Dataset Information

A Model of Indel Evolution by Finite-State, Continuous-Time Machines.

ABSTRACT: We introduce a systematic method of approximating finite-time transition probabilities for continuous-time insertion-deletion models on sequences. The method uses automata theory to describe the action of an infinitesimal evolutionary generator on a probability distribution over alignments, where both the generator and the alignment distribution can be represented by pair hidden Markov models (HMMs). In general, combining HMMs in this way induces a multiplication of their state spaces; to control this, we introduce a coarse-graining operation to keep the state space at a constant size. This leads naturally to ordinary differential equations for the evolution of the transition probabilities of the approximating pair HMM. The TKF91 model emerges as an exact solution to these equations for the special case of single-residue indels. For the more general case of multiple-residue indels, the equations can be solved by numerical integration. Using simulated data, we show that the resulting distribution over alignments, when compared to previous approximations, is a better fit over a broader range of parameters. We also propose a related approach to develop differential equations for sufficient statistics to estimate the underlying instantaneous indel rates by expectation maximization. Our code and data are available at https://github.com/ihh/trajectory-likelihood.

SUBMITTER: Holmes I

PROVIDER: S-EPMC7768254 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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A Model of Indel Evolution by Finite-State, Continuous-Time Machines.

Holmes Ian I

Genetics 20201005 4

We introduce a systematic method of approximating finite-time transition probabilities for continuous-time insertion-deletion models on sequences. The method uses automata theory to describe the action of an infinitesimal evolutionary generator on a probability distribution over alignments, where both the generator and the alignment distribution can be represented by pair hidden Markov models (HMMs). In general, combining HMMs in this way induces a multiplication of their state spaces; to contro ...[more]

PMID: 33020189

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Project description:BackgroundState-space models are important tools for quality control and analysis of error-prone animal movement data. The near real-time (within 24 h) capability of the Argos satellite system can aid dynamic ocean management of human activities by informing when animals enter wind farms, shipping lanes, and other intensive use zones. This capability also facilitates the use of ocean observations from animal-borne sensors in operational ocean forecasting models. Such near real-time data provision requires rapid, reliable quality control to deal with error-prone Argos locations.MethodsWe formulate a continuous-time state-space model to filter the three types of Argos location data (Least-Squares, Kalman filter, and Kalman smoother), accounting for irregular timing of observations. Our model is deliberately simple to ensure speed and reliability for automated, near real-time quality control of Argos location data. We validate the model by fitting to Argos locations collected from 61 individuals across 7 marine vertebrates and compare model-estimated locations to contemporaneous GPS locations. We then test assumptions that Argos Kalman filter/smoother error ellipses are unbiased, and that Argos Kalman smoother location accuracy cannot be improved by subsequent state-space modelling.ResultsEstimation accuracy varied among species with Root Mean Squared Errors usually <5 km and these decreased with increasing data sampling rate and precision of Argos locations. Including a model parameter to inflate Argos error ellipse sizes in the north - south direction resulted in more accurate location estimates. Finally, in some cases the model appreciably improved the accuracy of the Argos Kalman smoother locations, which should not be possible if the smoother is using all available information.ConclusionsOur model provides quality-controlled locations from Argos Least-Squares or Kalman filter data with accuracy similar to or marginally better than Argos Kalman smoother data that are only available via fee-based reprocessing. Simplicity and ease of use make the model suitable both for automated quality control of near real-time Argos data and for manual use by researchers working with historical Argos data.

Dataset Information

A Model of Indel Evolution by Finite-State, Continuous-Time Machines.

Publications

A Model of Indel Evolution by Finite-State, Continuous-Time Machines.

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