successive animals encountered at random from an assemblage will belong to the
same species:
(^) where the n
i are the numbers in the sample of the i
th species. Fifty years ago it was
believed that knowing and comparing diversity measures, such as L, among
assemblages from different habitats and sites, would provide strong ecological
insights. Those mostly did not materialize.
(^) Howard Sanders, the leader of benthic studies along a transect from Gay Head
(Martha’s Vineyard) to Bermuda, was greatly impressed with the observation that
faunal diversity does not decrease with the descent to depth. He expressed assemblage
diversity with “rarefaction curves”. Such curves (Fig. 13.14) from a variety of sites
show that, while benthos of shallow tropical seas (the Bay of Bengal in Sanders’
comparison) can be more diverse than Sargasso Sea benthos, most shallow benthic
habitats have fewer species per individual than the deep northwest Atlantic. What are
these curves? They are “synthetic” species–area curves. Gerlach (1972) developed an
actual species–area curve for benthos from the Baltic Sea (Fig. 13.15), which is a plot
of the cumulative number of species as the number of sieved grabs included in the
sample is increased, that is, as area sampled is increased. The steepness of such a
curve is a measure of its species equitability. Also, the higher its asymptote, that is the
more total species, the more diverse it is. If it is steep, then the more likely it is that
the next animal that a given worm meets crawling through the mud will be something
new, something unexpected and challenging. The higher the curve, the more likely
that it will meet something new and unexpected eventually. Rarefaction curves
(Sanders 1968, 1969) are just species–area curves modeled statistically from very
large faunal analyses. The calculations for increasing sample size, for n specimens up
to the actual sample size, N, where Ni is the number of the ith species among S
species, go according to:
Fig. 13.14 Areas bounding rarefaction curves for polychaetes and pelecypods
combined from different marine benthic areas. The deep sea, despite its trophic
poverty and nearly invariant conditions, has many species and high species
equitability.
(After Sanders 1968.)