Diagnosing the uncertainty of taxa relative abundances derived from count data

When working with micropaleontological assemblage data it is necessary to accept that the true population can never be quantified fully. Thus, the investigator must count individuals in the hope of obtaining a representative sample and then determine the uncertainty associated with the taxa relative abundances. Such uncertainties can be obtained by assuming that the relative abundances originate from a multinomial distribution for which a confidence region can be obtained using existing statistical methods. For assemblages containing more than three taxa, however, the determination and representation of multinomial confidence regions become exceedingly cumbersome. Here we outline a simple method that allows diagnostic values of the multinomial confidence region to be calculated for any number of taxa. Examples of such values are the most extreme relative abundances, which allow the user to quantify the interval of a given taxon within the confidence region and the maximum/minimum values of various diversity indices. ► We show how values diagnostic of multinomial confidence regions can be calculated. ► Expressions for the extremes of multinomial confidence regions are provided. ► Extremes of indices within multinomial confidence regions are calculated.