ABSTRACT
Department of Statistics, University of Washington, Seattle, Seattle, Washington, USA
Mandev S. Gill
Department of Biostatistics, University of California, Los Angeles, Los Angeles, California, USA
Marc A. Suchard
Departments of Biomathematics, Human Genetics, and Biostatistics, University of California, Los Angeles, Los Angeles, California, USA
Vladimir N. Minin
Department of Statistics, University of Washington, Seattle, Seattle, Washington, USA
CONTENTS
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 11.2 General model formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
11.2.1 Likelihood for sequence alignment . . . . . . . . . . . . . . . . . . . . . . 232 11.2.2 Coalescent prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 11.2.3 Posterior inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
11.3 Priors on effective population size trajectory . . . . . . . . . . . . . . . . . . . . 236 11.3.1 Multiple change-point models . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 11.3.2 Coalescent as a point process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 11.3.3 Gaussian process-based nonparametrics . . . . . . . . . . . . . . . . . 237
11.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 11.4.1 Fixed genealogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 11.4.2 Accounting for genealogical uncertainty . . . . . . . . . . . . . . . . 241
11.5 Extensions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 11.5.1 Multiple loci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 11.5.2 Effect of population structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 11.5.3 Coalescent and infectious disease dynamics . . . . . . . . . . . . . 245
Algorithms, and
Changes in population size affect the variability of population gene frequencies in natural populations, allowing genetic variation in present-day and recent-past molecular sequence data to help recover the more distant past demographic history of the population. This variability also enables researchers to examine the factors driving past population dynamics and to establish molecular surveillance of emerging infectious diseases. For example, Campos et al. (2010) analyze ancient and modern musk ox mtDNA samples dated from 56, 900 radiocarbon years old to present and recover the population dynamics throughout the late Pleistocene to the present; 63 RNA sequences of hepatitis C virus (HCV) obtained in 1993 effectively reveal the dynamics of HCV infections in Egypt over the past century (Pybus et al., 2003); and human influenza A/H3N2 subtype sequences sampled over a 12-year period in New York state return estimates of the seasonal population dynamics of human influenza A/H3N2 (Rambaut et al., 2008).
