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Abstract Reconstructing the evolutionary history of different groups of organisms provides insight into how life originated and diversified on Earth. Phylogenetic trees are commonly used to estimate this evolutionary history. Within Bayesian phylogenetics a major step in estimating a tree is in choosing an appropriate model of character evolution. While the most common character data used is molecular sequence data, morphological data remains a vital source of information. The use of morphological characters allows for the incorporation fossil taxa, and despite advances in molecular sequencing, continues to play a significant role in neontology. Moreover, it is the main data source that allows us to unite extinct and extant taxa directly under the same generating process. We therefore require suitable models of morphological character evolution, the most common being the Mk Lewis model. While it is frequently used in both palaeobiology and neontology, it is not known whether the simple Mk substitution model, or any extensions to it, provide a sufficiently good description of the process of morphological evolution. In this study we investigate the impact of different morphological models on empirical tetrapod datasets. Specifically, we compare unpartitioned Mk models with those where characters are partitioned by the number of observed states, both with and without allowing for rate variation across sites and accounting for ascertainment bias. We show that the choice of substitution model has an impact on both topology and branch lengths, highlighting the importance of model choice. Through simulations, we validate the use of the model adequacy approach, posterior predictive simulations, for choosing an appropriate model. Additionally, we compare the performance of model adequacy with Bayesian model selection. We demonstrate how model selection approaches based on marginal likelihoods are not appropriate for choosing between models with partition schemes that vary in character state space (i.e., that vary in Q-matrix state size). Using posterior predictive simulations, we found that current variations of the Mk model are often performing adequately in capturing the evolutionary dynamics that generated our data. We do not find any preference for a particular model extension across multiple datasets, indicating that there is no “one size fits all” when it comes to morphological data and that careful consideration should be given to choosing models of discrete character evolution. By using suitable models of character evolution, we can increase our confidence in our phylogenetic estimates, which should in turn allow us to gain more accurate insights into the evolutionary history of both extinct and extant taxa. 

Abstract Phylogenetic trees establish a historical context for the study of organismal form and function. Most phylogenetic trees are estimated using a model of evolution. For molecular data, modeling evolution is often based on biochemical observations about changes between character states. For example, there are four nucleotides, and we can make assumptions about the probability of transitions between them. By contrast, for morphological characters, we may not know a priori how many characters states there are per character, as both extant sampling and the fossil record may be highly incomplete, which leads to an observer bias. For a given character, the state space may be larger than what has been observed in the sample of taxa collected by the researcher. In this case, how many evolutionary rates are needed to even describe transitions between morphological character states may not be clear, potentially leading to model misspecification. To explore the impact of this model misspecification, we simulated character data with varying numbers of character states per character. We then used the data to estimate phylogenetic trees using models of evolution with the correct number of character states and an incorrect number of character states. The results of this study indicate that this observer bias may lead to phylogenetic error, particularly in the branch lengths of trees. If the state space is wrongly assumed to be too large, then we underestimate the branch lengths, and the opposite occurs when the state space is wrongly assumed to be too small. 

Abstract Poor fit between models of sequence or trait evolution and empirical data is known to cause biases and lead to spurious conclusions about evolutionary patterns and processes. Bayesian posterior prediction is a flexible and intuitive approach for detecting such cases of poor fit. However, the expected behavior of posterior predictive tests has never been characterized for evolutionary models, which is critical for their proper interpretation. Here, we show that the expected distribution of posterior predictive P-values is generally not uniform, in contrast to frequentist P-values used for hypothesis testing, and extreme posterior predictive P-values often provide more evidence of poor fit than typically appreciated. Posterior prediction assesses model adequacy under highly favorable circumstances, because the model is fitted to the data, which leads to expected distributions that are often concentrated around intermediate values. Nonuniform expected distributions of P-values do not pose a problem for the application of these tests, however, and posterior predictive P-values can be interpreted as the posterior probability that the fitted model would predict a dataset with a test statistic value as extreme as the value calculated from the observed data. 

Abstract Identifying along which lineages shifts in diversification rates occur is a central goal of comparative phylogenetics; these shifts may coincide with key evolutionary events such as the development of novel morphological characters, the acquisition of adaptive traits, polyploidization or other structural genomic changes, or dispersal to a new habitat and subsequent increase in environmental niche space. However, while multiple methods now exist to estimate diversification rates and identify shifts using phylogenetic topologies, the appropriate use and accuracy of these methods are hotly debated. Here we test whether five Bayesian methods—Bayesian Analysis of Macroevolutionary Mixtures (BAMM), two implementations of the Lineage-Specific Birth–Death–Shift model (LSBDS and PESTO), the approximate Multi-Type Birth–Death model (MTBD; implemented in BEAST2), and the Cladogenetic Diversification Rate Shift model (ClaDS2)—produce comparable results. We apply each of these methods to a set of 65 empirical time-calibrated phylogenies and compare inferences of speciation rate, extinction rate, and net diversification rate. We find that the five methods often infer different speciation, extinction, and net-diversification rates. Consequently, these different estimates may lead to different interpretations of the macroevolutionary dynamics. The different estimates can be attributed to fundamental differences among the compared models. Therefore, the inference of shifts in diversification rates is strongly method dependent. We advise biologists to apply multiple methods to test the robustness of the conclusions or to carefully select the method based on the validity of the underlying model assumptions to their particular empirical system. 

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