Coherent Stochastic Models for Macroevolution

This is joint work with Lea Popovic and Maxim Krikun.

Brief motivation

There is a substantial literature on comparing data on different aspects of macroevolution -- the evolutionary history of speciations and extinctions -- with the predictions of simple ``pure chance" stochastic models. Available data includes The fit of simple models, and of more elaborate models incorporating conjectured biological process, have been studied in these contexts. While data-motivated models are scientifically natural, a mathematical aesthetic suggests a somewhat different approach: start with a ``pure chance" model which encompasses simultaneously all the kinds of data that one might hope to find. Here are two instances of what one would like such a coherent model to provide. (We emphasize the latter because biological literature tends to assume that a model can be applied at any level, without enquiring whether this assumption is logically self-consistent).

Outline of model

Our purpose is to present what is arguably the mathematically fundamental such model. The underlying model is simple -- a critical branching process conditioned to have $n$ lineages at the present time. Though hardly new in concept, our focus on conditioning to have $n$ lineages (for comparison with real clades on $n$ extant taxa) makes our results somewhat new in detail. To model higher-order taxa (genera, say) we start by assuming that each new species has some chance to be sufficiently different that it should be considered a new genus. The remaining details of defining genera, bearing in mind one desires monophyletic genera, can be handled in several different ways (see draft paper for details). Part of the project is to examine whether these different schemes for defining genera make a qualitative difference.

Overview of results

Our results are derived as asymptotics for large $n$, even though we envisage using them for rather small values, say $n = 20$.