Nonparametric lower bounds for species richness and shared species richness under sampling without replacement

Area of Science:

• Ecology
• Biodiversity Science
• Statistical Ecology

Background:

• Traditional species richness estimators assume sampling with replacement, leading to overestimation with high sampling fractions.
• These conventional methods fail to converge to true species richness as sampling fraction approaches one.
• Sampling without replacement is common in ecological surveys, necessitating more robust estimation techniques.

Purpose of the Study:

• To develop nonparametric lower bounds for species richness in single and multiple communities.
• To address limitations of existing estimators in scenarios with sampling without replacement and high sampling fractions.
• To provide universally valid estimators for diverse species abundance distributions and detection probabilities.

Main Methods:

• Proposed nonparametric lower bounds based on abundance data and replicated incidence data.
• Derived bounds under general sampling models, accommodating heterogeneous detectability and spatial aggregation.
• Validated estimators using real-world datasets and subsamples from large surveys.

Main Results:

• The proposed lower bounds accurately estimate species richness, converging to true values as sampling fraction approaches one.
• Demonstrated universal validity across various species abundance patterns and detection probabilities.
• Showcased reliable performance compared to previous estimators, particularly in high-sampling fraction scenarios.

Conclusions:

• Developed robust, universally applicable nonparametric lower bounds for species richness estimation.
• The new methods overcome limitations of traditional estimators in sampling without replacement scenarios.
• These bounds offer improved accuracy for biodiversity assessments in ecological research.