Phylogenetic Stochastic Mapping without Matrix Exponentiation

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organisms carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and work 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, that 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.Comment: 33 pages, including appendice

Phylodynamic Patterns in Pathogen Ecology and Evolution.

The rapid evolution of viral pathogens requires us to consider epidemiological, ecological and evolutionary processes as coupled together and occurring at the same timescale. Rotavirus and influenza account for high levels of morbidity and mortality worldwide and are two important examples of such dynamics. In this work, I investigate the different evolutionary and ecological processes that shape the antigenic structure and phylogenetic characteristics of these two viruses. In the first part of my work, I use a theoretical model of influenza A/H3N2 to identify the relative importance of antigenic novelty, competition between lineages, and changes in the susceptibility of the host population to circulating strains in determining the evolutionary and epidemiological trajectory of the virus. I develop this model further to correspond with patterns of immunity and infection observed in rotavirus, and investigate how reassortment, the swapping of gene segments between viruses, influences the formation and replacement of rotavirus genotypes through immune mediated processes. In the second part of my work, I use a tool (SeasMig), which I developed, to infer alternative stochastically generated migration and mutation events along phylogenetic trees in a Bayesian manner. Using SeasMig, I first show how the seasonality of A/H3N2 influenza incidence corresponds to rates of immigration and emigration of the virus. Subsequently, I tease out the different evolutionary and ecological processes, which drive changes in the US rotavirus population following onset of routine vaccination. My work has implications for identifying likely evolutionary mechanisms, which may lead to reduced vaccine efficacy, and for vaccine strain selection.PhDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113494/1/dzinder_1.pd

Bayesian Phylogeography Finds Its Roots

As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers unique opportunities to engage in this statistical endeavor. Here we introduce a Bayesian framework for inference, visualization and hypothesis testing of phylogeographic history. By implementing character mapping in a Bayesian software that samples time-scaled phylogenies, we enable the reconstruction of timed viral dispersal patterns while accommodating phylogenetic uncertainty. Standard Markov model inference is extended with a stochastic search variable selection procedure that identifies the parsimonious descriptions of the diffusion process. In addition, we propose priors that can incorporate geographical sampling distributions or characterize alternative hypotheses about the spatial dynamics. To visualize the spatial and temporal information, we summarize inferences using virtual globe software. We describe how Bayesian phylogeography compares with previous parsimony analysis in the investigation of the influenza A H5N1 origin and H5N1 epidemiological linkage among sampling localities. Analysis of rabies in West African dog populations reveals how virus diffusion may enable endemic maintenance through continuous epidemic cycles. From these analyses, we conclude that our phylogeographic framework will make an important asset in molecular epidemiology that can be easily generalized to infer biogeogeography from genetic data for many organisms

Seasonality in the migration and establishment of H3N2 Influenza lineages with epidemic growth and decline

Background: Influenza A/H3N2 has been circulating in humans since 1968, causing considerable morbidity and mortality. Although H3N2 incidence is highly seasonal, how such seasonality contributes to global phylogeographic migration dynamics has not yet been established. Results: Incorporating seasonally varying migration rates improves the modeling of migration. In our global model, windows of increased immigration map to the seasonal timing of epidemic spread, while windows of increased emigration map to epidemic decline. Seasonal patterns also correlate with the probability that local lineages go extinct and fail to contribute to long term viral evolution, as measured through the trunk of the phylogeny. However, the fraction of the trunk in each community was found to be better determined by its overall human population size Conclusions: Seasonal migration and rapid turnover within regions is sustained by the invasion of 'fertile epidemic grounds' at the end of older epidemics. Thus, the current emphasis on connectivity, including air-travel, should be complemented with a better understanding of the conditions and timing required for successful establishment.Models which account for migration seasonality will improve our understanding of the seasonal drivers of influenza,enhance epidemiological predictions, and ameliorate vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread. Further work is also needed on additional conditions that contribute to the persistence and long term evolution of influenza within the human population,such as spatial heterogeneity with respect to climate and seasonalityComment: in BMC Evolutionary Biology 2014, 1

Optimization strategies for fast detection of positive selection on phylogenetic trees

Motivation: The detection of positive selection is widely used to study gene and genome evolution, but its application remains limited by the high computational cost of existing implementations. We present a series of computational optimizations for more efficient estimation of the likelihood function on large-scale phylogenetic problems. We illustrate our approach using the branch-site model of codon evolution. Results: We introduce novel optimization techniques that substantially outperform both CodeML from the PAML package and our previously optimized sequential version SlimCodeML. These techniques can also be applied to other likelihood-based phylogeny software. Our implementation scales well for large numbers of codons and/or species. It can therefore analyse substantially larger datasets than CodeML. We evaluated FastCodeML on different platforms and measured average sequential speedups of FastCodeML (single-threaded) versus CodeML of up to 5.8, average speedups of FastCodeML (multi-threaded) versus CodeML on a single node (shared memory) of up to 36.9 for 12 CPU cores, and average speedups of the distributed FastCodeML versus CodeML of up to 170.9 on eight nodes (96 CPU cores in total). Availability and implementation: ftp://ftp.vital-it.ch/tools/FastCodeML/. Contact: [email protected] or [email protected]

Optimization strategies for fast detection of positive selection on phylogenetic trees.

MOTIVATION: The detection of positive selection is widely used to study gene and genome evolution, but its application remains limited by the high computational cost of existing implementations. We present a series of computational optimizations for more efficient estimation of the likelihood function on large-scale phylogenetic problems. We illustrate our approach using the branch-site model of codon evolution. RESULTS: We introduce novel optimization techniques that substantially outperform both CodeML from the PAML package and our previously optimized sequential version SlimCodeML. These techniques can also be applied to other likelihood-based phylogeny software. Our implementation scales well for large numbers of codons and/or species. It can therefore analyse substantially larger datasets than CodeML. We evaluated FastCodeML on different platforms and measured average sequential speedups of FastCodeML (single-threaded) versus CodeML of up to 5.8, average speedups of FastCodeML (multi-threaded) versus CodeML on a single node (shared memory) of up to 36.9 for 12 CPU cores, and average speedups of the distributed FastCodeML versus CodeML of up to 170.9 on eight nodes (96 CPU cores in total).Availability and implementation: ftp://ftp.vital-it.ch/tools/FastCodeML/. CONTACT: [email protected] or [email protected]

On FPGA implementations for bioinformatics, neural prosthetics and reinforcement learning problems.

Mak Sui Tung Terrence.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 132-142).Abstracts in English and Chinese.Abstract --- p.iList of Tables --- p.ivList of Figures --- p.vAcknowledgements --- p.ixChapter 1. --- Introduction --- p.1Chapter 1.1 --- Bioinformatics --- p.1Chapter 1.2 --- Neural Prosthetics --- p.4Chapter 1.3 --- Learning in Uncertainty --- p.5Chapter 1.4 --- The Field Programmable Gate Array (FPGAs) --- p.7Chapter 1.5 --- Scope of the Thesis --- p.10Chapter 2. --- A Hybrid GA-DP Approach for Searching Equivalence Sets --- p.14Chapter 2.1 --- Introduction --- p.16Chapter 2.2 --- Equivalence Set Criterion --- p.18Chapter 2.3 --- Genetic Algorithm and Dynamic Programming --- p.19Chapter 2.3.1 --- Genetic Algorithm Formulation --- p.20Chapter 2.3.2 --- Bounded Mutation --- p.21Chapter 2.3.3 --- Conditioned Crossover --- p.22Chapter 2.3.4 --- Implementation --- p.22Chapter 2.4 --- FPGAs Implementation of GA-DP --- p.24Chapter 2.4.1 --- System Overview --- p.25Chapter 2.4.2 --- Parallel Computation for Transitive Closure --- p.26Chapter 2.4.3 --- Genetic Operation Realization --- p.28Chapter 2.5 --- Discussion --- p.30Chapter 2.6 --- Limitation and Future Work --- p.33Chapter 2.7 --- Conclusion --- p.34Chapter 3. --- An FPGA-based Architecture for Maximum-Likelihood Phylogeny Evaluation --- p.35Chapter 3.1 --- Introduction --- p.36Chapter 3.2 --- Maximum-Likelihood Model --- p.39Chapter 3.3 --- Hardware Mapping for Pruning Algorithm --- p.41Chapter 3.3.1 --- Related Works --- p.41Chapter 3.3.2 --- Number Representation --- p.42Chapter 3.3.3 --- Binary Tree Representation --- p.43Chapter 3.3.4 --- Binary Tree Traversal --- p.45Chapter 3.3.5 --- Maximum-Likelihood Evaluation Algorithm --- p.46Chapter 3.4 --- System Architecture --- p.49Chapter 3.4.1 --- Transition Probability Unit --- p.50Chapter 3.4.2 --- State-Parallel Computation Unit --- p.51Chapter 3.4.3 --- Error Computation --- p.54Chapter 3.5 --- Discussion --- p.56Chapter 3.5.1 --- Hardware Resource Consumption --- p.56Chapter 3.5.2 --- Delay Evaluation --- p.57Chapter 3.6 --- Conclusion --- p.59Chapter 4. --- Field Programmable Gate Array Implementation of Neuronal Ion Channel Dynamics --- p.61Chapter 4.1 --- Introduction --- p.62Chapter 4.2 --- Background --- p.63Chapter 4.2.1 --- Analog VLSI Model for Hebbian Synapse --- p.63Chapter 4.2.2 --- A Unifying Model of Bi-directional Synaptic Plasticity --- p.64Chapter 4.2.3 --- Non-NMDA Receptor Channel Regulation --- p.65Chapter 4.3 --- FPGAs Implementation --- p.65Chapter 4.3.1 --- FPGA Design Flow --- p.65Chapter 4.3.2 --- Digital Model of NMD A and AMPA receptors --- p.65Chapter 4.3.3 --- Synapse Modification --- p.67Chapter 4.4 --- Results --- p.68Chapter 4.4.1 --- Simulation Results --- p.68Chapter 4.5 --- Discussion --- p.70Chapter 4.6 --- Conclusion --- p.71Chapter 5. --- Continuous-Time and Discrete-Time Inference Networks for Distributed Dynamic Programming --- p.72Chapter 5.1 --- Introduction --- p.74Chapter 5.2 --- Background --- p.77Chapter 5.2.1 --- Markov decision process (MDPs) --- p.78Chapter 5.2.2 --- Learning in the MDPs --- p.80Chapter 5.2.3 --- Bellman Optimal Criterion --- p.80Chapter 5.2.4 --- Value Iteration --- p.81Chapter 5.3 --- A Computational Framework for Continuous-Time Inference Network --- p.82Chapter 5.3.1 --- Binary Relation Inference Network --- p.83Chapter 5.3.2 --- Binary Relation Inference Network for MDPs --- p.85Chapter 5.3.3 --- Continuous-Time Inference Network for MDPs --- p.87Chapter 5.4 --- Convergence Consideration --- p.88Chapter 5.5 --- Numerical Simulation --- p.90Chapter 5.5.1 --- Example 1: Random Walk --- p.90Chapter 5.5.2 --- Example 2: Random Walk on a Grid --- p.94Chapter 5.5.3 --- Example 3: Stochastic Shortest Path Problem --- p.97Chapter 5.5.4 --- Relationships Between λ and γ --- p.99Chapter 5.6 --- Discrete-Time Inference Network --- p.100Chapter 5.6.1 --- Results --- p.101Chapter 5.7 --- Conclusion --- p.102Chapter 6. --- On Distributed g-Learning Network --- p.104Chapter 6.1 --- Introduction --- p.105Chapter 6.2 --- Distributed Q-Learniing Network --- p.108Chapter 6.2.1 --- Distributed Q-Learning Network --- p.109Chapter 6.2.2 --- Q-Learning Network Architecture --- p.111Chapter 6.3 --- Experimental Results --- p.114Chapter 6.3.1 --- Random Walk --- p.114Chapter 6.3.2 --- The Shortest Path Problem --- p.116Chapter 6.4 --- Discussion --- p.120Chapter 6.4.1 --- Related Work --- p.121Chapter 6.5 --- FPGAs Implementation --- p.122Chapter 6.5.1 --- Distributed Registering Approach --- p.123Chapter 6.5.2 --- Serial BRAM Storing Approach --- p.124Chapter 6.5.3 --- Comparison --- p.125Chapter 6.5.4 --- Discussion --- p.127Chapter 6.6 --- Conclusion --- p.128Chapter 7. --- Summary --- p.129Bibliography --- p.132AppendixChapter A. --- Simplified Floating-Point Arithmetic --- p.143Chapter B. --- "Logarithm, Exponential and Division Implementation" --- p.144Chapter B.1 --- Introduction --- p.144Chapter B.2 --- Approximation Scheme --- p.145Chapter B.2.1 --- Logarithm --- p.145Chapter B.2.2 --- Exponentiation --- p.147Chapter B.2.3 --- Division --- p.148Chapter C. --- Analog VLSI Implementation --- p.150Chapter C.1 --- Site Function --- p.150Chapter C.1.1 --- Multiplication Cell --- p.150Chapter C.2 --- The Unit Function --- p.153Chapter C.3 --- The Inference Network Computation --- p.154Chapter C.4 --- Layout --- p.157Chapter C.5 --- Fabrication --- p.159Chapter C.5.1 --- Testing and Characterization --- p.16

Efficient Bayesian inference under the structured coalescent

Motivation: Population structure significantly affects evolutionary dynamics. Such structure may be due to spatial segregation, but may also reflect any other gene-flow-limiting aspect of a model. In combination with the structured coalescent, this fact can be used to inform phylogenetic tree reconstruction, as well as to infer parameters such as migration rates and subpopulation sizes from annotated sequence data. However, conducting Bayesian inference under the structured coalescent is impeded by the difficulty of constructing Markov Chain Monte Carlo (MCMC) sampling algorithms (samplers) capable of efficiently exploring the state space. Results: In this article, we present a new MCMC sampler capable of sampling from posterior distributions over structured trees: timed phylogenetic trees in which lineages are associated with the distinct subpopulation in which they lie. The sampler includes a set of MCMC proposal functions that offer significant mixing improvements over a previously published method. Furthermore, its implementation as a BEAST 2 package ensures maximum flexibility with respect to model and prior specification. We demonstrate the usefulness of this new sampler by using it to infer migration rates and effective population sizes of H3N2 influenza between New Zealand, New York and Hong Kong from publicly available hemagglutinin (HA) gene sequences under the structured coalescent. Availability and implementation: The sampler has been implemented as a publicly available BEAST 2 package that is distributed under version 3 of the GNU General Public License at http://compevol.github.io/MultiTypeTree. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin