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4 M. Sarà and S. Morand

matrix from the unoccupied area is the boundary 1982). All regressions between contrasts were
line, which defines the condition of maximum forced through the origin (Garland et al., 1992). In
nestedness. A perfectly nested matrix is a ‘cold’ order to verify that contrasts were properly
matrix (temperature 0°). Unexpected absences or standardized we performed a regression of the
presences will increase the temperature of the absolute values of standardized contrasts vs.
matrix, i.e. the disorder, decreasing the nested- their standard deviations (Garland et al., 1992)
ness of the given data set. The significance of using CAIC. We used a working phylogeny of
the order is tested by random permutations of the mammal species in the data set derived from
original data. several sources (see Catzeflis et al., 1995; Cooper
We compiled a matrix of the presence/absence & Fortey, 1998; Morand & Poulin, 1998; Morand
of 31 mammal species on 45 west Mediterranean & Harvey, 2000)
islands (Appendix 1). There is a negative relationship between body
size and density (the so-called ‘energy equivalent’
rule of Damuth, 1981, 1987) that it is neces-
Comparative analyses
sary to account for. We then corrected density
As emphasized by Harvey & Pagel (1991) and for body mass by using residuals of the linear
Harvey (1996), ecologists should incorporate regression.
phylogenetic information in their investigations.
For example, Morand & Poulin (1998) have
shown that not controlling for confounding phylo- RESULTS
genetic effects may lead to false conclusions in
Nested pattern
the case of density–body mass relationships in
mammals. A nested pattern was observed, with a tempera-
We used two different comparative methods: ture of 4.9° being measured for the matrix of
the eigenvector method (Diniz-Filho et al., 1998) presence/absence of mammals on island. The
and the phylogenetically independent contrast matrix temperature was statistically colder than
method (Felsenstein, 1985). those of the random matrices (51.0° ± 3.9;
The eigenvector method has been recently P < 0.00001; over 1000 permutations).
proposed by Diniz-Filho et al. (1998) as a new
method to estimate and correct for phylogenetic
Density and body size
inertia. A principal co-ordinate analysis (PCA) is
performed on a pairwise phylogenetic distance A significant relationship was found between
matrix between species. Eigenvectors and eigen- body size and density (Ordinary Least Squares
values are extracted from this analysis. Each [OLS] slope –0.72 ± 0.14, r = 0.69, P < 0.0001)
eigenvector represents the amount of the phylo- using cross species values. The relationship was
genetic variance related to the relative magnitude
of its associated eigenvalue. Traits under analysis
are regressed on eigenvectors retained by a
broken-stick model and the residuals express the
Table 2 Results of a multiple linear regression on
independent evolution of each species; whereas
maximum mammal density (mainland populations)
estimated values express phylogenetic trends (r = 0. 80; F 3,27 = 16. 27, P < 0. 0001). The two first
in data. eigenvectors of the principal component analysis of
We used the phylogenetically independent the phylogenetic matrix of mammal species
contrasts method (Felsenstein, 1985; Harvey & contribute significantly to the variance explained
Pagel, 1991; Garland et al., 1992; Harvey, 1996) in
order to resolve the problem of non-independence Independent Partial slope P
of data (i.e. traits measured across different species). variables (± )
We used the CAIC computer application (Purvis
Body mass –0.51 ± 0.16 0.0034
& Rambaut, 1995) for independent contrasts
Eigenvector 1 0.09 ± 0.04 0.0262
analyses. Quantitative data were log-arithmically
Eigenvector 2 0.12 ± 0.16 0.003
transformed in order to stabilize variance (Harvey,
© 2002 Blackwell Science Ltd, Diversity and Distributions, 8, 1–9