A critical branching process model for biodiversity
studies the following simple model for a phylogenetic
tree on n species, intended as a null model not
incorporating any particular conjectured biological effect.
The purpose of this page is to show more extensive simulations
than can fit into a journal paper.
- Each species goes extinct, or speciates, at the same constant stochastic rate.
- The clade originated a random time ago, uniform on
(0, - infinity).
- Condition on exactly n species currently.
Phylogenetic trees (lineages) of extant species
A phylogenetic tree on n species derived from molecular
biology data shows lineages without identifying ancestral species.
The following pictures illustrate such trees generated
within our model.
We show 10 realizations for each of several values of n.
n = 8
n = 12
n = 20
n = 8
n = 12
n = 20
The simulations should be self-explanatory -- some comments below.
Figure 3 in the paper shows three of the n = 20 realizations.
The conceptual point is that the simulations show substantial
variability between realizations, so that one might
attribute different biological interpretations to different
realizations of the same process.
Our conclusion is that it seems almost impossible to verify
assertions such as logistic or exponential growth of a clade
of these sizes,
based only on the phylogeny of extant species.
Instead one needs to study collections of phylogenies.
Comments on the pictures
The time unit is the mean species lifetime.
The phylogenies show only lineages, although the model
explicitly models extinct species, and the number of species
as a function of time is plotted on the left.
The distribution of the various summary statistics
follows the theoretical distributions derived in the paper
for the large-n limit.
The complete clade
Figures 1,2,7 in the paper show different aspects of one realization
(n = 20)
of the complete clade within our model.
First is the entire clade: each species represented by a
vertices line from time of origin to time of extinction.
Second is the part of the picture showing only extant species
and their ancestral species.
Third is the induced tree on fine genera,
as defined in the paper.
Here are copies of these pictures for three more realizations:
In fact to make pictures fit the page we chose smaller-than-median