Abstract
ABSTRACTPhylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous. This is despite biological intuition that evolution is rather punctuated than gradual. On the other hand, there has been a number of recent proposals of evolutionary models with jump components. However, as we are only beginning to understand the behaviour of branching Ornstein–Uhlenbeck (OU) processes the asymptotics of branching OU processes with jumps is an even greater unknown. In this work we build up on a previous study concerning OU with jumps evolution on a pure birth tree. We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process. We furthermore, also use this work to illustrate the simulation and graphic generation possibilities of the mvSLOUCH package.
Publisher
Cold Spring Harbor Laboratory
Reference21 articles.
1. CLT for Ornstein-Uhlenbeck branching particle system;Elect. J. Probab,2015
2. K. Bartoszek : The Laplace Motion in Phylogenetic Comparative Methods, Proceedings of the Eighteenth National Conference on Applications of Mathematics in Biology and Medicine, Krynica Morska, 2012, pp. 25–30.
3. Quantifying the effects of anagenetic and cladogenetic evolution;Math. Biosci,2014
4. K. Bartoszek : A Central Limit Theorem for punctuated equilibrium, ArXiv e-prints (2016), 1602.05189.
5. A phylogenetic comparative method for studying multivariate adaptation