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Control of crop pests by shifting host plant availability and natural enemy activity at landscape scales has great potential to enhance the sustainability of agriculture. However, mainstreaming natural pest control requires improved understanding of how its benefits can be realized across a variety of agroecological contexts. Empirical studies suggest significant but highly variable responses of natural pest control to land-use change. Current ecological models are either too specific to provide insight across agroecosystems or too generic to guide management with actionable predictions. We suggest obtaining the full benefit of available empirical, theoretical, and methodological knowledge by combining trait-mediated understanding from correlative studies with the explicit representation of causal relationships achieved by mechanistic modeling. To link these frameworks, we adapt the concept of archetypes, or context-specific generalizations, from sustainability science. Similar responses of natural pest control to land-use gradients across cases that share key attributes, such as functional traits of focal organisms, indicate general processes that drive system behavior in a context-sensitive manner. Based on such observations of natural pest control, a systematic definition of archetypes can provide the basis for mechanistic models of intermediate generality that cover all major agroecosystems worldwide. Example applications demonstrate the potential for upscaling understanding and improving predictions of natural pest control, based on knowledge transfer and scientific synthesis. A broader application of this mechanistic archetype approach promises to enhance ecology's contribution to natural resource management across diverse regions and social-ecological contexts. ANR; BMBF; FORMAS; FWF; MINECO; NWO; PT-DLR; Helmholtz-Zentrum fur Umweltforschung; iDiv - German Research Foundation [DFG-FZT 118, 202548816]; Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS); SLU Centre for Biological Control; Strategic research area Biodiversity and Ecosystem services in a Changing Climate (BECC); US Dept. of Agriculture, National Institute of Food and Agriculture (NIFA) [2020-67021-32477]; Volkswagen Foundation [A118199] Published version 2013-2014 BiodivERsA/FACCE-JPI joint call for research proposals (project ECODEAL), with the national funders ANR, BMBF, FORMAS, FWF, MINECO, NWO and PT-DLR; Helmholtz-Zentrum fur Umweltforschung; iDiv, funded by the German Research Foundation, Grant/Award Numbers: DFG-FZT 118, 202548816; Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS); SLU Centre for Biological Control; Strategic research area Biodiversity and Ecosystem services in a Changing Climate (BECC); US Dept. of Agriculture, National Institute of Food and Agriculture (NIFA), Grant/Award Number: 2020-67021-32477; Volkswagen Foundation through a Freigeist Fellowship, Grant/Award Number: A118199

Well parameterized epidemiological models including accurate representation of contacts are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here, we fit age-stratified models, including re-estimation of relative contact rates between age classes, to public data describing the 2020–2021 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing approximate Bayesian computation (ABC) methodology with model-based proposals (MBPs) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalization rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrization of dynamic transmission models that can inform data-driven public health policy and interventions.This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Modern epidemiological analyses to understand and combat the spread of disease depend critically on access to, and use of, data. Rapidly evolving data, such as data streams changing during a disease outbreak, are particularly challenging. Data management is further complicated by data being imprecisely identified when used. Public trust in policy decisions resulting from such analyses is easily damaged and is often low, with cynicism arising where claims of ‘following the science’ are made without accompanying evidence. Tracing the provenance of such decisions back through open software to primary data would clarify this evidence, enhancing the transparency of the decision-making process. Here, we demonstrate a Findable, Accessible, Interoperable and Reusable (FAIR) data pipeline. Although developed during the COVID-19 pandemic, it allows easy annotation of any data as they are consumed by analyses, or conversely traces the provenance of scientific outputs back through the analytical or modelling source code to primary data. Such a tool provides a mechanism for the public, and fellow scientists, to better assess scientific evidence by inspecting its provenance, while allowing scientists to support policymakers in openly justifying their decisions. We believe that such tools should be promoted for use across all areas of policy-facing research. This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

International audience; Pathogens such as African swine fever virus (ASFV) are an increasing threat to global livestock production with implications for economic well-being and food security. Quantification of epidemiological parameters, such as transmission rates and latent and infectious periods, is critical to inform efficient disease control. Parameter estimation for livestock disease systems is often reliant upon transmission experiments, which provide valuable insights in the epidemiology of disease but which may also be unrepresentative of at-risk populations and incur economic and animal welfare costs. Routinely collected mortality data are a potential source of readily available and representative information regarding disease transmission early in outbreaks. We develop methodology to conduct exact Bayesian parameter inference from mortality data using reversible jump Markov chain Monte Carlo incorporating multiple routes of transmission (e.g. within-farm secondary and background transmission from external sources). We use this methodology to infer epidemiological parameters for ASFV using data from outbreaks on nine farms in the Russian Federation. This approach improves inference on transmission rates in comparison with previous methods based on approximate Bayesian computation, allows better estimation of time of introduction and could readily be applied to other outbreaks or pathogens.

Foot and mouth disease (FMD) burden disproportionally affects Africa where it is considered endemic. Smallholder livestock keepers experience significant losses due to disease, but the dynamics and mechanisms underlying persistence at the herd-level and beyond remain poorly understood. We address this knowledge gap using stochastic, compartmental modelling to explore FMD virus (FMDV) persistence, outbreak dynamics and disease burden in individual cattle herds within an endemic setting. Our analysis suggests repeated introduction of virus from outside the herd is required for long-term viral persistence, irrespective of carrier presence. Risk of new disease exposures resulting in significant secondary outbreaks is reduced by the presence of immune individuals giving rise to a period of reduced risk, the predicted duration of which suggests that multiple strains of FMDV are responsible for observed yearly herd-level outbreaks. Our analysis suggests management of population turnover could potentially reduce disease burden and deliberate infection of cattle, practiced by local livestock keepers in parts of Africa, has little effect on the duration of the reduced risk period but increases disease burden. This work suggests that FMD control should be implemented beyond individual herds but, in the interim, herd management may be used to reduced FMD impact to livestock keepers.

Objectives: To develop a Critical Appraisal tool for non-computational-specialist public health professionals to assess the quality and relevance of modelling studies about Test and Trace (and Protect – TTP) programmes’ impact on COVID-19 transmission.Study Design: Decision-making tool developmentMethods: Using Tugwell et al.’s Health Care Effectiveness equation as a conceptual framework, combined with a purposive search of the relevant early modeling literature, we developed six critical appraisal questions for the rapid assessment of modeling studies related to the evaluation of TTP programmes’ effectiveness.Results: By applying the Critical Appraisal tool to selected recent COVID-19 modeling studies we demonstrate how models can be evaluated using the six questions to evaluate internal and external validity, and relevance.Conclusions: These six critical appraisal questions are able to discriminate between modeling studies of higher and lower quality and relevance to evaluating TTP programmes’ impact. However, these questions require independent validation in a larger and systematic sample of relevant modeling studies which have appeared in later stages of the pandemic.

We develop and apply analytically tractable generative models of livestock movements at national scale. These go beyond current models through mechanistic modelling of heterogeneous trade partnership network dynamics and the trade events that occur on them. Linking resulting animal movements to disease transmission between farms yields analytical expressions for the basic reproduction number R 0 . We show how these novel modelling tools enable systems approaches to disease control, using R 0 to explore impacts of changes in trading practices on between-farm prevalence levels. Using the Scottish cattle trade network as a case study, we show our approach captures critical complexities of real-world trade networks at the national scale for a broad range of endemic diseases. Changes in trading patterns that minimize disruption to business by maintaining in-flow of animals for each individual farm reduce R 0 , with the largest reductions for diseases that are most challenging to eradicate. Incentivizing high-risk farms to adopt such changes exploits ‘scale-free’ properties of the system and is likely to be particularly effective in reducing national livestock disease burden and incursion risk. Encouragingly, gains made by such targeted modification of trade practices scale much more favourably than comparably targeted improvements to more commonly adopted farm-level biosecurity.

Rice hoppers can cause devastation to rice crops in SE Asia via disease spread and direct feeding. Current regulation is through pesticides; however, a more sustainable approach is to use the natural enemies of the hoppers. Here, we show how the combination of a process‐based model and field data can give insights into natural pest control, beyond those obtained through direct analysis of the field data. We use a stage‐structured host‐parasitoid model based on time‐delay ordinary differential equations (using the r package “stagePop”; Kettle & Nutter, 2015; Methods in Ecology and Evolution 6:1484–1490) to investigate the interactions of four parasitoid genera and an egg predator on the eggs of two hopper hosts: the brown plant hopper (Nilaparvata lugens (Stal)) and the green leaf hopper (Nephottetix spp.). Model parameters are derived from 62 (×3) datasets from experiments in the Philippines. In these experiments, hopper eggs on rice plants were exposed in the field for 3 days and then taken back to the laboratory. The number of emerging hopper nymphs and parasitoid adults were then recorded. Single‐host and mixed host experiments were performed. The field data are not sufficient to fully constrain the model parameters so our results are given in terms of the value of an unknown parameter (γ; the number of hopper eggs killed per successful parasitism) which may be ascertained via future experiments. Synthesis and applications. Our model experiments suggest that although parasitoids are most likely the main control on hopper egg abundance, and despite the fact that the egg predator also consumes parasitoid eggs, the two‐enemy system (parasitoids and predators) is more effective at hopper egg control than if either enemy is present alone. Our results provide evidence in support of ecological engineering approaches that promote both parasitoids and egg predators.

This work resulted from a workshop (Towards an integrated assessment of the environmental risks posed by non-native species, GMOs and wildlife diseases) held as part of the UK Population Biology Network (UKPopNet) and funded by the Natural Environment Research Council (Agreement R8-H12-01) and English Nature. Its development was stimulated by the workshop on ‘Frameworks used in Invasion Science’ hosted by the DSI-NRF Centre of Excellence for Invasion Biology that was supported by the National Research Foundation of South Africa and Stellenbosch University. Emerging microparasite (e.g. viruses, bacteria, protozoa and fungi) epidemics and the introduction of non-native pests and weeds are major biosecurity threats worldwide. The likelihood of these threats is often estimated from probabilities of their entry, establishment, spread and ease of prevention. If ecosystems are considered equivalent to hosts, then compartment disease models should provide a useful framework for understanding the processes that underpin non-native species invasions. To enable greater cross-fertilisation between these two disciplines, the Epidemiological Framework for Biological Invasions (EFBI) is developed that classifies ecosystems in relation to their invasion status: Susceptible, Exposed, Infectious and Resistant. These states are linked by transitions relating to transmission, latency and recovery. This viewpoint differs markedly from the species-centric approaches often applied to non-native species. It allows generalisations from epidemiology, such as the force of infection, the basic reproductive ratio R0, super-spreaders, herd immunity, cordon sanitaire and ring vaccination, to be discussed in the novel context of non-native species and helps identify important gaps in the study of biological invasions. The EFBI approach highlights several limitations inherent in current approaches to the study of biological invasions including: (i) the variance in non-native abundance across ecosystems is rarely reported; (ii) field data rarely (if ever) distinguish source from sink ecosystems; (iii) estimates of the susceptibility of ecosystems to invasion seldom account for differences in exposure to non-native species; and (iv) assessments of ecosystem susceptibility often confuse the processes that underpin patterns of spread within -and between- ecosystems. Using the invasion of lakes as a model, the EFBI approach is shown to present a new biosecurity perspective that takes account of ecosystem status and complements demographic models to deliver clearer insights into the dynamics of biological invasions at the landscape scale. It will help to identify whether management of the susceptibility of ecosystems, of the number of vectors, or of the diversity of pathways (for movement between ecosystems) is the best way of limiting or reversing the population growth of a non-native species. The framework can be adapted to incorporate increasing levels of complexity and realism and to provide insights into how to monitor, map and manage biological invasions more effectively. Publisher PDF

Funding: Scottish Government through the Strategic Research Programme of the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS). James Hutton Institute and the Universities of Aberdeen and Dundee through a Scottish Food Security Alliance (Crops) PhD studentship. (D.J.). 1. Aphid populations frequently include phenotypes that are resistant to parasitism by hymenopterous parasitoid wasps, which is often attributed to the presence of ‘protective’ facultative endosymbionts residing in aphid tissues, particularly Hamiltonella defensa. In field conditions, under parasitoid pressure, the observed coexistence of aphids with and without protective symbionts cannot be explained by their difference in fitness alone. 2. Using the cereal aphid Rhopalosiphum padi as a model, we propose an alternative mechanism whereby parasitoids are more efficient at finding common phenotypes of aphid and experience a fitness cost when switching to the less common phenotype. 3. We construct a model based on delay differential equations and parameterise and validate the model with values within the ranges obtained from experimental studies. We then use it to explore possible effects on system dynamics under conditions of environmental stress, using our existing data on the effects of drought stress in crops as an example. 4. We show the ‘switching penalty’ incurred by parasitoids leads to stable coexistence of aphids with and without H. defensa and provides a potential mechanism for maintaining phenotypic diversity amongst host organisms. We show that drought‐induced reduction in aphid development time has little impact. However, greater reduction in fecundity on droughted plants of symbiont‐protected aphids can cause insect population cycles when the system would be stable in the absence of drought stress. 5. The stabilizing effect of the increased efficiency in dealing with more commonly encountered host phenotypes is applicable to a broad range of consumer‐resource systems and could explain stable coexistence in competitive environments. The loss of stable coexistence when drought has different effects on the competing aphid phenotypes highlights the importance of scenario testing when considering biocontrol for pest management. Postprint

Natural control of crop pests has the potential to complement or replace intensive agricultural practices, but its mainstream application requires reliable predictions in diverse socioecological settings. In lack of a widely accepted model of natural pest control, we review existing modelling approaches and critically examine their potential to provide understanding and predictions across agricultural landscapes. Models that explicitly represent the underlying mechanisms are better positioned to represent the diversity and context sensitivity of natural pest control than correlative models. Such mechanistic models have used diverse techniques to represent crop-pest-enemy combinations at various spatiotemporal scales. However, certain regions of the world and socioeconomic aspects of natural pest control are underrepresented, while modelling approaches are restricted by a fundamental trade-off between generality and realism. We propose that modelling natural pest control across agroecosystems requires a framework of context-specific generalizations, based on empirical evidence and theoretical expectations. Reviewed models of natural pest control indicate potential attributes of such a general predictive framework.

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development of application specific implementations. This paper introduces "posterior-based proposals" (PBPs), a new type of MCMC update applicable to a huge class of statistical models (whose conditional dependence structures are represented by directed acyclic graphs). PBPs generates large joint updates in parameter and latent variable space, whilst retaining good acceptance rates (typically 33%). Evaluation against other approaches (from standard Gibbs / random walk updates to state-of-the-art Hamiltonian and particle MCMC methods) was carried out for widely varying model types: an individual-based model for disease diagnostic test data, a financial stochastic volatility model, a mixed model used in statistical genetics and a population model used in ecology. Whilst different methods worked better or worse in different scenarios, PBPs were found to be either near to the fastest or significantly faster than the next best approach (by up to a factor of 10). PBPs therefore represent an additional general purpose technique that can be usefully applied in a wide variety of contexts., 54 pages, 11 figures, 2 tables

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration., Author summary Mathematical models of the spread and progression of communicable disease in populations are important tools in efforts to prevent and control outbreaks. A common class of disease models assume that infection is transmitted directly from infectious to susceptible individuals when they are in close proximity—so called direct transmission models. These are used widely and have proven invaluable as simplified descriptions of a wide array of infectious diseases in diverse populations. However, many pathogens spread through indirect, environmental routes of transmission, for example via contact with contaminated water sources in the case of cholera, or inhalation of infectious airborne droplets for respiratory infections, such as Covid-19. We show that direct transmission models work well for such pathogens with short environmental lifetimes and where hosts shed pathogens into the environment at high rates. This means that we do not require information about environmental pathogen levels to understand the behaviour of outbreaks caused by these pathogens. When shedding rates are also low, e.g., with macroparasitic infections, or when variable environmental factors play a role in transmissibility, then explicit modelling of both the pathogen and environmental transmission will provide a more accurate picture than a direct transmission approximation.

Natural control of invertebrate crop pests has the potential to complement or replace conventional insecticide-based practices, but its mainstream application is hampered by predictive unreliability across agroecosystems. Inconsistent responses of natural pest control to changes in landscape characteristics have been attributed to ecological complexity and system-specific conditions. Here, we review agroecological models and their potential to provide predictions of natural pest control across agricultural landscapes. Existing models have used a multitude of techniques to represent specific crop-pest-enemy systems at various spatiotemporal scales, but less wealthy regions of the world are underrepresented. A realistic representation of natural pest control across systems appears to be hindered by a practical trade-off between generality and realism. Nonetheless, observations of context-sensitive, trait-mediated responses of natural pest control to land-use gradients indicate the potential of ecological models that explicitly represent the underlying mechanisms. We conclude that modelling natural pest control across agroecosystems should exploit existing mechanistic techniques towards a framework of contextually bound generalizations. Observed similarities in causal relationships can inform the functional grouping of diverse agroecosystems worldwide and the development of the respective models based on general, but context-sensitive, ecological mechanisms. The combined use of qualitative and quantitative techniques should allow the flexible integration of empirical evidence and ecological theory for robust predictions of natural pest control across a wide range of agroecological contexts and levels of knowledge availability. We highlight challenges and promising directions towards developing such a general modelling framework. (Less)

Ecology studies the interactions between individuals, species and the environment. The ability to predict the dynamics of ecological systems would support the design and monitoring of control strategies and would help to address pressing global environmental issues. It is also important to plan for efficient use of natural resources and maintenance of critical ecosystem services. The mathematical modelling of ecological systems often includes nontrivial specifications of processes that influence the birth, death, development and movement of individuals in the environment, that take into account both biotic and abiotic interactions. To assist in the specification of such models, we introduce MELA, a process algebra for Modelling in Ecology with Location Attributes. Process algebras allow the modeller to describe concurrent systems in a high-level language. A key feature of concurrent systems is that they are composed of agents that can progress simultaneously but also interact - a good match to ecological systems. MELA aims to provide ecologists with a straightforward yet flexible tool for modelling ecological systems, with particular emphasis on the description of space and the environment. Here we present four example MELA models, illustrating the different spatial arrangements which can be accommodated and demonstrating the use of MELA in epidemiological and predator-prey scenarios., In Proceedings QAPL'16, arXiv:1610.07696

LEGATO stands for “Land-use intensity and Ecological EnGineering—Assessment Tools for risks and Opportunities in irrigated rice based production systems.”

In this article, we present Three-Valued spatio-temporal Logic (TSTL), which enriches the available spatiotemporal analysis of properties expressed in Signal spatio-temporal Logic (SSTL), to give further insight into the dynamic behavior of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and specific extended monitoring algorithms to check the validity of TSTL formulas. We introduce a reliability requirement for TSTL monitoring and an automatic procedure to verify it. Two case studies demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and privacy preservation based on spatial stochastic population models.

Individuals differ widely in their contribution to the spread of infection within and across populations. Three key epidemiological host traits affect infectious disease spread: susceptibility (propensity to acquire infection), infectivity (propensity to transmit infection to others) and recoverability (propensity to recover quickly). Interventions aiming to reduce disease spread may target improvement in any one of these traits, but the necessary statistical methods for obtaining risk estimates are lacking. In this paper we introduce a novel software tool called SIRE (standing for “Susceptibility, Infectivity and Recoverability Estimation”), which allows for the first time simultaneous estimation of the genetic effect of a single nucleotide polymorphism (SNP), as well as non-genetic influences on these three unobservable host traits. SIRE implements a flexible Bayesian algorithm which accommodates a wide range of disease surveillance data comprising any combination of recorded individual infection and/or recovery times, or disease diagnostic test results. Different genetic and non-genetic regulations and data scenarios (representing realistic recording schemes) were simulated to validate SIRE and to assess their impact on the precision, accuracy and bias of parameter estimates. This analysis revealed that with few exceptions, SIRE provides unbiased, accurate parameter estimates associated with all three host traits. For most scenarios, SNP effects associated with recoverability can be estimated with highest precision, followed by susceptibility. For infectivity, many epidemics with few individuals give substantially more statistical power to identify SNP effects than the reverse. Importantly, precise estimates of SNP and other effects could be obtained even in the case of incomplete, censored and relatively infrequent measurements of individuals’ infection or survival status, albeit requiring more individuals to yield equivalent precision. SIRE represents a new tool for analysing a wide range of experimental and field disease data with the aim of discovering and validating SNPs and other factors controlling infectious disease transmission., Author summary Effective approaches to reduce the spread of infectious disease transmission in populations are urgently needed. Reduction in disease spread is most effectively achieved by reducing, separately or in combination, individual (i) “susceptibility”, i.e. the relative risk to become infected when exposed to infectious individuals or material, (ii) “infectivity”, i.e. the propensity to transmit infection to others when infected, and/or by (iii) improving “recoverability”, i.e. the propensity to recover. However, to date it is impossible to assess how these three key epidemiological traits controlling disease transmission in a population are regulated by specific genes or interventions, as the necessary statistical methods for estimating genetic and non-genetic effects from available disease surveillance data don’t exist. This paper introduces a novel statistical method that can estimate, for the first time, genetic and non-genetic effects for host susceptibility, infectivity and recoverability simultaneously from a wide range of realistic disease surveillance data. The method has been incorporated into a user-friendly, freely available software tool called SIRE. SIRE can be applied to a range of experimental and field data and will help to move disease control significantly forward by simultaneously targeting multiple host traits affecting infectious disease spread.

1. Wildlife disease surveillance is the first line of defence against infectious disease. Fluctuations in host populations and disease prevalence are a known feature of wildlife disease systems. However, the impact of such heterogeneities on the performance of surveillance is currently poorly understood. 2. We present the first systematic exploration of the effects of fluctuations prevalence and host population size on the efficacy of wildlife disease surveillance systems. In this study efficacy is measured in terms of ability to estimate long term prevalence and detect disease risk. 3. Our results suggest that for many wildlife disease systems fluctuations in population size and disease lead to bias in surveillance-based estimates of prevalence and over-confidence in assessments of both the precision of prevalence estimates and the power to detect disease. 4. Neglecting such ecological effects may lead to poorly designed surveillance and ultimately to incorrect assessments of the risks posed by disease in wildlife. This will be most problematic in systems where prevalence fluctuations are large and disease fade-outs occur. Such fluctuations are determined by the interaction of demography and disease dynamics and although particularly likely in highly fluctuating populations typical of fecund short lived hosts, can’t be ruled out in more stable populations of longer lived hosts. 5. Synthesis and Applications: Fluctuations in population size and disease prevalence should be considered in the design and implementation of wildlife disease surveillance and the framework presented here provides a template for conducting suitable power calculations. Ultimately understanding the impact of fluctuations in demographic and epidemiological processes will enable improvements to wildlife disease surveillance systems leading to better characterisation of, and protection against endemic, emerging and re-emerging disease threats.

While model evidence is considered by Bayesian statisticians as a gold standard for model selection (the ratio in model evidence between two models giving the Bayes factor), its calculation is often viewed as too computationally demanding for many applications. By contrast, the widely used deviance information criterion (DIC), a different measure that balances model accuracy against complexity, is commonly considered a much faster alternative. However, recent advances in computational tools for efficient multi-temperature Markov chain Monte Carlo algorithms, such as steppingstone sampling (SS) and thermodynamic integration schemes, enable efficient calculation of the Bayesian model evidence. This paper compares both the capability (i.e. ability to select the true model) and speed (i.e. CPU time to achieve a given accuracy) of DIC with model evidence calculated using SS. Three important model classes are considered: linear regression models, mixed models and compartmental models widely used in epidemiology. While DIC was found to correctly identify the true model when applied to linear regression models, it led to incorrect model choice in the other two cases. On the other hand, model evidence led to correct model choice in all cases considered. Importantly, and perhaps surprisingly, DIC and model evidence were found to run at similar computational speeds, a result reinforced by analytically derived expressions.

Livestock epidemics have the potential to give rise to significant economic, welfare, and social costs. Incursions of emerging and re-emerging pathogens may lead to small and repeated outbreaks. Analysis of the resulting data is statistically challenging but can inform disease preparedness reducing potential future losses. We present a framework for spatial risk assessment of disease incursions based on data from small localized historic outbreaks. We focus on between-farm spread of livestock pathogens and illustrate our methods by application to data on the small outbreak of Classical Swine Fever (CSF) that occurred in 2000 in East Anglia, UK. We apply models based on continuous time semi-Markov processes, using data-augmentation Markov Chain Monte Carlo techniques within a Bayesian framework to infer disease dynamics and detection from incompletely observed outbreaks. The spatial transmission kernel describing pathogen spread between farms, and the distribution of times between infection and detection, is estimated alongside unobserved exposure times. Our results demonstrate inference is reliable even for relatively small outbreaks when the data-generating model is known. However, associated risk assessments depend strongly on the form of the fitted transmission kernel. Therefore, for real applications, methods are needed to select the most appropriate model in light of the data. We assess standard Deviance Information Criteria (DIC) model selection tools and recently introduced latent residual methods of model assessment, in selecting the functional form of the spatial transmission kernel. These methods are applied to the CSF data, and tested in simulated scenarios which represent field data, but assume the data generation mechanism is known. Analysis of simulated scenarios shows that latent residual methods enable reliable selection of the transmission kernel even for small outbreaks whereas the DIC is less reliable. Moreover, compared with DIC, model choice based on latent residual assessment correlated better with predicted risk.

In this paper we present Three-Valued Spatio-Temporal Logic (TSTL), which enriches the available spatio-temporal analysis of properties expressed in Signal Spatio-Temporal Logic (SSTL), to give further insight into the dynamic behaviour of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and aspecific extended monitoring algorithm to check the validity of TSTL formulas.We conclude with two case studies that demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and control programmes based on spatial stochastic population models.

Culling wildlife to control disease can lead to both decreases and increases in disease levels, with apparently conflicting responses observed, even for the same wildlife–disease system. There is therefore a pressing need to understand how culling design and implementation influence culling's potential to achieve disease control. We address this gap in understanding using a spatial metapopulation model representing wildlife living in distinct groups with density-dependent dispersal and framed on the badger–bovine tuberculosis (bTB) system. We show that if population reduction is too low, or too few groups are targeted, a ‘perturbation effect’ is observed, whereby culling leads to increased movement and disease spread. We also demonstrate the importance of culling across appropriate time scales, with otherwise successful control strategies leading to increased disease if they are not implemented for long enough. These results potentially explain a number of observations of the dynamics of both successful and unsuccessful attempts to control TB in badgers including the Randomized Badger Culling Trial in the UK, and we highlight their policy implications. Additionally, for parametrizations reflecting a broad range of wildlife–disease systems, we characterize ‘Goldilocks zones’, where, for a restricted combination of culling intensity, coverage and duration, the disease can be reduced without driving hosts to extinction.