Convergence and parallelism: is a new life ahead of old concepts?

In comparative biology, character observations initially separate similar and dissimilar characters. Only similar characters are considered for phylogeny reconstruction; their homology is attested in a two-step process, firstly a priori of phylogeny reconstruction by accurate similarity statements, and secondly a posteriori of phylogeny analysis by congruence with other characters. Any pattern of non-homology is then a homoplasy, commonly, but vaguely, associated with "convergence". In this logical scheme, there is no way to analyze characters which look similar, but cannot meet usual criteria for homology statements, i.e., false similarity detected a priori of phylogenetic analysis, even though such characters may represent evolutionarily significant patterns of character transformations. Because phylogenies are not only patterns of taxa relationships but also references for evolutionary studies, we propose to redefine the traditional concepts of parallelism and convergence to associate patterns of non-homology with explicit theoretical contexts: homoplasy is restricted to non-similarity detected a posteriori of phylogeny analysis and related to parallelism; non-similarity detected a priori of phylogenetic analysis and necessarily described by different characters would then correspond to a convergence event s. str. We propose to characterize these characters as heterologous (heterology). Heterology and homoplasy correspond to different non-similarity patterns and processes; they are also associated with different patterns of taxa relationships: homoplasy can occur only in non-sister group taxa; no such limit exists for heterology. The usefulness of these terms and concepts is illustrated with patterns of acoustic evolution in ensiferan insects.