J. Comput. Biol. - Phylogenetic stochastic mapping without matrix exponentiation.

Tópicos

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Resumo

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices-an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods.

Resumo Limpo

phylogenet stochast map method reconstruct histori trait chang phylogenet tree relat speciesorgan carri trait stateoftheart method assum trait evolv accord continuoustim markov chain ctmc work well small state space comput slow consider larger state space eg space codon current methodolog reli exponenti ctmc infinitesim rate matricesan oper whose comput complex grow size ctmc state space cube work introduc new approach base ctmc techniqu call uniform use matrix exponenti phylogenet stochast map method base new markov chain mont carlo mcmc algorithm target distribut trait histori condit trait data observ tip tree comput complex mcmc method grow size ctmc state space squar moreov contrast compet matrix exponenti method rate matrix spars can leverag sparsiti increas comput effici algorithm use simul data illustr advantag mcmc algorithm investig larg state space need method outperform matrix exponenti approach show even moder larg state space codon mcmc method can signific faster current use matrix exponenti method

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