Unveiling the species-rank abundance distribution by generalizing the Good-Turing sample coverage theory

Area of Science:

• Ecology
• Biodiversity Science
• Statistical Ecology

Background:

• Estimating species relative abundance distributions (RADs) is crucial for understanding community structure.
• Conventional "plug-in" estimators using sample relative abundance (Pi) are biased due to incomplete biodiversity samples.
• Bias in Pi increases with species rarity, limiting accurate RAD estimation.

Purpose of the Study:

• To develop a novel statistical framework for estimating the complete species-rank abundance distribution (RAD).
• To address the challenge of characterizing true relative abundances in entire assemblages from incomplete samples.
• To improve the accuracy of biodiversity and community structure analyses.

Main Methods:

• Proposed a new estimator for the complete RAD using sample coverage concepts.
• Developed a method to adjust sample relative abundances (Pi) for detected species to reduce positive bias.
• Estimated relative abundances for undetected species using a lower bound on their numbers.
• Combined adjusted and estimated RADs for detected and undetected species, respectively.

Main Results:

• Demonstrated that Pi is a positively biased estimator of true relative abundance (pi), with bias increasing for rarer species.
• The proposed adjustment method effectively reduces bias in RAD estimation.
• Simulation results show the novel RAD curve accurately reflects the true RAD, outperforming the empirical RAD.
• The method was extended to incidence data and illustrated with forest spider and soil ciliate datasets.

Conclusions:

• The novel RAD estimator provides a more accurate representation of biodiversity and community structure.
• This framework offers a nonparametric resolution to estimating complete RADs from incomplete samples.
• The method is applicable to various diversity measures and broadly useful in ecological research.