Biology Reference
In-Depth Information
FIGURE 10.6 Vector comparison by resampling. (A) Two pairs of ancestor and descendant species, with
vectors indicating directions of change. Triangles and squares represent two different lineages; black filled sym-
bols are ancestors, gray are descendants. (B) Vectors translocated to show the angle between them (arc). (C) Same
vectors with simulated resampling sets, so the span of resampling sets can be compared to angle between the
original vectors.
of these confidence intervals to the size of angle between the vectors, we can judge
whether the two directions are significantly different.
In a somewhat more complex case ( Figure 10.7A ), we might sample our evolving
lineages at several successive points (stratigraphic levels or possibly locations along a
cline). We could still compare the net difference (between end points) or the average
directions (resampling all intermediate levels, as well as the endpoints) but, even in the
latter case, we would be discarding much of the data on changes in direction. Adams and
Collyer (2009) propose treating the trajectory as a shape. The trajectory shapes are
obtained by Procrustes superimposition (centering, rescaling to centroid size
1, rotating
to minimize the summed squared distances between corresponding points; the only
difference is that the shape trajectories are likely to have higher dimensionality than
anatomical shapes). After superimposition ( Figure 10.7B ), comparison of populations of
trajectories can be performed by MANOVA but, based on expectations of small sample
sizes, Adams and Collyer suggest that a resampling strategy is more likely to give infor-
mative results.
This approach may be useful for comparing phyletic trends such as responses of herbi-
vores to climate change, or invasion of soft substrate by diverse bivalves. It would be pos-
sible to test whether representatives of different clades responded differently (e.g.
antelope vs deer), however, there are some important limitations to bear in mind. First, as
with Procrustes superimposition of anatomical shapes, the trajectory shapes must have the
same number of points. It is not imperative that the levels have the same range or spacing,
but they are likely to be more informative if they are on similar scales. Comparing
responses to climate change over millions of years in two geological epochs is apt to be
more meaningful than comparing those historical trends to altitudinal or latitudinal gradi-
ents. Second, the method is not designed to compare branching or reticulate patterns. At
first glance this may not seem like a big problem; however, differences in branching time
relative to directional changes would pose serious challenges to the comparability of the
trajectories.
5
Search WWH ::




Custom Search