Biology Reference
In-Depth Information
are robust to branch length errors (
Martins and Garland, 1991; Diaz-Uriarte and Garland,
1998; Rohlf, 2006
).
Stone (2011)
shows that changes in branch length and even small
changes in topology usually have little effect on the phylogenetic covariance matrix and,
thus, have little effect on results. Small topological changes only have large effects when
they change the position of a particularly influential data point (analogous to the effect
of an influential point on a regression). Large errors in topology will have more substantial
effects (
Martins and Garland, 1991; Symonds, 2002
), but Martins and Garland argue that
topological errors so large as to be misleading are unlikely for any reasonably well-studied
taxon.
PGLS regression includes an estimate of the
y
-intercept. This is the same value as would
be obtained by forcing PIC regression through the PGLS mean. The mean computed from
PGLS is equal to the estimated value of the root under the squared change parsimony
optimization. In fact, PGLS can be used to infer trait values at all nodes, and these
estimates also are the same as the reconstructions using squared change parsimony
optimization.
It is now well established that PIC and PGLS produce the same statistical results
when the Brownian motion model is used to predict the expected covariances. The advan-
tages of PGLS are that it is a more generalized method and more readily adapted to
other evolutionary models (by making the appropriate modifications of the phylogenetic
variance
covariance matrix;
Rohlf, 2001
). Another advantage, demonstrated by
Revell
(2009)
, is that it is possible to generate standardized values for taxa in the original
measurement space, which then can be used for visualization or for analyses in other
applications, (e.g. an ANOVA on size-standardized data). As Revell points out, it would
still be advisable to use phylogenetic methods for the subsequent analysis.
A third approach to the problem of phylogenetic non-independence is to simulate
evolution of the trait(s) on the tree using an appropriate evolutionary model, build a null
distribution, and evaluate the position of the observed data relative to the population of
simulations (
Martins and Garland, 1991; Garland et al., 1993
). One potential advantage of
this approach is that it has the capacity to simulate evolution under various models,
including ones for which the expected error structure is not easily derived. The interested
reader is referred to
Garland et al. (2005)
and references therein for further guidance.
For possible extensions of this approach, for example to test competing hypotheses about
evolutionary processes, the reader is directed to on-going projects by Harmon and
colleagues (e.g.
Eastman et al., 2011
).
A Note on Phylogenetic “Signal” or “Constraint”
Several writers have characterized the methods discussed here as correcting for phy-
logenetic signal, and some have taken the further step of inferring that this signal is
evidence of constraints on the evolutionary process. It should be clear by this point that
the signal to which they are referring is nothing more than congruence with phylogeny.
Rohlf (2006)
makes the point that the phylogenetic comparative methods do not correct
the parameter estimate. They do not remove the proportion of the variance that is due to
common ancestry, so they should not be regarded as analogous to size standardization by
