Tropical Forest Community Ecology

Spatial Variation in Tree Species Composition 15

populations, excludin gintra-population diversity,

would be (see also Lande 1996):

βNeik,l =Dkl−

Dkk+Dll

2

=

1

2

∑S

i= 1

(

xki−xli

) 2

(2.4)

This measure of strict beta-diversity is propor-
tional to the squared Euclidean distance between
siteiand sitek, a quantity already used in the
ecological literature (Ricklefs and Lau 1980). The
total diversity across a total ofKpopulations can
then be defined as

DT=

1

K

∑K

k= 1

Dkk+

1

K^2

∑K

k= 1

∑K

l= 1

βkNei,l

The first term is the contribution of local diversity,
while the second term is the contribution of strict
beta-diversity (Nei 1987, Lande 1996, Chaveet al.
2007).
The Steinhaus index provides an index of beta-
diversity that is based on species abundance. This
index was also called the Renkonen index or the
complement of the Bray–Curtis index (i.e., Stein-
haus index equals one minus the Bray–Curtis
index). Note that historically, the first reference
to this index was due to O. Renkonen and it
would be more appropriately named after this
author (Renkonen 1938, Plotkin and Muller-
Landau 2002). This index of similarity between
siteskandlreads:

βSteinhausk,l =

∑S

i= 1 min

(

Nki,Nli

)

(

Nk+Nl

)

/ 2

whereNk =

∑S

i= 1 Nkiis the total number of

individuals in samplek. The correspondin gindex

of diversity would then be 1−βSteinhausk,l. The

Steinhaus index of similarity can be rewritten

approximately in terms of relative abundances

where the sample sizes are not too dissimilar:

βSteinhausk,l ≈

∑

imin(xki,xli). The Nei index is

more intuitive than the Steinhaus index, because

a probabilistic interpretation of the latter is less

obvious. Recently, Green and Plotkin (2007)

have offered a samplin gtheory for betadiversity

includingspeciesabundance,therebygeneralizing

results of Plotkin and Muller-Landau (2002).

Species are but one way of measurin gbiodi-

versity. This implicitly assumes that all species

are independent units. Any evolutionary biologist

knows that this is far from true: species are orga-

nized accordin gto a definite structure, and this

structure is defined by their evolutionary history.

Indeed,twospeciesinthesamegenustendtoshare

a larger amount of evolutionary history than two

species in different genera.Pavoineet al. (2005)

called the amount of unshared evolutionary his-

tory of a species, its ‘originality’, and Nee and

May (1997) and Purviset al. (2000) discussed

this effect in light on conservation biology, as a

means for evaluatin gthe potential loss of evolu-

tionary history link to species extinction. Based on

this reasoning, Faith (1992) proposed to measure

the biological diversity of a species assemblage

by the amount of evolutionary history in this

assemblage. If a dated phylogenetic hypothesis is

available for a given species assemblage, then one

may implement Faith’s biodiversity index by mea-

surin gthe total branch len gth in the phylo genetic

tree, measured in millions of years. One recent

example of measurin gthe ‘phylo genetic’ diversity

of plant species assemblage is due to Forestet al.

(2007). Nei’s (1973) measure of local diversity

based on a probabilistic interpretation can also be

generalized to account for the amount of shared

evolutionary history amon gspecies. This fact has

been formalized mathematically by Rao (1982),

but it is only recently that it has received some

further scrutiny (Pavoineet al. 2005, Chaveet al.

2007).

SEARCHING FOR ENVIRONMENTAL

CORRELATES OF SPATIAL

VARIATION IN DIVERSITY

Plant ecologists have long sought to predict

species occurrence from environmental charac-

teristics, both soil and climate (Warmin g1909,

Braun-Blanquet 1932, Whittaker 1956). There

is a vast literature reportin gcorrelations between

floristic variables and environmental or geograph-

ical variables usin ga lar ge number of different

statistical methods. Unfortunately, these methods