Transcript Species Diversity

Species Diversity
• Incorporate both diversity and their relative
abundances
• Three important assumptions
– (1) all individuals assigned to a specific class are
assumed to be equal (e.g. no recognition of age, size,
or sex classes; if so, impact disproportionate)
– (2) all species or classes are assumed to be equally
different from one another (e.g. no keystone species
identified)
– (3) community structure is assumed to be measure in
appropriate units (e.g. for animals, individuals but for
plants perhaps biomass or percent cover)
Species Diversity
• Perhaps the most commonly used index is
the Shannon-Wiener diversity index
H’ = -∑ pi ln(pi)
where pi is the relative abundance of the I th
species (∑ pi = 1.0)
Problems
• Most importantly, cannot be interpreted in
a biologically meaningful way
• They lack a probabilistic basis and
consequently, cannot evaluate the
biological or statistical differences between
two communities (H’ of 1.7 vs. 2.0)
Potential Solutions
• Still a need to quantify communities
(1) Abandon the idea of incorporating both
evenness and species richness into a
single index
(2) Use explicit null models to estimate the
nonbiological effects of sample size on
species richness and species evenness
(although little work on evenness has
been conducted)
Problems: Species Richness
• Species richness is not only influenced by
the number of individuals, the species
richness of the surrounding community,
and area
Example
• Unless two communities are censused
exhaustively and identically, it is
inappropriate to compare simple species
counts
• Compare communities from two different
age pine plantations (Table 2.1)
• Young forests: 243 individuals of 31
species vs. 63 individuals of 9 species
• Distribution of species
(between young and
old pine plantations)
considered in the
carabid beetle study
Solution: Rarefaction
• Sanders (1968) addressed the problem of
comparing the species richness of different
habitats in a study of marine communities
• Using an algorithm for “rarefying” the large
samples (based on random subsamples of
individuals)
• The rarefied sampled can then be directly
compared to the smaller sample
• If conducted for a number of different
abundances, a rarefaction can be plotted
Rarefaction Curves
• Because
subsampling is
used, it also
generates a
probability
distribution (CI)
Rarefaction
• The correct rarefaction model is based on
the hypergeometric distribution, sampling
without replacement (e.g. jackknife) from
some parent distribution (the observed
collection)
Assumptions of Rarefaction
• 1) sampling has been sufficient to
guarantee an adequate characterization of
the parent distribution (if too small, all
samples converge at the coordinate (1,1))
• 2) the spatial distribution of individuals is
random
Assumptions of Rarefaction
• 3) the samples to be compared are
taxonomically “similar” and are drawn from the
“same” community type
• 4) standardized sampling techniques are used
for all collections
• 5) rarefaction can be used for interpolation to a
smaller sample size, but not for extrapolation to
a larger sample size (unless distribution is
assumed; but species accumulation curves may
be better)
Statistical Issues
•
Rarefaction can be used to ask two
different questions
1) For a collection of N individuals of S
species, what is the expected number of
species in a small sample of n individuals
2) What is the likelihood that two collections
of sizes N and n were both drawn from
the same parent distribution
Statistical Considerations
• It is important to calculate rarefaction
curves along their full length, that is, for
several different values of n
• For a collection of S species and N
individuals, a minimum of S + 1
subsamples of n, evenly spaced along the
x axis, should be used to construct the
curve
Extrapolation of Rarefaction
• Most promising nonparametric estimators have
been adapted from mark-and-recapture statistics
• For a single collection of species, the best
estimator of total species richness is
Stot = Sobs + (a2 / 2b)
a is the number of species with a single individuals
b is the number of species with two individuals
Criticisms of Rarefaction
• Several criticisms of rarefaction include:
– It assumes a random spatial distribution of
individuals
– It loses information about species identity and
relative abundance
– Is difficult to calculate by hand
However, all but the last are leveled at most
diversity indices and computer software has
addressed the last