Biology Reference
In-Depth Information
Martins and Garland, 1991; Garland et al., 2005; Martins and Hansen, 1997; Rohlf, 2001,
2006
). To understand the core of this problem, it is important to keep in mind that to
perform any sort of statistical analysis, we need a model of a random distribution so we
can determine whether our data deviate meaningfully from that model distribution. We
need that model if we want to determine whether the mean of one trait differs between
samples or if we want to determine whether traits are correlated in their distribution
among samples. We must also be able to assume that our samples are randomly drawn
from the population they represent; only then can we determine whether our samples are
more or less similar than expected. The Brownian motion model of evolutionary change
can be used to generate an expected distribution of values for a randomly evolving trait
(as can other evolutionary models). The problem is that taxa representing an evolving
lineage usually cannot be treated as equally independent samples of that distribution.
For a single, unbranching lineage, the Brownian motion model predicts that most changes
will be small and no one direction of change is more likely than any other; and although a
large change (either a single step or a run) is unlikely, longer branches provide more opportu-
nities for one to occur. If one had a set of taxa with the same trait value at a given starting
time, the mean of the set at any later time is expected to be the starting value, but the variance
of that trait is expected to increase as a function of the elapsed time. More important, there is
no expectation that one pair of taxa will be more similar than another pair of taxa. This
unlikely scenario, often represented by a star phylogeny (
Figure 10.1A
), differs greatly from
the usual situation in which taxa vary in degree of relatedness, that is, the amount of time
that has passed since splitting from their most recent common ancestor (
Figure 10.1B
).
In a branching lineage, the Brownian motion model predicts that similarity will be a
function of relatedness. If the lineage branched early in the clade's history (group X, see
Figure 10.1B
), it is likely the common ancestor (the branch point) had a small but non-zero
deviation from the root, but its descendants are more likely to have deviations that are
larger and in different directions. A lineage that branched more recently (group Y, see
Figure 10.1B
) is much more likely to have a common ancestor that diverged far from the
root and descendants that differ little from their relatively younger common ancestor.
Therein lies the crux of the statistical problem
similarity is predicted by common ances-
try, so taxa cannot be treated as independent samples.
The non-independence of taxa is a problem for analyzing correlations as well as for
analyzing differences between means. The structure of phylogenetic relationships predicts
the same pattern of similarity for all traits. If two taxa are closely related, they will be
similar in jaw length, and tooth shape, and every other trait. In
Figure 10.2
, one set of taxa
is clustered around one pair of ancestral values; another set of taxa is clustered around a
FIGURE 10.1
Two hypothetical phy-
logenies that differ in variation of relat-
edness of tip taxa. (A) A star phylogeny
with four lineages diverging simulta-
neously from a single common ancestor.
(B) The root gives rise to two lineages
that branch at different times.
