The definition, recognition, and interpretation of convergent evolution, and two new measures for quantifying and assessing the significance of convergence

Convergent evolution is an important phenomenon in the history of life. Despite this, there is no common definition of convergence used by biologists. Instead, several conceptually different definitions are employed. The primary dichotomy is between pattern-based definitions, where independently evolved similarity is sufficient for convergence, and process-based definitions, where convergence requires a certain process to produce this similarity. The unacknowledged diversity of definitions can lead to problems in evolutionary research. Process-based definitions may bias researchers away from studying or recognizing other sources of independently evolved similarity, or lead researchers to interpret convergent patterns as necessarily caused by a given process. Thus, pattern-based definitions are recommended. Existing measures of convergence are reviewed, and two new measures are developed. Both are pattern based and conceptually minimal, quantifying nothing but independently evolved similarity. One quantifies the amount of phenotypic distance between two lineages that is closed by subsequent evolution; the other simply counts the number of lineages entering a region of phenotypic space. The behavior of these measures is explored in simulations; both show acceptable Type I and Type II error. The study of convergent evolution will be facilitated if researchers are explicit about working definitions of convergence and adopt a standard toolbox of convergence measures.