Detection of adaptive shifts on phylogenies using shifted stochastic processes on a tree

TL;DR

This paper develops a statistical framework to detect adaptive shifts in trait evolution on phylogenetic trees, addressing model identifiability issues and proposing algorithms for scenario enumeration, estimation, and model selection.

Contribution

It introduces a recursive algorithm for scenario enumeration, an EM-based maximum likelihood estimation method, and a model selection procedure for detecting adaptive shifts in phylogenetic trait evolution.

Findings

Models with shifts are not always identifiable.

The proposed algorithms effectively enumerate equivalent scenarios.

The model selection procedure accurately estimates the number of shifts.

Abstract

Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic tree relating the species. We consider shifts in the process parameters, which reveal fast adaptation to changes of ecological niches. We show that models with shifts are not identifiable in general. Constraining the models to be parsimonious in the number of shifts partially alleviates the problem but several evolutionary scenarios can still provide the same joint distribution for the extant species. We provide a recursive algorithm to enumerate all the equivalent scenarios and to count the effectively different scenarios. We introduce an incomplete-data framework and develop a maximum likelihood estimation procedure based on the EM algorithm. Finally, we propose a model selection procedure, based on the cardinal of effective scenarios, to estimate the number of shifts and prove an oracle inequality.