Evaluating consumptive and nonconsumptive predator effects on prey density using field time-series data.

Determining the degree to which predation affects prey abundance in natural communities constitutes a key goal of ecological research. Predators can affect prey through both consumptive effects (CEs) and nonconsumptive effects (NCEs), although the contributions of each mechanism to the density of prey populations remain largely hypothetical in most systems. Common statistical methods applied to time-series data cannot elucidate the mechanisms responsible for hypothesized predator effects on prey density (e.g., differentiate CEs from NCEs), nor can they provide parameters for predictive models. State-space models (SSMs) applied to time-series data offer a way to meet these goals. Here, we employ SSMs to assess effects of an invasive predatory zooplankter, Bythotrephes longimanus, on an important prey species, Daphnia mendotae, in Lake Michigan. We fit mechanistic models in an SSM framework to seasonal time series (1994-2012) using a recently developed, maximum-likelihood-based optimization method, iterated filtering, which can overcome challenges in ecological data (e.g., nonlinearities, measurement error, and irregular sampling intervals). Our results indicate that B. longimanus strongly influences D. mendotae dynamics, with mean annual peak densities of B. longimanus observed in Lake Michigan estimated to cause a 61% reduction in D. mendotae population growth rate and a 59% reduction in peak biomass density. Further, the observed B. longimanus effect is most consistent with an NCE via reduced birth rates. The SSM approach also provided estimates for key biological parameters (e.g., demographic rates) and the contribution of dynamic stochasticity and measurement error. Our study therefore provides evidence derived directly from survey data that the invasive zooplankter B. longimanus is affecting zooplankton demographics and offer parameter estimates needed to inform predictive models that explore the effect of B. longimanus under different scenarios, such as climate change.

Monte Carlo profile confidence intervals for dynamic systems.

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.

Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo.

Genetic sequences from pathogens can provide information about infectious disease dynamics that may supplement or replace information from other epidemiological observations. Most currently available methods first estimate phylogenetic trees from sequence data, then estimate a transmission model conditional on these phylogenies. Outside limited classes of models, existing methods are unable to enforce logical consistency between the model of transmission and that underlying the phylogenetic reconstruction. Such conflicts in assumptions can lead to bias in the resulting inferences. Here, we develop a general, statistically efficient, plug-and-play method to jointly estimate both disease transmission and phylogeny using genetic data and, if desired, other epidemiological observations. This method explicitly connects the model of transmission and the model of phylogeny so as to avoid the aforementioned inconsistency. We demonstrate the feasibility of our approach through simulation and apply it to estimate stage-specific infectiousness in a subepidemic of human immunodeficiency virus in Detroit, Michigan. In a supplement, we prove that our approach is a valid sequential Monte Carlo algorithm. While we focus on how these methods may be applied to population-level models of infectious disease, their scope is more general. These methods may be applied in other biological systems where one seeks to infer population dynamics from genetic sequences, and they may also find application for evolutionary models with phenotypic rather than genotypic data.

Dynamics affecting the risk of silent circulation when oral polio vaccination is stopped.

Waning immunity could allow transmission of polioviruses without causing poliomyelitis by promoting silent circulation (SC). Undetected SC when oral polio vaccine (OPV) use is stopped could cause difficult to control epidemics. Little is known about waning. To develop theory about what generates SC, we modeled a range of waning patterns. We varied both OPV and wild polio virus (WPV) transmissibility, the time from beginning vaccination to reaching low polio levels, and the infection to paralysis ratio (IPR). There was longer SC when waning continued over time rather than stopping after a few years, when WPV transmissibility was higher or OPV transmissibility was lower, and when the IPR was higher. These interacted in a way that makes recent emergence of prolonged SC a possibility. As the time to reach low infection levels increased, vaccine rates needed to eliminate polio increased and a threshold was passed where prolonged low-level SC emerged. These phenomena were caused by increased contributions to the force of infection from reinfections. The resulting SC occurs at low levels that would be difficult to detect using environmental surveillance. For all waning patterns, modest levels of vaccination of adults shortened SC. Previous modeling studies may have missed these phenomena because (1) they used models with no or very short duration waning and (2) they fit models to paralytic polio case counts. Our analyses show that polio case counts cannot predict SC because nearly identical polio case count patterns can be generated by a range of waning patterns that generate different patterns of SC. We conclude that the possibility of prolonged SC is real but unquantified, that vaccinating modest fractions of adults could reduce SC risk, and that joint analysis of acute flaccid paralysis and environmental surveillance data can help assess SC risks and ensure low risks before stopping OPV.

Dynamic Variation in Sexual Contact Rates in a Cohort of HIV-Negative Gay Men.

Human immunodeficiency virus (HIV) transmission models that include variability in sexual behavior over time have shown increased incidence, prevalence, and acute-state transmission rates for a given population risk profile. This raises the question of whether dynamic variation in individual sexual behavior is a real phenomenon that can be observed and measured. To study this dynamic variation, we developed a model incorporating heterogeneity in both between-person and within-person sexual contact patterns. Using novel methodology that we call iterated filtering for longitudinal data, we fitted this model by maximum likelihood to longitudinal survey data from the Centers for Disease Control and Prevention's Collaborative HIV Seroincidence Study (1992-1995). We found evidence for individual heterogeneity in sexual behavior over time. We simulated an epidemic process and found that inclusion of empirically measured levels of dynamic variation in individual-level sexual behavior brought the theoretical predictions of HIV incidence into closer alignment with reality given the measured per-act probabilities of transmission. The methods developed here provide a framework for quantifying variation in sexual behaviors that helps in understanding the HIV epidemic among gay men.

Inference for nonlinear dynamical systems.

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.