Aaron A. King

Bio: Aaron A. King is an academic researcher from University of Michigan. The author has contributed to research in topics: Population & Markov process. The author has an hindex of 36, co-authored 98 publications receiving 5874 citations. Previous affiliations of Aaron A. King include Fred Hutchinson Cancer Research Center & University of Tennessee.

Phylogenetic Comparative Analysis: A Modeling Approach for Adaptive Evolution

Abstract: Biologists employ phylogenetic comparative methods to study adaptive evolution. However, none of the popular methods model selection directly. We explain and develop a method based on the Ornstein-Uhlenbeck (OU) process, first proposed by Hansen. Ornstein-Uhlenbeck models incorporate both selection and drift and are thus qualitatively different from, and more general than, pure drift models based on Brownian motion. Most importantly, OU mod- els possess selective optima that formalize the notion of adaptive zone. In this article, we develop the method for one quantitative character, discuss interpretations of its parameters, and provide code implementing the method. Our approach allows us to translate hy- potheses regarding adaptation in different selective regimes into ex- plicit models, to test the models against data using maximum-like- lihood-based model selection techniques, and to infer details of the evolutionary process. We illustrate the method using two worked examples. Relative to existing approaches, the direct modeling ap- proach we demonstrate allows one to explore more detailed hy- potheses and to utilize more of the information content of com- parative data sets than existing methods. Moreover, the use of a model selection framework to simultaneously compare a variety of hy- potheses advances our ability to assess alternative evolutionary explanations.

Inference for nonlinear dynamical systems

Abstract: Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in these models have been a constraint on their application. We present a new method that makes maximum likelihood estimation feasible for partially-observed nonlinear stochastic dynamical systems (also known as state-space models) where this was not previously the case. The method is based on a sequence of filtering operations which are shown to converge to a maximum likelihood parameter estimate. We make use of recent advances in nonlinear filtering in the implementation of the algorithm. We apply the method to the study of cholera in Bangladesh. We construct confidence intervals, perform residual analysis, and apply other diagnostics. Our analysis, based upon a model capturing the intrinsic nonlinear dynamics of the system, reveals some effects overlooked by previous studies.

Inapparent infections and cholera dynamics

Abstract: In many infectious diseases, an unknown fraction of infections produce symptoms mild enough to go unrecorded, a fact that can seriously compromise the interpretation of epidemiological records This is true for cholera, a pandemic bacterial disease, where estimates of the ratio of asymptomatic to symptomatic infections have ranged from 3 to 100 (refs 1-5) In the absence of direct evidence, understanding of fundamental aspects of cholera transmission, immunology and control has been based on assumptions about this ratio and about the immunological consequences of inapparent infections Here we show that a model incorporating high asymptomatic ratio and rapidly waning immunity, with infection both from human and environmental sources, explains 50 yr of mortality data from 26 districts of Bengal, the pathogen's endemic home We find that the asymptomatic ratio in cholera is far higher than had been previously supposed and that the immunity derived from mild infections wanes much more rapidly than earlier analyses have indicated We find, too, that the environmental reservoir (free-living pathogen) is directly responsible for relatively few infections but that it may be critical to the disease's endemicity Our results demonstrate that inapparent infections can hold the key to interpreting the patterns of disease outbreaks New statistical methods, which allow rigorous maximum likelihood inference based on dynamical models incorporating multiple sources and outcomes of infection, seasonality, process noise, hidden variables and measurement error, make it possible to test more precise hypotheses and obtain unexpected results Our experience suggests that the confrontation of time-series data with mechanistic models is likely to revise our understanding of the ecology of many infectious diseases

Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity

Abstract: Dengue, a mosquito-borne virus of humans, infects over 50 million people annually. Infection with any of the four dengue serotypes induces protective immunity to that serotype, but does not confer long-term protection against infection by other serotypes. The immunological interactions between serotypes are of central importance in understanding epidemiological dynamics and anticipating the impact of dengue vaccines. We analysed a 38-year time series with 12 197 serotyped dengue infections from a hospital in Bangkok, Thailand. Using novel mechanistic models to represent different hypothesized immune interactions between serotypes, we found strong evidence that infection with dengue provides substantial short-term cross-protection against other serotypes (approx. 1–3 years). This is the first quantitative evidence that short-term cross-protection exists since human experimental infection studies performed in the 1950s. These findings will impact strategies for designing dengue vaccine studies, future multi-strain modelling efforts, and our understanding of evolutionary pressures in multi-strain disease systems.

Plug-and-play inference for disease dynamics: measles in large and small populations as a case study.

Abstract: Statistical inference for mechanistic models of partially observed dynamic systems is an active area of research. Most existing inference methods place substantial restrictions upon the form of models that can be fitted and hence upon the nature of the scientific hypotheses that can be entertained and the data that can be used to evaluate them. In contrast, the so-called plug-and-play methods require only simulations from a model and are thus free of such restrictions. We show the utility of the plug-and-play approach in the context of an investigation of measles transmission dynamics. Our novel methodology enables us to ask and answer questions that previous analyses have been unable to address. Specifically, we demonstrate that plug-and-play methods permit the development of a modelling and inference framework applicable to data from both large and small populations. We thereby obtain novel insights into the nature of heterogeneity in mixing and comment on the importance of including extra-demographic stochasticity as a means of dealing with environmental stochasticity and model misspecification. Our approach is readily applicable to many other epidemiological and ecological systems.

Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.

Abstract: The relationship between the two estimates of genetic variation at the DNA level, namely the number of segregating sites and the average number of nucleotide differences estimated from pairwise comparison, is investigated. It is found that the correlation between these two estimates is large when the sample size is small, and decreases slowly as the sample size increases. Using the relationship obtained, a statistical method for testing the neutral mutation hypothesis is developed. This method needs only the data of DNA polymorphism, namely the genetic variation within population at the DNA level. A simple method of computer simulation, that was used in order to obtain the distribution of a new statistic developed, is also presented. Applying this statistical method to the five regions of DNA sequences in Drosophila melanogaster, it is found that large insertion/deletion (greater than 100 bp) is deleterious. It is suggested that the natural selection against large insertion/deletion is so weak that a large amount of variation is maintained in a population.

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2)

Abstract: Estimation of the prevalence and contagiousness of undocumented novel coronavirus [severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2)] infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here, we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model, and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV-2, including the fraction of undocumented infections and their contagiousness. We estimate that 86% of all infections were undocumented [95% credible interval (CI): 82–90%] before the 23 January 2020 travel restrictions. The transmission rate of undocumented infections per person was 55% the transmission rate of documented infections (95% CI: 46–62%), yet, because of their greater numbers, undocumented infections were the source of 79% of the documented cases. These findings explain the rapid geographic spread of SARS-CoV-2 and indicate that containment of this virus will be particularly challenging.

Stochastic Differential Equations

Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

GEIGER: investigating evolutionary radiations.

Abstract: Summary: GEIGER is a new software package, written in the R language, to describe evolutionary radiations. GEIGER can carry out simulations, parameter estimation and statistical hypothesis testing. Additionally, GEIGER’s simulation algorithms can be used to analyze the statistical power of comparative approaches. Availability: This open source software is written entirely in the R language and is freely available through the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org/.