Spatial Variation in Tree Species Composition 17clayey (Sabatieret al.1997, Clarket al. 1999a),
ridge, valley, or mid-slope (Harmset al. 2001).
The full environmental variability among
several sites is described by a collection of envi-
ronmental distance matrices. Correlations are
then directly performed between the floristic dis-
tance matrix, as defined in Equation (2.4) for
instance, and environmental dissimilarity matri-
ces. Alternatively, several environmental dissim-
ilarity measures can be combined into one
compound variable, such as Gower’s index (Gower
1971, Legendre and Legendre 1998, Pottset al.
2002). Another important predictive variable
when comparin gthe floristics of two samplin g
units is their geographical distance. As we shall
see below, a correlation between diversity and
geographical distance should be consistent with
a prominent role of dispersal limitation. In the
case of a fragmented habitat, it may be advis-
able to use an “effective distance” rather than
the straight-line distance among sites, a distance
that takes into account the habitat heterogeneity
amon gplots.
Ordination methods provide a powerful frame-
work for detectin genvironmental correlations,
and illustratin gthem graphically (ter Braak
1987). These methods enable the visualiza-
tion of beta-diversity over several sites, on
a two-dimensional plot. Observed patterns are
qualitatively interpreted in terms of the envi-
ronmental variables (Whittaker’s 1967 indi-
rect gradient analysis), or are directly regressed
against these environmental variables (direct
gradient analysis). The ordination axes often
represent either linear combinations of species
abundance data or linear combinations of envi-
ronmentalvariables.Adisadvantageof ordination
is that it is difficult to provide a biological inter-
pretation of these axes. Another disadvantage of
ordination is that it is difficult to grasp the rel-
ative merit of the numerous existin gordination
methods. As a result, most users are led to treat
statistical techniques as cookin grecipes rather
than intuitively interpretable statistical methods,
and consequently do not make full use of the data,
or interpret these methods inappropriately (for an
illustration, see the controversy between Legendre
et al. 2005 andTuomisto and Ruokolainen 2006).
The different ordination techniques are compared
and contrasted by, for example, ter Braak (1987),
ter Braak and Prentice (1988), and Legendre and
Legendre (1998).
Floristic diversity may also be modeled by mul-
tiple regressions on environmental dissimilarity
and geographical distance matrices (Borcardet al.
1992, Legendre and Legendre 1998, Ohman and
Spies 1998). The significance of correlations is
then measured usin gMantel tests for simple
regressions, or partial Mantel tests for multiple
regressions. This approach has been widely used
in the recent literature (Pottset al. 2002, Phillips
et al. 2003, Tuomistoet al. 2003a), but it has
also yielded a remarkable amount of controversy
over which an appropriate method should be used
to partition the causes of variation of diversity
into geographical and environmental distance.
Legendreet al. (2005) reviewed these methods
and listed the potential pitfalls related to them.
In particular, they emphasized that partition-
in gon distance matrices should not be used to
study the variation in community composition
amon gsites, because the variance of a dissimi-
larity matrix amon gsites cannot be interpreted
as a measure of beta diversity. The direct result
of usin gthis method is that the amount of
explained variation is underestimated, and tests
of significance had less power than the tests
associated with the canonical ordination method.
TuomistoandRuokolainen(2006)contendedthat
both approaches have merits, and especially that
methods based on distance matrices were more
appropriate to test the neutral theory of biodiver-
sity (Hubbell 2001). On this controversy, it should
be simply stated that (1) Legendreet al. (2005)
provide compellin gand indisputable evidence for
why ordination methods are superior to dis-
tance methods, (2) in contrast with Tuomisto and
Ruokolainen (2006)’s main statement, ordination
methods can be used to test the neutral theory
(Chustet al. 2006), (3) given that many published
results have already made use of distance matri-
ces, it should be possible to use these results and
gain biological insight, but these results should
not be over-interpreted, (4) in any case, users are
advised at least to publish analyses based on corre-
lation of distance matrices together with analyses
based on ordination methods. I will further dis-
cuss at length these approaches below, as they