Sampling through time and phylodynamic inference with coalescent and birth-death models

Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the birth-death-sampling model, in the context of estimating population size and birth rates in a population growing exponentially according to the birth-death branching process. For sequences sampled at a single time, we found the coalescent and the birth-death-sampling model gave virtually indistinguishable results in terms of the growth rates and fraction of the population sampled, even when sampling from a small population. For sequences sampled at multiple time points, we find that the birth-death model estimators are subject to large bias if the sampling process is misspecified. Since birth-death-sampling models incorporate a model of the sampling process, we show how much of the statistical power of birth-death-sampling models arises from the sequence of sample times and not from the genealogical tree. This motivates the development of a new coalescent estimator, which is augmented with a model of the known sampling process and is potentially more precise than the coalescent that does not use sample time information.Comment: Submitte

Additive uncorrelated relaxed clock models for the dating of genomic epidemiology phylogenies

Phylogenetic dating is one of the most powerful and commonly used methods of drawing epidemiological interpretations from pathogen genomic data. Building such trees requires considering a molecular clock model which represents the rate at which substitutions accumulate on genomes. When the molecular clock rate is constant throughout the tree then the clock is said to be strict, but this is often not an acceptable assumption. Alternatively, relaxed clock models consider variations in the clock rate, often based on a distribution of rates for each branch. However, we show here that the distributions of rates across branches in commonly used relaxed clock models are incompatible with the biological expectation that the sum of the numbers of substitutions on two neighbouring branches should be distributed as the substitution number on a single branch of equivalent length. We call this expectation the additivity property. We further show how assumptions of commonly used relaxed clock models can lead to estimates of evolutionary rates and dates with low precision and biased confidence intervals. We therefore propose a new additive relaxed clock model where the additivity property is satisfied. We illustrate the use of our new additive relaxed clock model on a range of simulated and real datasets, and we show that using this new model leads to more accurate estimates of mean evolutionary rates and ancestral dates

Complex Population Dynamics and the Coalescent Under Neutrality

Estimates of the coalescent effective population size Ne can be poorly correlated with the true population size. The relationship between Ne and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of Ne such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics

Random Networks with Tunable Degree Distribution and Clustering

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references, reorganized reference

Share2Quit: Web-Based Peer-Driven Referrals for Smoking Cessation

BACKGROUND: Smoking is the number one preventable cause of death in the United States. Effective Web-assisted tobacco interventions are often underutilized and require new and innovative engagement approaches. Web-based peer-driven chain referrals successfully used outside health care have the potential for increasing the reach of Internet interventions. OBJECTIVE: The objective of our study was to describe the protocol for the development and testing of proactive Web-based chain-referral tools for increasing the access to Decide2Quit.org, a Web-assisted tobacco intervention system. METHODS: We will build and refine proactive chain-referral tools, including email and Facebook referrals. In addition, we will implement respondent-driven sampling (RDS), a controlled chain-referral sampling technique designed to remove inherent biases in chain referrals and obtain a representative sample. We will begin our chain referrals with an initial recruitment of former and current smokers as seeds (initial participants) who will be trained to refer current smokers from their social network using the developed tools. In turn, these newly referred smokers will also be provided the tools to refer other smokers from their social networks. We will model predictors of referral success using sample weights from the RDS to estimate the success of the system in the targeted population. RESULTS: This protocol describes the evaluation of proactive Web-based chain-referral tools, which can be used in tobacco interventions to increase the access to hard-to-reach populations, for promoting smoking cessation. CONCLUSIONS: Share2Quit represents an innovative advancement by capitalizing on naturally occurring technology trends to recruit smokers to Web-assisted tobacco interventions

Edge-Based Compartmental Modeling for Infectious Disease Spread Part III: Disease and Population Structure

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of the disease or population from the simplistic assumptions of Part I. We allow the population to have structure due to effects such as demographic detail or multiple types of risk behavior the disease to have more complicated natural history. We introduce these modifications in the static network context, though it is straightforward to incorporate them into dynamic networks. We also consider serosorting, which requires using the dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here

Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes all individuals have the same contact rate and contacts are fleeting. This paper is the first of three investigating edge-based compartmental modeling, a technique eliminating these assumptions. In this paper, we derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of contact duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model. This paper focuses on the technique and how to apply it in different contexts. The companion papers investigate choosing the appropriate level of complexity for a model and how to apply edge-based compartmental modeling to populations with various sub-structures

Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased