Picture gallery

The paper 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.

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.

Postscript n = 8 n = 12 n = 20
PDF 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: Postscript PDF

In fact to make pictures fit the page we chose smaller-than-median size realizations.