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Citation for Study 16060

About Citation title: "A non-stationary Markov model detects directional evolution in hymenopteran morphology".
About Study name: "A non-stationary Markov model detects directional evolution in hymenopteran morphology".
About This study is part of submission 16060 (Status: Published).


Klopfstein S., Vilhelmsen L., & Ronquist F. 2015. A non-stationary Markov model detects directional evolution in hymenopteran morphology. Systematic Biology, 64(6): 1089-1103.


  • Klopfstein S.
  • Vilhelmsen L.
  • Ronquist F. Phone +46-8 5195 4094


Directional evolution has played an important role in shaping the morphological, ecological and molecular diversity of life. However, standard substitution models assume stationarity of the evolutionary process over the time scale examined, thus hampering the study of directionality. Here we explore a simple, non-stationary model of evolution for discrete data, which assumes that the state frequencies at the root differ from the equilibrium frequencies of the homogeneous evolutionary process along the rest of the tree (i.e., the process is non-stationary, non-reversible, but homogeneous). Within this framework, we develop a Bayesian approach for testing directional versus stationary evolution using a reversible-jump algorithm. Simulations show that when only data from extant taxa is available, the success in inferring directionality is strongly dependent on the evolutionary rate, the shape of the tree, the relative branch lengths, and the number of taxa. Given suitable evolutionary rates (0.1 to 0.5 expected substitutions between root and tips), accounting for directionality improves tree inference and often allows correct rooting of the tree without the use of an outgroup. As an empirical test, we apply our method to study directional evolution in hymenopteran morphology. We focus on three character systems: wing veins, muscles, and sclerites. We find strong support for a trend towards loss of wing veins and muscles, while stationarity cannot be ruled out for sclerites. Adding fossil and time information in a total-evidence dating approach, we show that accounting for directionality results in more precise estimates not only of the ancestral state at the root of the tree, but also of the divergence times. Our model relaxes the assumption of stationarity and reversibility by adding a minimum of additional parameters, and is thus well suited to studying the nature of the evolutionary process in datasets of limited size, such as morphology.


continuous-time Markov model, Bayesian inference, directional selection, positive selection, neutral evolution, Symphyta, Hymenoptera, morphology, non-stationary

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