  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

Quantitative Methods