Two Gaussian Bridge Processes for Mapping Continuous Trait Evolution along Phylogenetic Trees

Dwueng-Chwuan Jhwueng

doi:10.3390/math9161998

Abstract

Gaussian processes are powerful tools for modeling trait evolution along phylogenetic trees. As the value of a trait may change randomly throughout the evolution, two Gaussian bridge processes, the Brownian bridge (BB) and the Ornstein–Uhlenbeck bridge (OUB), are proposed for mapping continuous trait evolution for a group of related species along a phylogenetic tree, respectively. The corresponding traitgrams to the two bridge processes are created to display the evolutionary trajectories. The novel models are applied to study the body mass evolution of a group of marsupial species.

Highlights

Evolution is the change in the heritable traits of biological populations over successive generations [1]
This work aims to provide a tool for exploring the evolutionary trajectories built along a given phylogenetic tree with known topology and branch lengths and the traits observed at the tips of the tree
The result is concordant with the property of the Brownian bridge that the middle accounts for the most uncertainty

Summary

Introduction

Evolution is the change in the heritable traits of biological populations over successive generations [1]. Evolution occurs ubiquitously on our planet because all species need to survive by adapting themselves to the living environment. The trait value, such as body mass, may change across generations in the evolutionary history. Scientists use mathematical models and computing tools to describe the behavior of change in trait evolution. The change of a trait value for a species can be modeled by a stochastic variable of continuous type varying with time. Let the stochastic variable xt be a species’ trait value at time t, xt solves the onedimensional stochastic differential Equation (SDE) in Equation (1)

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