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State–space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics, animal movement, and capture–recapture data, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological variation and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been proposed. However, the variety and complexity of these procedures can limit the ability of ecologists to formulate and fit their own SSMs. We provide the knowledge for ecologists to create SSMs that are robust to common, and often hidden, estimation problems, and the model selection and validation tools that can help them assess how well their models fit their data. We present a review of SSMs that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications. The review is accompanied by an in-depth tutorial that demonstrates how SSMs can be fitted and validated in R. Together, the review and tutorial present an introduction to SSMs that will help ecologists to formulate, fit, and validate their models.

Sustained and coordinated vaccination efforts have brought polio eradication within reach. Anticipating the eradication of wild poliovirus (WPV) and the subsequent challenges in preventing its re-emergence, we look to the past to identify why polio rose to epidemic levels in the mid-20th century, and how WPV persisted over large geographic scales. We analyzed an extensive epidemiological dataset, spanning the 1930s to the 1950s and spatially replicated across each state in the United States, to glean insight into the drivers of polio's historical expansion and the ecological mode of its persistence prior to vaccine introduction. We document a latitudinal gradient in polio's seasonality. Additionally, we fitted and validated mechanistic transmission models to data from each US state independently. The fitted models revealed that: (1) polio persistence was the product of a dynamic mosaic of source and sink populations; (2) geographic heterogeneity of seasonal transmission conditions account for the latitudinal structure of polio epidemics; (3) contrary to the prevailing \"disease of development\" hypothesis, our analyses demonstrate that polio's historical expansion was straightforwardly explained by demographic trends rather than improvements in sanitation and hygiene; and (4) the absence of clinical disease is not a reliable indicator of polio transmission, because widespread polio transmission was likely in the multiyear absence of clinical disease. As the world edges closer to global polio eradication and continues the strategic withdrawal of the Oral Polio Vaccine (OPV), the regular identification of, and rapid response to, these silent chains of transmission is of the utmost importance.

Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and more detailed evolutionary hypotheses, including adaptive hypotheses with multiple selective optima and hypotheses with rate variation within and across lineages. The statistical performance of these sophisticated models has received relatively little systematic attention, however. We conducted an extensive simulation study to quantify the statistical properties of a class of models toward the simpler end of the spectrum that model phenotypic evolution using Ornstein-Uhlenbeck processes. We focused on identifying where, how, and why these methods break down so that users can apply them with greater understanding of their strengths and weaknesses. Our analysis identifies three key determinants of performance: a discriminability ratio, a signal-to-noise ratio, and the number of taxa sampled. Interestingly, we find that model-selection power can be high even in regions that were previously thought to be difficult, such as when tree size is small. On the other hand, we find that model parameters are in many circumstances difficult to estimate accurately, indicating a relative paucity of information in the data relative to these parameters. Nevertheless, we note that accurate model selection is often possible when parameters are only weakly identified. Our results have implications for more sophisticated methods inasmuch as the latter are generalizations of the case we study.

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 models 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 hypotheses regarding adaptation in different selective regimes into explicit models, to test the models against data using maximum‐likelihood‐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 approach we demonstrate allows one to explore more detailed hypotheses and to utilize more of the information content of comparative data sets than existing methods. Moreover, the use of a model selection framework to simultaneously compare a variety of hypotheses advances our ability to assess alternative evolutionary explanations.

The spread of dengue and other arboviruses constitutes an expanding global health threat. The extensive heterogeneity in population distribution and potential complexity of movement in megacities of low and middle-income countries challenges predictive modeling, even as its importance to disease spread is clearer than ever. Using surveillance data at fine resolution following the emergence of the DENV4 dengue serotype in Rio de Janeiro, we document a pattern in the size of successive epidemics that is invariant to the scale of spatial aggregation. This pattern emerges from the combined effect of herd immunity and seasonal transmission, and is strongly driven by variation in population density at sub-kilometer scales. It is apparent only when the landscape is stratified by population density and not by spatial proximity as has been common practice. Models that exploit this emergent simplicity should afford improved predictions of the local size of successive epidemic waves. Population density can influence the dynamics of emerging infections, but the specific effects at a local (within-city) level are not well understood. Here, the authors investigate the influence of population density on dynamics of dengue outbreaks in Rio de Janeiro and propose that this variable holds the key to how space should be aggregated.

Iterated filtering algorithms are stochastic optimization procedures for latent variable models that recursively combine parameter perturbations with latent variable reconstruction. Previously, theoretical support for these algorithms has been based on the use of conditional moments of perturbed parameters to approximate derivatives of the log likelihood function. Here, a theoretical approach is introduced based on the convergence of an iterated Bayes map. An algorithm supported by this theory displays substantial numerical improvement on the computational challenge of inferring parameters of a partially observed Markov process. Significance Many scientific challenges involve the study of stochastic dynamic systems for which only noisy or incomplete measurements are available. Inference for partially observed Markov process models provides a framework for formulating and answering questions about these systems. Except when the system is small, or approximately linear and Gaussian, state-of-the-art statistical methods are required to make efficient use of available data. Evaluation of the likelihood for a partially observed Markov process model can be formulated as a filtering problem. Iterated filtering algorithms carry out repeated Monte Carlo filtering operations to maximize the likelihood. We develop a new theoretical framework for iterated filtering and construct a new algorithm that dramatically outperforms previous approaches on a challenging inference problem in disease ecology.

Incidence of whooping cough, unlike many other childhood diseases for which there is an efficacious vaccine, has been increasing over the past twenty years despite high levels of vaccine coverage. Its reemergence has been particularly noticeable among teenagers and adults. Many hypotheses have been put forward to explain these two patterns, but parsimonious reconciliation of clinical data on the limited duration of immunity with both pre- and postvaccine era age-specific incidence remains a challenge. We consider the immunologically relevant, yet epidemiologically largely neglected, possibility that a primed immune system can respond to a lower dose of antigen than a naive one. We hypothesize that during the prevaccine era teenagers' and adults' primed immunity was frequently boosted by reexposure, so maintaining herd immunity in the face of potentially eroding individual immunity. In contrast, low pathogen circulation in the current era, except during epidemic outbreaks, allows immunity to be lost before reexposure occurs. We develop and analyze an age-structured model that encapsulates this hypothesis. We find that immune boosting must be more easily triggered than primary infection to account for age-incidence data. We make age-specific and dynamical predictions through bifurcation analysis and simulation. The boosting model proposed here parsimoniously captures four key features of pertussis data from highly vaccinated countries: (i) the shift in age-specific incidence, (ii) reemergence with high vaccine coverage, (iii) the possibility for cyclic dynamics in the pre- and postvaccine eras, and (iv) the apparent shift from susceptible-infectious-recovered (SIR)-like to susceptible-infectious-recovered-susceptible (SIRS)-like phenomenology of infection and immunity to Bordetella pertussis.

There is growing interest in understanding the nature and consequences of interactions among infectious agents. Pathogen interactions can be operational at different scales, either within a co-infected host or in host populations where they co-circulate, and can be either cooperative or competitive. The detection of interactions among pathogens has typically involved the study of synchrony in the oscillations of the protagonists, but as we show here, phase association provides an unreliable dynamical fingerprint for this task. We assess the capacity of a likelihood-based inference framework to accurately detect and quantify the presence and nature of pathogen interactions on the basis of realistic amounts and kinds of simulated data. We show that when epidemiological and demographic processes are well understood, noisy time series data can contain sufficient information to allow correct inference of interactions in multi-pathogen systems. The inference power is dependent on the strength and time-course of the underlying mechanism: stronger and longer-lasting interactions are more easily and more precisely quantified. We examine the limitations of our approach to stochastic temporal variation, under-reporting, and over-aggregation of data. We propose that likelihood shows promise as a basis for detection and quantification of the effects of pathogen interactions and the determination of their (competitive or cooperative) nature on the basis of population-level time-series data.

The role of climate forcing in the population dynamics of infectious diseases has typically been revealed via retrospective analyses of incidence records aggregated across space and, in particular, over whole cities. Here, we focus on the transmission dynamics of rotavirus, the main diarrheal disease in infants and young children, within the megacity of Dhaka, Bangladesh. We identify two zones, the densely urbanized core and the more rural periphery, that respond differentially to flooding. Moreover, disease seasonality differs substantially between these regions, spanning variation comparable to the variation from tropical to temperate regions. By combining process-based models with an extensive disease surveillance record, we show that the response to climate forcing is mainly seasonal in the core, where a more endemic transmission resulting from an asymptomatic reservoir facilitates the response to the monsoons. The force of infection in this monsoon peak can be an order of magnitude larger than the force of infection in the more epidemic periphery, which exhibits little or no post-monsoon outbreak in a pattern typical of nearby rural areas. A typically smaller peak during the monsoon season nevertheless shows sensitivity to interannual variability in flooding. High human density in the core is one explanation for enhanced transmission during troughs and an associated seasonal monsoon response in this diarrheal disease, which unlike cholera, has not been widely viewed as climate-sensitive. Spatial demographic, socioeconomic, and environmental heterogeneity can create reservoirs of infection and enhance the sensitivity of disease systems to climate forcing, especially in the populated cities of the developing world.