# DETECTION OF ADAPTIVE SHIFTS ON PHYLOGENIES USING SHIFTED STOCHASTIC PROCESSES ON A TREE

## TL;DR

This paper introduces a method to detect adaptive shifts in species traits on phylogenetic trees using statistical models and algorithms.

## Contribution

A novel algorithm and statistical framework for identifying adaptive shifts in evolutionary traits while addressing model identifiability issues.

## Key findings

- Models with adaptive shifts are generally not identifiable without constraints.
- A recursive algorithm can enumerate equivalent evolutionary scenarios.
- A maximum likelihood estimation procedure and model selection method are developed.

## 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.