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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
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