River Ecology and Restoration - River Dynamics and Integrated River Management - page 667

ecologists prefer small sampling areas as long as a sufficient number of species can be sampled.
Figure 10.40 shows the relation of the number of species in a sample and the sampling area at each site
(Duan et al., 2007). The sampling area at each site should be at least 1 m 2 for a relatively reliable value of
richness.

Fig. 10.40 Relation of the species richness in a sample and the sampling area at each site

The number density of individuals (abundance), N , is generally dynamic. If a bio-community colonizes a
habitat at time t 0 , the number density increases with time t and finally reaches equilibrium after a period
of time. A differential equation describing the dynamic process of the number density growth is suggested
(Ricklefs, 2001):

d N N

§ ·

rN 1

¹

(10.5)

¨ ¸

d t K

©

in which r represents the intrinsic exponential growth rate of the population when its size is very small
(that is, close to 0), and K is the carrying capacity of the environment, which represents the number of
individuals that the environment can support. This equation is called the logistic equation. So long as N
does not exceed the carrying capacity K , that is, N / K is less than 1, the number density continues to
increase, albeit at a slowing rate. When N exceeds the value of K , the ratio N / K exceeds 1, d N /d t becomes
negative, and the density decreases. K is the eventual equilibrium size of number density growing according
to the logistic equation. Integration of the logistic equation yields

K

N (10.6)

KN
N

rt

1

0

e

0

where N 0 is the number density of individuals at time t 0. The logistic equation may be used for a
species, e.g., black carp in Tongting Lake, or for a bio-community, e.g., benthic macro-invertebrates at a
section of a stream.
The abundance (density number) of a particular species reflects the balance between a large number of
factors and processes, variations in each of which result in small increments or decrements in abundance.
Population distribution models account for the evenness (equitability) of distribution of species, which fit
various distributions to known models, such as the geometric series, log series, lognormal, or broken
stick. In a large sample of individuals, species often distribute themselves normally over the logarithmic
abundance categories.

10.3.2.2 Diversity Indices
Not all species should contribute equally to the estimate of total diversity, because their functional roles
in the community vary, to some degree, in proportion to their overall abundance. Ecologists have formulated