> Dating phylogenetic trees
trees of fossil taxa
To date a phylogenetic
tree of fossil taxa and provide a treefile with branch lengths scaled
A treefile with branch
lengths scaled to number of character changes and first appearance
dates (in millions of years) for each taxon.
The standard method of
dating a phylogenetic tree of fossil occurrences is to make each
internal node the age of its oldest descendant. However, in practical
terms this means many branches have a duration of zero million years
(as a hypothetical ancestor and its immediate descendant will have the
same age). In fact each bifurcation will always have at least one such
zero duration branch and consequently at least half of the branches in
a tree are zero duration in length. Aside from being unrealistic this
complicates any measure of a "rate between cladogenetic events"
(Cloutier 1991, p28) as the divisor is zero, meaning rates can only be
zero or infinity. A simple solution to this problem was arrived at
independently by Derstler (1982) and Forey (1988), which was to add
some constant to the divisor in each case. However, the size of
this constant varies between authors. Derstler (1982) used 1 million
years, Forey (1988) 5 million years and Cloutier (1991) 2 million
years. However, in application these approaches all suffer from the
problem of creating large amounts of unsampled history. This is
exacerbated in very speciose or very asymmetric phylogenies as
successive nodes are 'crowbarred' apart by this equal spacing. (In my
experience this can lead to some clades having unrealistically early
origins.) A better solution was provided by Ruta et
al. (2006). They argued that,
after applying the standard method, whenever a zero duration branch is
encountered it should be assigned a positive length by 'sharing' time
with a preceding, non-zero duration branch. They further stated that
the proportion of sharing should be dictated by the branches' lengths
in terms of character changes (i.e. biasing the results towards a null
hypothesis of equal rates). (This can still lead to zero duration
branches, but only where there are no changes so that the rate would be
zero in any case). Brusatte et
al. (2008) adopted a similar
approach, but shared out the time equally between branches. Here a
function for use in the freely available statistical progamming
is provided. This performs dating of the tree using either the
standard, Ruta et al.
(2006) or Brusatte et al.
1. Install and run R
2. Install the APE
library from within R and load it using:
3. Copy and paste the following line into R and hit enter:
4. Load a treefile (with branch lengths) and store it in the variable
"tree". (NB: these can be produced by software such as PAUP*
by ensuring the correct option is selected when saving a tree.)
in NEXUS format - the standard output from PAUP*)
5. Create a text file of ages (first appearance in millions of years)
for your taxa ensuring taxon names appear in exactly the same form as
the treefile, e.g.:
6. This can then be read into R:
7. If using the Ruta et al.
(2006) method you will need to first calibrate your tree using Wagner's
(1997) patristic dissimilarity metric. This can be done using the pat.dist.phylo
function, but requires an additional vector of missing states for each
character. This can be done by creating a text file and reading it in
in the same manner as the ages, but this time storing it as "comp".
8. The patristic dissimilarity tree can be created using the original
tree and the "comp" vector created above. In addition the total number
of characters should be specified with "nchar=", like this:
9. Now we can create a tree with branch lengths scaled to time. For the
ages, rlen=1, method="standard")
For the Ruta et al.
ages, rlen=1, method="ruta", ptree)
For the Brusatte et al.
ages, rlen=1, method="equal")
(NB: the "rlen=" part specifies a root length (in millions of years)
that should always be positive. This is redundant in the standard
method, but necessary for both the other two as it means there will
always be some preceding time to be shared. In practice you may want to
vary the length of "rlen" to see how much it affects your results.)
Brusatte, S. L., M. J.
Benton, M. Ruta and G. T. Lloyd, 2008. Superiority, competition, and
opportunism in the evolutionary radiation of dinosaurs. Science,
Cloutier, R., 1991.
Patterns, trends, and rates of evolution within the Actinistia. Environmental
Biology of Fishes, 32,
Derstler, K. L., 1982.
Estimating the rate of morphological change in fossil groups. Proceedings
of the Third North American Paleontological Convention,
Forey, P. L., 1988.
Golden jubilee for the coelacanth Latimeria
Ruta, M., P. J. Wagner
and M. I. Coates, 2006. Evolutionary patterns in early tetrapods. I.
Rapid initial diversification followed by decrease in rates of
character change. Proceedings
of the Royal Society B-Biological Sciences,
Wagner, P. J., 1997.
Patterns of morphologic diversification among the Rostroconchia. Paleobiology,