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The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture. Computing the likelihood of data observed at the leaves is costly as the size and complexity of the phylogeny grows. Efficient algorithms exist for trees, but cannot be applied to networks. We show that a vast array of models for trait evolution along phylogenetic networks can be reformulated as graphical models, for which efficient belief propagation algorithms exist. We provide a brief review of belief propagation on general graphical models, then focus on linear Gaussian models for continuous traits. We show how belief propagation techniques can be applied for exact or approximate (but more scalable) likelihood and gradient calculations, and prove novel results for efficient parameter inference of some models. We highlight the possible fruitful interactions between graphical models and phylogenetic methods. For example, approximate likelihood approaches have the potential to greatly reduce computational costs for phylogenies with reticulations. This article is part of the theme issue ‘“A mathematical theory of evolution”: phylogenetic models dating back 100 years’.
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This content will become publicly available on May 19, 2026
When the Map Fails the Territory: Hidden State Models, Complex Traits and the Evolution of Bird Migration
Phylogenetic comparative methods often rely on simplifying complex biological traits into discrete categories, potentially obscuring evolutionary patterns and generally limiting inferences. This dissertation confronts this ``map versus territory" problem by developing and evaluating methodological approaches that integrate known and unknown trait complexity into macroevolutionary analyses. To establish the statistical power of discrete methods in detecting trait complexity, I first demonstrate the utility of structured hidden Markov models (SHMMs) for identifying underlying continuous architectures, like threshold traits, within simulated and empirical discrete datasets (Chapter ref{ch:1}). Taking bird migration as an example of a hard-to-measure complex trait, I then develop new continuous metrics of bird movement from large-scale community science (eBird) data, using entropy-based measures and phylogenetically aligned component analysis (PACA) to reveal a multi-dimensional structure of evolutionarily relevant combinations of traits, representing underlying movement behavior in North American birds (Chapter ref{ch:2}). Next, I fit SHMMs informed by this structure to global and North American bird phylogenies, testing hypotheses about how migration may have evolved, while accounting for classification ambiguity (Chapter ref{ch:3}). I show that models incorporating hidden states that imitate the structure from Chapter ref{ch:2} were often preferred over generalized hidden Markov models and standard Markov models, suggesting that migration both contains hidden complexity and evolves along specific pathways. Overall, this dissertation provides a methodological framework for integrating continuous data and theoretical knowledge into discrete trait analyses, demonstrating a more holistic treatment of how to treat complex discretized traits like avian migration in phylogenetic comparative methods.
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- Award ID(s):
- 1942717
- PAR ID:
- 10656883
- Publisher / Repository:
- Virginia Tech
- Date Published:
- Format(s):
- Medium: X
- Institution:
- Virginia Tech
- Sponsoring Org:
- National Science Foundation
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