Stochastic Models for Phylogenetic Trees

These pages form a complement to a project (with Lea Popovic and Maxim Krikun) we call Coherent Stochastic Models for Macroevolution. Part of the idea is that the behavior of higher-order taxa (genera, families etc) should emerge from a species-level model rather than being modeled directly.

Overview of project: model and results.

There exists a 2004 draft document (PDF) covering the whole project. This is not intended for publication as is, but is being made into 3 papers.

A critical branching process model for biodiversity deals with the species-level model. One aspect of the model we emphasize is that qualitative behavior of different realizations can appear quite different: see our picture gallery of simulations.
Stochastic Models for Phylogenetic Trees on Higher-order Taxa describes a way to combine the species-level model with schemes for classifying species into genera, and starts analytic study of the resulting trees on genera.
Five statistical questions about the Tree of Life (draft available on request) is the final overview paper aimed at biologists; the 5 questions we select are
- For a clade on $n$ extant species, write $m \geq n$ for the maximum number of coexisting species at any past time; how large do we expect a priori that the ratio $m/n$ might be?
- From a correct phylogeny of the extant species of a clade, what can we deduce about past speciation and extinction rates?
- What proportion of extant species are in fact descendants of still-extant ancestral species, and how does this compare with predictions of models?
- When one moves from trees on species to trees on sets of species (whether traditional higher order taxa, or clades within PhyloCode) does one expect trees to become more unbalanced as a purely logical consequence of tree structure, without signifying any real biological phenomenon?
- How do we expect that fluctuation rates for counts of higher order taxa should compare to fluctuation rates for number of species?