Figure 1. Geometric representations of three directions that the evolution of homologous entities can follow. The x-axis represents time and the y-axis represents percentage divergence from the common ancestor, with 0% represented by the faint dotted lines. (a) The usual direction of evolution is divergent, with the descendant lineages becoming progressively more different from their common ancestor (indicated by the filled circle at the node) and from each other (indicated by the solid lines) over time. (b) Convergent evolution occurs when lineages first diverge and then subsequently regain similarity over time, as shown here between time 1 and 0. (c) Parallel evolution occurs when the descendant lineages neither lose nor gain similarity over time, but follow parallel evolutionary paths, as show here from time 2 through time 0. Both convergence and parallel evolution will slow the normal divergence of lineages, as indicated by the dashed lines in (a).

Figure 2. Geometric representation of convergent evolution of unrelated protein sequences. Two completely unrelated proteins might be expected to have between about 5% and 20% sequence identity, depending on amino acid composition, as represented at time 4. If two proteins, or other biological entities, gained significant similarity over time (as indicated by the solid lines), then they would be considered to have ‘converged’ in sequence and/or function.

Figure 3. Evolutionary mechanisms that can produce the same amino acid at a given position in the sequences of homologous proteins. (a) In the case of patristic similarities, the descendant sequences are identical due to shared common ancestry. (b) In the case of homoplastic similarities, the two descendants are identical due to independent gain of the same amino acid at the same position in the protein sequences. See text for further explanation of the different subtypes within two categories. Similar mechanistic principles apply to nucleotide sequences and organismal traits.