Predicting species richness in tropical lichenized fungi with ‘modular’ combinations of character states
A numerical approach is presented to predict the number of potentially undiscovered species in groups of species that exhibit a ‘modular’ combination of character states, that is, nearly ‘free’ combination that is not random but allows for a wide range of cross-combination of character states. The method uses a character correlation index (CCI) based on observed versus expected frequencies of pairwise character state combinations in known species of a group to estimate the degree of potentially positive and negative evolutionary constraints in the co-occurrence of character states. For instance, if a character state combination, such as ‘muriform ascospores’ and ‘presence of norstictic acid’, occurs less frequently than expected by chance, it indicates the presence of a negative evolutionary constraint. If no such constraint is detected, but a particular character combination has not yet been observed in a described species, it can be predicted that yet undescribed species will exhibit that combination. The method can therefore be used to detect ‘gaps’ in the taxonomic record, i.e. character combinations that have not been detected in known species but are likely to occur in undiscovered species. Modular combination of character states appears to be particularly common in Fungi, including lichens, and the method was here used to predict species richness in the lichen genus Graphis, specifically the Graphisscripta group. A total of 42 species is known in this group and, out of a total of 240 possible character state combinations, a further 48 were found likely to represent undiscovered species, suggesting that the real species number in this group is close to 90 or about twice the number now known. This agrees well with previous estimates for undiscovered diversity of tropical lichen species and for the first time gives a taxonomic prediction of how such ‘missing’ species are expected to look like.