Tropical Forest Community Ecology

14 Jérôme Chave

acb

Plot A Plot B

Figure 2.1 Various ways of measurin gthe species
overlap between two sites, plot A and plot B. In this
example, each plot contains five individuals and three
species, two of which are shared between the two plots
(defined ascin the main text). The number of species
only in plot A,a, is equal to one, and the number of
species only in plot B,b, is also one. Thus, for instance,
the Sørensen index isβSørensen= 2 /3, and the Jaccard
index isβJaccard= 2 /5.

Koleffet al.’s approach provides a consistent
framework for comparin gpreviously published
measures of species overlap. However, it veils
a number of samplin gissues: the true num-
ber of species in a landscape is usually larger
than a+b+c unless the two samples are
very large and effectively contain most species
(Colwell and Coddington 1994). In addition,
alpha-diversity tends to be underestimated. A
simple argument can be used to estimate the
influence of these biases on the calculation
of beta-diversity indices. Species accumulation
curves suggest that for larger samples, species
richness is less underestimated than for smaller
ones, henceDγshould in general be less under-
estimated thanDα. Thus, both indices defined
in Equations (2.1) and (2.2) should be overes-
timated. Chaoet al.(2000) devised statistically
unbiased estimates for species overlap between
two communities, when samplin gis accounted
for (see also Magurran 2004). This approach
has seldom been used in tropical plant ecol-
ogy (but see Chazdon et al. 1998). Plotkin
and Muller-Landau (2002) addressed the closely
related question of how well similarity indices

are estimated given that only small fractions of

the total landscape can be sampled, and given

that one knows the local species abundance dis-

tributions and aggregation patterns. They devel-

oped an exact formula for the expected Sørensen

index, and provided methods for estimatin gthe

model’s parameters. Much of this recent work

remains to be introduced into the community

ecologist’s toolbox, and freely available statistical

software may help serve this goal (e.g., EstimateS,

http://viceroy.eeb.uconn.edu/EstimateS,developed

by R.K. Colwell).

Another approach for estimatin gbeta-diversity

is based on species abundance and produces mea-

sures that are generally less biased than those

based on presence/absence data. Local diversity

may be measured as the probability that two indi-

viduals taken at random from the community

belon gto different species, a quantity known in

ecology as the Simpson index. Among-site overlap

may be defined as the probability that two indi-

viduals taken from two communities belon gto

different species. Such a measure of species over-

lap has been used in the literature (Wolda 1981,

Leighet al. 1993, Chave and Leigh 2002) and is

similar to the Morisita–Horn index. DefiningNik

as the number of individuals of speciesiin site

k, thenxik =Nik/

∑

iNikis the relative abun-

dance of speciesiin sitek.The probability that two

individuals, one from sitek, the other from sitel,

both belon gto speciesiisxikxil, hence the proba-

bility that the two individuals belon gto different

species is

Dkl= 1 −

∑

i

xikxil (2.3)

These indices cannot be simply deduced from

species numbersa,b,cas above. Also, this measure

places the emphasis on abundant species rather

than on rare species and is asymptotically unbi-

ased for large samples. This measure of diversity

has a simple probabilistic interpretation, and it

is formally equivalent to a universally used mea-

sure of local and spatial diversity in the closely

related discipline of population genetics, which

leads to formulas for the additive partitioning

between local and landscape diversity. Nei (1973)

showed that a measure of diversity between two