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Within-species trait variation may be the result of genetic variation, environmental variation, or measurement error, for example. In phylogenetic comparative studies, failing to account for within-species variation has many adverse effects, such as increased error in testing hypotheses about evolutionary correlations, biased estimates of evolutionary rates, and inaccurate inference of the mode of evolution. These adverse effects were demonstrated in studies that considered a tree-like underlying phylogeny. Comparative methods on phylogenetic networks are still in their infancy. The impact of within-species variation on network-based methods has not been studied. Here, we introduce a phylogenetic linear model in which the phylogeny can be a network to account for within-species variation in the continuous response trait assuming equal within-species variances across species. We show how inference based on the individual values can be reduced to a problem using species-level summaries, even when the within-species variance is estimated. Our method performs well under various simulation settings and is robust when within-species variances are unequal across species. When phenotypic (within-species) correlations differ from evolutionary (between-species) correlations, estimates of evolutionary coefficients are pulled towards the phenotypic coefficients for all methods we tested. Also, evolutionary rates are either underestimated or overestimated, depending on the mismatch between phenotypic and evolutionary relationships. We applied our method to morphological and geographical data from Polemonium. We find a strong negative correlation of leaflet size with elevation, despite a positive correlation within species. Our method can explore the role of gene flow in trait evolution by comparing the fit of a network to that of a tree. We find marginal evidence for leaflet size being affected by gene flow and support for previous observations on the challenges of using individual continuous traits to infer inheritance weights at reticulations. Our method is freely available in the Julia package PhyloNetworks.
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A variable-rate quantitative trait evolution model using penalized-likelihood
In recent years it has become increasingly popular to use phylogenetic comparative methods to investigate heterogeneity in the rate or process of quantitative trait evolution across the branches or clades of a phylogenetic tree. Here, I present a new method for modeling variability in the rate of evolution of a continuously-valued character trait on a reconstructed phylogeny. The underlying model of evolution is stochastic diffusion (Brownian motion), but in which the instantaneous diffusion rate (σ 2 ) also evolves by Brownian motion on a logarithmic scale. Unfortunately, it’s not possible to simultaneously estimate the rates of evolution along each edge of the tree and the rate of evolution of σ 2 itself using Maximum Likelihood. As such, I propose a penalized-likelihood method in which the penalty term is equal to the log-transformed probability density of the rates under a Brownian model, multiplied by a ‘smoothing’ coefficient, λ, selected by the user. λ determines the magnitude of penalty that’s applied to rate variation between edges. Lower values of λ penalize rate variation relatively little; whereas larger λ values result in minimal rate variation among edges of the tree in the fitted model, eventually converging on a single value of σ 2 for all of the branches of the tree. In addition to presenting this model here, I have also implemented it as part of my phytools R package in the function multirateBM . Using different values of the penalty coefficient, λ, I fit the model to simulated data with: Brownian rate variation among edges (the model assumption); uncorrelated rate variation; rate changes that occur in discrete places on the tree; and no rate variation at all among the branches of the phylogeny. I then compare the estimated values of σ 2 to their known true values. In addition, I use the method to analyze a simple empirical dataset of body mass evolution in mammals. Finally, I discuss the relationship between the method of this article and other models from the phylogenetic comparative methods and finance literature, as well as some applications and limitations of the approach.
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- Award ID(s):
- 1759940
- PAR ID:
- 10391204
- Date Published:
- Journal Name:
- PeerJ
- Volume:
- 9
- ISSN:
- 2167-8359
- Page Range / eLocation ID:
- e11997
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.7717/peerj.11997
