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Fig. 4. Use of computer simulations to illustrate how Type I error rates for
testing an association between two traits can be inflated by ignoring
phylogenetic relationships. Shown are three distributions of ordinary,
non-phylogenetic, Pearson product–moment correlations of tip data. In
each of the three figures, data were simulated along the phylogeny shown,
under a simple Brownian motion model of character evolution (see
Fig. 2), with the correlation
between the two traits set to zero
(Martins and Garland, 1991;
Garland et al., 1993). (A)
Data simulated along a `star' phylogeny, here depicted as a `comb.' The upper
95th percentile is +0.504, which is statistically indistinguishable from the
conventional critical value of +0.497. Compared with this distribution, the
correlation for the real data on lizards (+0.585; see text) would be
considered statistically significant at P<0.05. (B) Data simulated
along the hierarchical topology, but with less extreme branch lengths
(arbitrary values as suggested by Pagel,
1992) than for the real branch lengths shown in (C). For these
simulated data, the 95th percentile is +0.641, which is larger than the
conventional critical value. Judged against this empirical null distribution,
the correlation for the real data would be considered statistically
non-significant (P>0.05). (C) Simulations along the actual
phylogeny used by Garland et al.
(1991). The simulated data
include an even greater number of sets for which the correlation is strongly
positive, as compared with (B). The 95th percentile is +0.828, which is much
larger than the nominal one-tailed critical value for testing a correlation
coefficient (+0.497). If the phylogeny shown in C is close to reality, and if
evolution has been similar to Brownian motion, then the results of C are more
trustworthy than those of A.
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