Sample Size for Concurrent Species Detection in a Species-Rich Assemblage

TL;DR

This paper develops a multinomial-based method and tables for calculating the minimum sample size needed to detect multiple species simultaneously in stratigraphic samples, improving accuracy over traditional binomial approaches.

Contribution

It introduces a multinomial distribution approach for sample size estimation in multi-species detection, providing practical tables for various scenarios, which enhances biostratigraphic sampling accuracy.

Findings

Multinomial distribution yields larger sample sizes than binomial for multiple species detection.

300 specimens are insufficient to reliably detect more than one species at 95% confidence.

Using larger samples can revise interpretations of microfossil history and improve biostratigraphic resolution.

Abstract

Monitoring the distribution of microfossils in stratigraphic successions is an essential tool for biostratigraphic, evolutionary and paleoecologic/paleoceanographic studies. To estimate the relative abundance (%) of a given species, it is necessary to estimate in advance the minimum number of specimens to be used in the count (n). This requires an a priori assumption about a specified level of confidence, and about the species population proportion (p). It is common use to apply the binomial distribution to determine n to detect the presence of more than one species in the same sample, although the multinomial distribution should necessarily be used instead. The mathematical theory of sample size computation using the multinomial distribution is adapted to the computation of n for any number of species to be detected together (K) at any level of confidence. Easy-to-use extensive tables show n, for a combination of K and p. These tables indicate a large difference for n between that indicated by the binomial and those by the multinomial distribution when many species are to be detected simultaneously. Counting only 300 specimens (with 95 % confidence level) or 500 (99 %) is not enough to detect more than one taxon. The reconstructed history of the micro-biosphere may therefore, in many instances, need to be largely revised. This revision should affect our understanding of the ecological and evolutionary relationships between the past changes in the biosphere and the other major reservoirs (hydrosphere, geosphere and atmosphere). In biostratigraphy and biochronology, using a much larger sample size, when more than one marker species is to be detected in the neighborhood of the same biozone boundary, may help clarifying the nature of the apparent inconsistencies given by the observed reversals in the ordinal (rank) biostratigraphic data shown as intersections of the correlation lines