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Cited by 146Plant Diversity and EvolutionGenomics and Phylogenetic StudiesEvolution and Paleontology Studies

Generalized hidden Markov models for phylogenetic comparative datasets

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Boyko, James D., Beaulieu, Jeremy M.·2021·Methods in Ecology and Evolution
DOI 10.1111/2041-210x.13534

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Abstract

Hidden Markov models (HMMs) have emerged as an important tool for understanding the evolution of characters that take on discrete states. Their flexibility and biological sensibility make them appealing for many phylogenetic comparative applications. Previously available packages placed unnecessary limits on the number of observed and hidden states that can be considered when estimating transition rates and inferring ancestral states on a phylogeny. To address these issues, we expanded the capabilities of the R package corHMM to handle n ‐state and n ‐character problems and provide users with a streamlined set of functions to create custom HMMs for any biological question of arbitrary complexity. We show that increasing the number of observed states increases the accuracy of ancestral state reconstruction. We also explore the conditions for when an HMM is most effective, finding that an HMM is an appropriate model when the degree of rate heterogeneity is moderate to high. Finally, we demonstrate the importance of these generalizations by reconstructing the phyllotaxy of the ancestral angiosperm flower. Partially contradicting previous results, we find the most likely state to be a whorled perianth, whorled androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modelling explicitly allowed for the correlated evolution of several flower characters.

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  • Although a phylogeny has been used during the collection of data, it is still important to control for any phylogenetic non-independence when analysing those data across genes, genomes and species.

    “Although a phylogeny has been used during the collection of such data, it is still important to control for any phylogenetic non-independence when analysing those data across genes, genomes and species93.”

    From A phylogenetic approach to comparative genomics (2025) · cites this paper as [93]

    The Worked example and methods (§2.3.2; page unavailable) uses a phylogeny to analyse traits across angiosperm species, supporting the general relevance of phylogenetic analysis. But the paper does not say that using a phylogeny during data collection leaves phylogenetic non-independence to be controlled during analysis, or address that point across genes and genomes. Its discussion of correlated traits (§4) concerns a different kind of dependence. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 42

  1. Beaulieu, J. M., & Donoghue, M. J. (2013). Fruit Evolution and Diversification in Campanulid Angiosperms. Evolution, 67(11), 3132-3144. doi:10.1111/evo.12180 · DOI
  2. Beaulieu, J. M., & O'Meara, B. C. (2016). Detecting Hidden Diversification Shifts in Models of Trait-Dependent Speciation and Extinction. Systematic Biology, 65(4), 583-601. doi:10.1093/sysbio/syw022 · DOI · Paper page
  3. Beaulieu, J. M., & O'Meara, B. C. (2019). Diversity and skepticism are vital for comparative biology: a response to Donoghue and Edwards (2019). American Journal of Botany, 106(5), 613-617. doi:10.1002/ajb2.1278 · DOI
  4. Beaulieu, J. M., O'Meara, B. C., & Donoghue, M. J. (2013). Identifying Hidden Rate Changes in the Evolution of a Binary Morphological Character: The Evolution of Plant Habit in Campanulid Angiosperms. Systematic Biology, 62(5), 725-737. doi:10.1093/sysbio/syt034 · DOI · Paper page
  5. Bollback, J. P. (2006). SIMMAP: stochastic character mapping of discrete traits on phylogenies. BMC Bioinformatics, 7(1), 88.
  6. Burnham, K. P., & Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.). New York: Springer-Verlag. Retrieved from https://www.springer.com/gp/book/9780387953649
  7. Caetano, D. S., O'Meara, B. C., & Beaulieu, J. M. (2018). Hidden state models improve state- dependent diversification approaches, including biogeographical models: HMM AND THE ADEQUACY OF SSE MODELS. Evolution, 72(11), 2308-2324. doi:10.1111/evo.13602 · DOI
  8. Chamberlin, T. C. (1890). The method of multiple working hypotheses. Science, 15(366), 92-96.
  9. Conner, J. K., Karoly, K., Stewart, C., Koelling, V. A., Sahli, H. F., & Shaw, F. H. (2011). Rapid Independent Trait Evolution despite a Strong Pleiotropic Genetic Correlation. The American Naturalist, 178(4), 429-441. doi:10.1086/661907 · DOI
  10. Cooper, N., Thomas, G. H., & FitzJohn, R. G. (2016). Shedding light on the 'dark side' of phylogenetic comparative methods. Methods in Ecology and Evolution, 7(6), 693-699. doi:10.1111/2041-210X.12533 · DOI
  11. Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.
  12. Eddy, S. R. (2004). What is a hidden Markov model? Nature Biotechnology, 22(10), 1315-1316. doi:10.1038/nbt1004-1315 · DOI
  13. Felsenstein, J., & Churchill, G. A. (1996). A Hidden Markov Model approach to variation among sites in rate of evolution. Molecular Biology and Evolution, 13(1), 93-104. doi:10.1093/oxfordjournals.molbev.a025575 · DOI
  14. Forster, M., & Sober, E. (1994). How to Tell When Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions. The British Journal for the Philosophy of Science, 45(1), 1-35. doi:10.1093/bjps/45.1.1 · DOI
  15. Galtier, N. (2001). Maximum-Likelihood Phylogenetic Analysis Under a Covarion-like Model. Molecular Biology and Evolution, 18(5), 866-873. doi:10.1093/oxfordjournals.molbev.a003868 · DOI
  16. Gascuel, O., & Steel, M. (2014). Predicting the Ancestral Character Changes in a Tree is Typically Easier than Predicting the Root State. Systematic Biology, 63(3), 421-435. doi:10.1093/sysbio/syu010 · DOI
  17. Grundler, M. C., & Rabosky, D. L. (2020). Macroevolutionary analysis of discrete traits with rate heterogeneity. BioRxiv, 2020.01.07.897777. doi:10.1101/2020.01.07.897777 · DOI
  18. Losos, J. B. (2011). Seeing the Forest for the Trees: The Limitations of Phylogenies in Comparative Biology: (American Society of Naturalists Address). The American Naturalist, 177(6), 709-727. doi:10.1086/660020 · DOI · Paper page
  19. Maddison, W. P., & FitzJohn, R. G. (2015). The Unsolved Challenge to Phylogenetic Correlation Tests for Categorical Characters. Systematic Biology, 64(1), 127-136. doi:10.1093/sysbio/syu070 · DOI · Paper page
  20. Maddison, W. P., Midford, P. E., Otto, S. P., & Oakley, T. (2007). Estimating a Binary Character's Effect on Speciation and Extinction. Systematic Biology, 56(5), 701-710. doi:10.1080/10635150701607033 · DOI
  21. Mahler, D. L., Revell, L. J., Glor, R. E., & Losos, J. B. (2010). Ecological opportunity and the rate of morphological evolution in the diversification of Greater Antillean anoles. Evolution: International Journal of Organic Evolution, 64(9), 2731-2745.
  22. Marazzi, B., Ané, C., Simon, M. F., DelgadoSalinas, A., Luckow, M., & Sanderson, M. J. (2012). Locating Evolutionary Precursors on a Phylogenetic Tree. Evolution, 66(12), 3918-3930. doi:10.1111/j.1558-5646.2012.01720.x · DOI
  23. Mayr, E. (1997). This is biology: The science of the living world. Universities Press.
  24. Mossel, E. (2003). On the Impossibility of Reconstructing Ancestral Data and Phylogenies. Journal of Computational Biology, 10(5), 669-676. doi:10.1089/106652703322539015 · DOI
  25. Mossel, E., & Peres, Y. (2003). Information flow on trees. The Annals of Applied Probability, 13(3), 817-844. doi:10.1214/aoap/1060202828 · DOI
  26. O'Meara, B. C. (2012). Evolutionary Inferences from Phylogenies: A Review of Methods. Annual Review of Ecology, Evolution, and Systematics, 43(1), 267-285. doi:10.1146/annurev-ecolsys-110411-160331 · DOI · Paper page
  27. O'Meara, B. C., Smith, S. D., Armbruster, W. S., Harder, L. D., Hardy, C. R., Hileman, L. C., … Diggle, P. K. (2016). Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity. Proceedings of the Royal Society B: Biological Sciences, 283(1830), 20152304. doi:10.1098/rspb.2015.2304 · DOI
  28. Pagel, M. (1994). Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters. Proc. R. Soc. Lond. B, 255(1342), 37-45. doi:10.1098/rspb.1994.0006 · DOI · Paper page
  29. Platt, J. R. (1964). Strong Inference. Science, 146(3642), 347-353.
  30. Rabosky, D. L., & Goldberg, E. E. (2015). Model Inadequacy and Mistaken Inferences of Trait- Dependent Speciation. Systematic Biology, 64(2), 340-355. doi:10.1093/sysbio/syu131 · DOI
  31. Román-Palacios, C., Scholl, J. P., & Wiens, J. J. (2019). Evolution of diet across the animal tree of life. Evolution Letters, 3(4), 339-347. doi:10.1002/evl3.127 · DOI
  32. Sanderson, M. J., & Donoghue, M. J. (1989). Patterns of Variation in Levels of Homoplasy. Evolution, 43(8), 1781-1795. doi:10.1111/j.1558-5646.1989.tb02626.x · DOI
  33. Sauquet, H., von Balthazar, M., Doyle, J. A., Endress, P. K., Magallón, S., Staedler, Y., & Schönenberger, J. (2018). Challenges and questions in reconstructing the ancestral flower of angiosperms: A reply to Sokoloff et al. American Journal of Botany, 105(2), 127-135. doi:10.1002/ajb2.1023 · DOI
  34. Sauquet, H., von Balthazar, M., Magallón, S., Doyle, J. A., Endress, P. K., Bailes, E. J., … Schönenberger, J. (2017). The ancestral flower of angiosperms and its early diversification. Nature Communications, 8(1), 16047. doi:10.1038/ncomms16047 · DOI
  35. Schultz, T. R., Cocroft, R. B., & Churchill, G. A. (1996). The Reconstruction of Ancestral Character States. Evolution, 50(2), 504-511. doi:10.1111/j.1558-5646.1996.tb03863.x · DOI
  36. Siepel, A., & Haussler, D. (2005). Phylogenetic Hidden Markov Models. In Statistical Methods in Molecular Evolution (pp. 325-351). New York: Springer-Verlag. doi:10.1007/0-387- 27733-1_12 · DOI
  37. Sober, E., & Steel, M. (2011). Entropy increase and information loss in Markov models of evolution. Biology & Philosophy, 26(2), 223-250. doi:10.1007/s10539-010-9239-x · DOI
  38. Sober, E., & Steel, M. (2014). Time and Knowability in Evolutionary Processes. Philosophy of Science, 81(4), 558-579. doi:10.1086/677954 · DOI
  39. Sokoloff, D. D., Remizowa, M. V., Bateman, R. M., & Rudall, P. J. (2018). Was the ancestral angiosperm flower whorled throughout? American Journal of Botany, 105(1), 5-15. doi:10.1002/ajb2.1003 · DOI
  40. Steel, M., & Penny, D. (2005). Maximum parsimony and the phylogenetic information in multistate characters. New York: Oxford University Press.
  41. Tarasov, S. (2019). Integration of Anatomy Ontologies and Evo-Devo Using Structured Markov Models Suggests a New Framework for Modeling Discrete Phenotypic Traits. Systematic Biology. doi:10.1093/sysbio/syz005 · DOI
  42. Townsend, J. P., & Naylor, G. (2007). Profiling Phylogenetic Informativeness. Systematic Biology, 56(2), 222-231. doi:10.1080/10635150701311362 · DOI

Cited by

Sorted by citations

Authors
Boyko, J. D., & Beaulieu, J. M.
Affiliations
University of Arkansas at Fayetteville (US)
Corresponding author
Boyko, James D.
ORCID
Venue
Methods in Ecology and Evolution
Publisher
Wiley
Published
2020-12-15
Volume
12
Issue
3
Pages
468-478
ISSN
2041-210X (ISSN-L)
DOI
10.1111/2041-210x.13534
OpenAlex
W3110394251
Cited by
146
References
2
Citations by year
2026: 32 · 2025: 36 · 2024: 34 · 2023: 23 · 2022: 14 · 2021: 6
FWCI
7.93
Type
journal article
Language
en
Open access
Licence
Locations
  • Methods in Ecology and Evolution (publishedVersion)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
Funders
University of Arkansas
Topics
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Plant Diversity and Evolution
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
  • Physical Sciences › Earth and Planetary Sciences › Paleontology › Evolution and Paleontology Studies
Keywords
hidden Markov models, phylogenetic comparative analysis, ancestral state reconstruction, transition rate estimation, phyllotaxis, rate heterogeneity, R package

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