures of substitution rates and transition-to-transversion ratios. Altogether, these results showcase significant new perspectives on basic mutational and evolutionary processes when multi-state homology models are adopted.