A versatile curve-fit model for linear to deeply concave rank abundance curves

A new, flexible curve-fit model for linear to concave rank abundance curves was conceptualized and validated using observational data. The model links the geometric-series model and log-series model and can also fit deeply concave rank abundance curves. The model is based - in an unconventional way - on the negative-binomial distribution and calculates (like the log-series model) a species-diversity index. The index is defined as the expected number of singleton species (species present with one individual) in an infinitely large sample. The new model could satisfy the need for more flexible curve-fit models with which differences and changes in the shape of the rank abundance curve can be more accurately investigated. The common rank abundance curve-fit models are lacking that flexibility.