# Selective Inference for Testing Trees and Edges in Phylogenetics

## TL;DR

This paper introduces a selective inference method for testing phylogenetic trees and edges, adjusting for selection bias, and providing more accurate p-values for phylogenetic model testing.

## Contribution

It proposes a novel selective inference framework that improves upon previous tests by controlling for selection bias in phylogenetic analysis.

## Key findings

- Selective p-values effectively control type-I error conditioned on selection.
- The method is applicable to broader model selection problems.
- Illustrated with a controversial phylogenetic case study.

## Abstract

Selective inference is considered for testing trees and edges in phylogenetic tree selection from molecular sequences. This improves the previously proposed approximately unbiased test by adjusting the selection bias when testing many trees and edges at the same time. The newly proposed selective inference $p$-value is useful for testing selected edges to claim that they are significantly supported if $p>1-\alpha$, whereas the non-selective $p$-value is still useful for testing candidate trees to claim that they are rejected if $p<\alpha$. The selective $p$-value controls the type-I error conditioned on the selection event, whereas the non-selective $p$-value controls it unconditionally. The selective and non-selective approximately unbiased $p$-values are computed from two geometric quantities called signed distance and mean curvature of the region representing tree or edge of interest in the space of probability distributions. These two geometric quantities are estimated by fitting a model of scaling-law to the non-parametric multiscale bootstrap probabilities. Our general method is applicable to a wider class of problems; phylogenetic tree selection is an example of model selection, and it is interpreted as the variable selection of multiple regression, where each edge corresponds to each predictor. Our method is illustrated in a previously controversial phylogenetic analysis of human, rabbit and mouse.