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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

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

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.

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.

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

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.

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R * , the number of groups infected by an initial infected group, which is a metapopulation level analogue of the basic reproduction number R 0 that provides a better characterization of disease spread in a metapopulation. However, existing approaches to calculate R * do not account for individual movements between locations which means we lack suitable tools for livestock systems. We address this gap using next-generation matrix approaches to capture movements explicitly and introduce novel tools to calculate R * in any populations coupled by individual movements. We show that depletion of infectives in the source group, which hastens its recovery, is a phenomenon with important implications for design and efficacy of movement-based controls. Underpinning our results is the observation that R * peaks at intermediate livestock movement rates. Consequently, under movement-based controls, infection could be controlled at high movement rates but persist at intermediate rates. Thus, once control schemes are present in a livestock system, a reduction in movements can counterintuitively lead to increased disease prevalence. We illustrate our results using four important livestock diseases (bovine viral diarrhoea, bovine herpes virus, Johne's disease and Escherichia coli O157) that each persist across different movement rate ranges with the consequence that a change in livestock movements could help control one disease, but exacerbate another.

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to ‘hindcast’ (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time., Author Summary We have developed a Bayesian approach that can estimate the historic trend of incidence from cross-sectional samples, without relying on ongoing surveillance. This could be used to evaluate changing disease trends, or to inform outbreak responses. We combine two or more diagnostic tests to estimate the time since infection for the individual, and the historic incidence trend in the population as a whole. We evaluate this procedure by applying it to simulated data from synthetic epidemics. Further, we evaluate its real-world applicability by applying it to two scenarios modelled after the UK 2007 bluetongue epidemic, and a small outbreak of whooping cough in Wisconsin, USA. We were able to recover the epidemic trends under a range of conditions using sample sizes of 30–100 individuals. In the scenarios modelled after real-world epidemics, the hindcasted epidemic curves would have provided valuable information about the distribution of infections. The described approach is generic, and applicable to a wide range of human, livestock and wildlife diseases. It can estimate trends in settings for which this is not possible using current methods, including for diseases or regions lacking in surveillance; recover the pattern of spread during the initial “silent” phase once an outbreak is detected; and can be used track emerging infections. Being able to estimate the past trends of diseases from single cross-sectional studies has far-reaching consequences for the design and practice of disease surveillance in all contexts.

The ability of species to modulate environmental conditions and resources has long been of interest. In the past three decades the impacts of these biotic modifiers have been investigated as ‘ecosystem engineers’, ‘niche constructors’, ‘facilitators’ and ‘keystone species’. This environmental modulation can vary spatially from extremely local to global, temporally from days to geological time, and taxonomically from a few to a very large number of species. Modulation impacts are pervasive and affect, inter alia, the climate, structural environments, disturbance rates, soils and the atmospheric chemical composition. Biotic modifiers may profoundly transform the projected environmental conditions, and consequently have a significant impact on the predicted occurrence of the focal species in species distribution models (SDMs). This applies especially when these models are projected into different geographical regions or into the future or the past, where these biotic modifiers may be absent, or other biotic modifiers may be present. We show that environmental modulation can be represented in SDMs as additional variables. In some instances it is possible to use the species (e.g. biotic modifiers) in order to reflect the modulation. This would apply particularly to cases where the effect is the result of a single or a small number of species (e.g. elephants transforming woodland to grassland). Where numerous species generate an effect (such as tree species making a forest, or grasses facilitating fire) that modulates the abiotic environment, the effect itself might be a better descriptor for the aggregated action of the numerous species. We refer to this ‘effect’ as the modulator. Much of the information required to incorporate environmental modulation effects in SDMs is already available from remote-sensing data and vegetation models.

A novel, yet generic, Bayesian approach to parameter inference in a stochastic, spatio-temporal model of dispersal and colonisation is developed and applied to the invasion of a region by an alien plant species. The method requires species distribution data from multiple time points, and accounts for temporal uncertainty in colonisation times inherent in such data. Covariates, such as climate parameters, altitude and land use, which capture variation in the suitability of sites for plant colonisation, are easily incorporated into the model. The method assumes no local extinction of occupied sites and thus is primarily applicable to modelling distribution data at relatively coarse spatial resolutions of plant species whose range is expanding over time. The implementation of the model and inference algorithm are illustrated through application to British floristic atlas data for the widespread alien Heracleum mantegazzianum (giant hogweed) assessed at a 10 × 10 km resolution in 1970 and 2000. We infer key characteristics of this species, predict its future spread, and use the resulting fitted model to inform a simulation-based assessment of the methodology. Simulated distribution data are used to validate the inference algorithm. Our results suggest that the accuracy of inference is not sensitive to the number of distribution time points, requiring only that there are at least two points in time when distributions are mapped. We demonstrate the utility of the modelling approach by making future forecasts and historic hindcasts of the distribution of giant hogweed in Great Britain. Giant hogweed is one of the worst alien plants in Britain and has rapidly increased its range since 1970, yet we highlight that a further 20% of land area remains susceptible to colonisation by this species. We use the robustness of this case study to discuss the potential for modelling distribution data for other species and at different spatial scales.

Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain changes in fine-scale community dynamics, their effect is sometimes fairly minimal, and demographic scenarios in which this difference is important have not been systematically investigated. We take a simple mean-field model which simulates birth, growth and death processes, and rewrite it with spatially distributed discrete individuals. Each individual's growth and mortality is determined by a competition measure which captures the effects of neighbours in a way which retains the conceptual simplicity of a generic, analytically-solvable model. Although the model is generic, we here parameterise it using data from Caledonian Scots Pine stands. The dynamics of simulated populations, starting from a plantation lattice configuration, mirror those of well-established qualitative descriptions of natural forest stand behaviour; an analogy which assists in understanding the transition from artificial to old-growth structure. When parameterised for Scots Pine populations, the signature of spatial processes is evident, but their effect on first-order statistics, such as density and biomass, is fairly limited. The sensitivity of this result to variation in each individual rate parameter is investigated; distinct differences between spatial and mean-field models are seen only upon alteration of the interaction strength parameters, and in low density populations. Under the Scots pine parameterisation, dispersal also has an effect on spatial structure, but not density and biomass. Only in more intense competitive scenarios does altering the relative scales of dispersal and interaction lead to a clear signal in first order behaviour. The study acts as an important reminder that, even in scenarios where individual processes are localised in space, simple models are often sufficient to capture many population scale aspects of observed ecological dynamics.

Plantation transformation is a goal of increasing interest to silviculturalists. The target forest state is characterised by high variance in age and size, and an irregular spatial structure, which leads to inhomogeneous interactions between, and consequent development of, trees in the stand. This presents a difficulty for traditional methods such as yield tables, and demands a more careful consideration of stand dynamics. On the other hand, while forestry has a great heritage of simulation, the level of complexity implemented at an individual level generally precludes direct understanding of stand scale behaviours, and leads to difficulties in verification with appropriate data. A promising approach is the application of relatively simple models developed by ecologists. These can be adapted to yield accurate representations of forest stands, while being highly amenable to analysis. Motivated by data from Scots pine (Pinus sylvestris L.) stands, we here apply a simple spatial birth-death-growth model to the comparison and analysis of transformation strategies for plantation stands. The model captures the effects of neighbours in a way which retains the conceptual simplicity of a generic, analytically solvable model, while allowing insights into the driving factors of population dynamics. Timing and intensity of management interventions, as opposed to their specific criteria, are of primary importance: thinnings of a moderate intensity performed over a long period produced the best results. Variation in the strategy applied leads to more subtle effects which transformation strategies must also take into account, such as the development of variation in size of the remaining trees (increased using spatially correlated thinnings), the survival chances of regeneration and “underplanted” trees, and the overall productivity of the stand (increased using spatially homogeneous crown thinning). Finally, we demonstrate the robustness of model predictions to fundamental choices of model formulation.

Traits have been widely used in plant ecology to understand the rules governing community assembly, and to characterize primary strategies that define community structure and ecosystem properties. Relatively little is known as to whether the traits that are ecologically important at macroecological scales are either variable, or of consequence at fine scales within species. We measured trait variation within populations of the grassland plants Festuca ovina L. and Koeleria macrantha (Ledeb.) Schult., to test the hypothesis that fine-scale intraspecific trait variation drives local community structure. Both species showed large genotypic variation for all traits. Size-related traits of genotypes of K. macrantha observed under monoculture predicted their performance in model grassland communities that possessed both genetic and species diversity. The same correspondence was much weaker for the experimental population of F. ovina. A trade-off in allocation between shoot mass and relative allocation to reproduction was evident in the experimental population of F. ovina. Furthermore, both species showed evidence of a positive relationship between specific leaf area (SLA) and allocation to culm mass. This trait covariation indicates the existence of intraspecific trade-offs in life-history and growth strategies similar to those used to define primary plant strategies, which potentially buffers both species abundance and species coexistence against environmental challenges.

Animal behaviour is often a function of the animal’s physiological state. Groups of animals will often contain individuals with a range of physiological states and the grazing behaviour of herbivores is affected by their physiological state. This study compared the grazing decisions of animals in groups of single and mixed physiological states. Using a grazing model that simulated individual herbivore behaviour in relation to environmental distributions of forage resource (grass) and parasites (faeces), we tested the hypothesis that an animal’s level of parasite exposure via the faecal–oral route is affected by the composition of physiological states in the group. Four physiological states were considered: parasite-naive, parasitized, lactating and parasite-immune animals. Baseline parasite exposure levels for each state were generated by simulating single-state groups and were compared to simulations of each of the six two-state combinations. In single-state groups parasitized animals had the least and lactating animals had the greatest levels of parasite exposure. When co-grazing with lactating animals, parasitized, immune and naive animals increased their parasite exposure, relative to single-state groups. When co-grazing with parasitized animals, lactating, immune and naive animals reduced their parasite exposure, relative to single-state groups. There was no difference in parasite exposure of the immune or naive animals co-grazing together when compared to the single-state groups. These results highlight the need to recognize the impact of the individual when studying group-living animals.

Populations living in a spatially and temporally changing environment can adapt to the changing optimum and/or migrate toward favorable habitats. Here we extend previous analyses with a static optimum to allow the environment to vary in time as well as in space. The model follows both population dynamics and the trait mean under stabilizing selection, and the outcomes can be understood by comparing the loads due to genetic variance, dispersal, and temporal change. With fixed genetic variance, we obtain two regimes: (1) adaptation that is uniform along the environmental gradient and that responds to the moving optimum as expected for panmictic populations and when the spatial gradient is sufficiently steep, and (2) a population with limited range that adapts more slowly than the environmental optimum changes in both time and space; the population therefore becomes locally extinct and migrates toward suitable habitat. We also use a population' genetic model with many loci to allow genetic variance to evolve, and we show that the only solution now has uniform adaptation.

SUMMARYMany of the most pervasive disease challenges to livestock are transmitted via oral contact with faeces (or by faecal–aerosol) and the current paper focuses on how disease risk may depend on: spatial heterogeneity, animal searching behaviour, different grazing systems and faecal deposition patterns including those representative of livestock and a range of wildlife. A spatially explicit agent-based model was developed to describe the impact of empirically observed foraging and avoidance behaviours on the risk of disease presented by investigative and grazing contact with both livestock and wildlife faeces. To highlight the role of spatial heterogeneity on disease risks an analogous deterministic model, which ignores spatial heterogeneity and searching behaviour, was compared with the spatially explicit agent-based model. The models were applied to assess disease risks in temperate grazing systems. The results suggest that spatial heterogeneity is crucial in defining the disease risks to which individuals are exposed even at relatively small scales. Interestingly, however, although sensitive to other aspects of behaviour such as faecal avoidance, it was observed that disease risk is insensitive to search distance for typical domestic livestock restricted to small field plots. In contrast disease risk is highly sensitive to distributions of faecal contamination, in that contacts with highly clumped distributions of wildlife contamination are rare in comparison to those with more dispersed contamination. Finally it is argued that the model is a suitable framework to study the relative inter- and intra-specific disease risks posed to livestock under different realistic management regimes.

Bovine tuberculosis (bTB; Mycobacterium bovis) is a bacterial infection of cattle that also affects certain wildlife species. Culling badgers (Meles meles), the principal wildlife host, results in perturbation of the badger population and an increased level of disease in cattle. Therefore, the priority for future management must be to minimize the risk of disease transmission by finding new ways to reduce the contact rate among the host community. At the farm level, targeting those individuals that represent an elevated risk of transmission might prove to be effective. At the landscape level, risk mapping can provide the basis for targeted surveillance of the host community. Here, we review the current evidence for bTB persistence in Britain and make recommendations for future management and research.

SUMMARYReduction in wildlife populations is a common method for the control of livestock infections which have wildlife hosts, but its success is dependent on the characteristics of the infection itself, as well as on the spatial and social structure of the wildlife host. Paratuberculosis (Mycobacterium avium subsp. paratuberculosis; Map) is a widespread and difficult infection to control in livestock populations and also has possible links to Crohn's disease in humans. Rabbits have recently been identified as a key wildlife species in terms of paratuberculosis persistence in the environment and risk to the wider host community, including cattle. Here we use a spatially explicit stochastic simulation model of Map dynamics in rabbit populations to quantify the effects of rabbit population control on infection persistence. The model parameters were estimated from empirical studies of rabbit population dynamics and rabbit-to-rabbit routes of Map transmission. Three rabbit control strategies were compared: single unrepeated population reductions based on removing individual animals; single unrepeated population reductions based on removal of entire social groups; and repeated annual population reductions based on removing individual animals. Unrealistically high rabbit culls (>95% population reduction) are needed if infection is to be eradicated from local rabbit populations with a single one-off population reduction event, either of individuals or social groups. Repeated annual culls are more effective at reducing the prevalence of infection in rabbit populations and eradicating infection. However, annual population reductions of >40% are required over extended periods of time (many years). Thus, using an approach which is both highly conservative and parsimonious with respect to estimating lower bounds on the time to eradicate the infection, we find that Map is extremely persistent in rabbit populations and requires significant and prolonged effort to achieve control.

One of the principal challenges in epidemiological modeling is to parameterize models with realistic estimates for transmission rates in order to analyze strategies for control and to predict disease outcomes. Using a combination of replicated experiments, Bayesian statistical inference, and stochastic modeling, we introduce and illustrate a strategy to estimate transmission parameters for the spread of infection through a two-phase mosaic, comprising favorable and unfavorable hosts. We focus on epidemics with local dispersal and formulate a spatially explicit, stochastic set of transition probabilities using a percolation paradigm for a susceptible–infected (S–I) epidemiological model. The S–I percolation model is further generalized to allow for multiple sources of infection including external inoculum and host-to-host infection. We fit the model using Bayesian inference and Markov chain Monte Carlo simulation to successive snapshots of damping-off disease spreading through replicated plant populations that differ in relative proportions of favorable and unfavorable hosts and with time-varying rates of transmission. Epidemiologically plausible parametric forms for these transmission rates are compared by using the deviance information criterion. Our results show that there are four transmission rates for a two-phase system, corresponding to each combination of infected donor and susceptible recipient. Knowing the number and magnitudes of the transmission rates allows the dominant pathways for transmission in a heterogeneous population to be identified. Finally, we show how failure to allow for multiple transmission rates can overestimate or underestimate the rate of spread of epidemics in heterogeneous environments, which could lead to marked failure or inefficiency of control strategies.

The importance of animal selection behaviour in determining spatial structure of grazing systems has implications for sustainable grazing management. Although changes in stocking density provide a mechanism for direct control of animal impact, grazing behaviour is also responsible for influencing vegetation dynamics. A spatially explicit grazing model was used to explore the impact of movement in search of higher intake (search rate) and search distance on spatial sward structure, specifically the distribution of sward surface height. The model simulated a two-stage grazing process in heterogeneous environments i.e. searching then biting. As search rate and search distance increased so the spatial variance of sward structure decreased. Changes in herbivore search rate have a greater impact on spatial variance of pastoral grazing systems than search distance. Herbivores foraging in heterogeneous environments with greater search rates may better utilise the available forage resources. Higher search rates in natural and agricultural systems may determine herbivore fitness and survival or production, respectively.

Summary 1 Paratuberculosis (Mycobacterium avium subspecies paratuberculosis; Map) is a widespread and difficult disease to control in livestock populations and also has possible links to Crohn's disease in humans. Rabbits (Oryctolagus cuniculus) have been identified recently as the key wildlife species in terms of paratuberculosis transmission to the wider host community. Here, we test the hypothesis that Map can persist in rabbit populations for extended periods of time in the absence of any external source of infection. 2 A spatially explicit stochastic simulation model of a generic host–disease interaction was developed to quantify the interplay between vertical and horizontal routes of transmission needed for the persistence of Map in rabbit populations and to test the hypothesis. The model was parameterized based on empirical studies on rabbit population dynamics and on rabbit-to-rabbit routes of Map transmission. 3 Predictions from the model suggest that any disease with susceptible–infected (SI) dynamics without disease-induced mortality can persist within a rabbit population in the absence of vertical transmission, providing the horizontal transmission coefficient, β, is greater than approximately 0·012. The inclusion of any vertical transmission reduces the value of β that is necessary for infection to persist. 4 Paratuberculosis persists in rabbit populations at all values of the horizontal and vertical transmission parameters in the range estimated from the field data and in many cases at all values within 95% confidence intervals around this range. The persistence of Map infection in rabbit populations in the absence of external sources of infection suggests that they may act as a reservoir of infection for sympatric livestock. 5 Synthesis and applications. Our findings, in combination with the ubiquitous distribution of rabbits in the United Kingdom and elsewhere, suggests that if Map becomes established in rabbit populations they are likely to provide widespread and persistent environmental distributions of infection and thus disease risk to livestock and potentially humans. Where local rabbit populations are infected they should be included in any future paratuberculosis control strategies. Because eradication of rabbits is often not a realistic option, control strategies should include reducing interspecific transmission risk from rabbits to livestock via the faecal–oral route.

We examined how decision-making processes at small spatial scales can account for individual movements and food intake at larger scales. Our experiment used two currencies that might affect animal decisions: food reward at the patch scale and spatial distribution of the patches. We used Soay sheep, Ovis aries, as the model species in conjunction with an artificial arena that allowed us to modify food-handling conditions and the distribution of the food patches to record variation in food intake of both sexes. The main variable that affected food intake was how efficient the animals were at avoiding patches that were depleted in previous visits. Intake was also affected by mouth size and the spatial distribution of the feeding stations. Sheep were more efficient at exploiting clustered patches with a high energy reward than a matrix of homogeneously distributed patches of lower energy reward. Females' intake was higher than males'; we discuss this in relation to different foraging strategies related to sexual differences in fibre digestibility and the distribution of food resources of different quality that both sexes might use in field conditions. The results indicated that variation in food-handling conditions at the patch level affects food intake at larger scales, providing support for the hypothesis that animal movement related to grazing activity is a hierarchical process, scaling up from bite size to large spatial scales. However, spatial memory is important for maximizing the use of patchily distributed food.

Parasitic nematodes represent one of the most pervasive and significant challenges to grazing livestock, and their intensity and distribution are strongly influenced by climate. Parasite levels and species composition have already shifted under climate change, with nematode parasite intensity frequently low in newly colonized areas, but sudden large-scale outbreaks are becoming increasingly common. These outbreaks compromise both food security and animal welfare, yet there is a paucity of predictions on how climate change will influence livestock parasites. This study aims to assess how climate change can affect parasite risk. Using a process-based approach, we determine how changes in temperature-sensitive elements of outbreaks influence parasite dynamics, to explore the potential for climate change to influence livestock helminth infections. We show that changes in temperate-sensitive parameters can result in nonlinear responses in outbreak dynamics, leading to distinct ‘tipping-points’ in nematode parasite burdens. Through applying two mechanistic models, of varying complexity, our approach demonstrates that these nonlinear responses are robust to the inclusion of a number of realistic processes that are present in livestock systems. Our study demonstrates that small changes in climatic conditions around critical thresholds may result in dramatic changes in parasite burdens.

Stochastic process models are useful in describing a broad range of individual-based phenomena and are increasingly being applied in ecology. However, the estimation of parameters in such models is an important issue which has typically received much less attention than the exploration of model behaviour. The difficulties of parameter estimation are compounded by the fact that in most situations the available data are incomplete in some sense. Here, we demonstrate how methods of Markov chain Monte Carlo (McMC) Gibbs sampling can be combined within reversible-jump Metropolis–Hastings McMC frameworks to produce a hybrid sampler which can be used to obtain estimates of parameters and missing data for a broad class of stochastic process rate models. We apply these methods to two stochastic models arising from the ecology of grazed ecosystems in order to display the benefits of the hybrid sampler and the usefulness of a stochastic modelling approach to experiments where limited data exist.

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models. They often provide insights into model behaviour and help validate simulation results. However, existing closure schemes typically fail in situations where the population distribution is highly skewed or extinctions occur. In this study we address these problems by introducing novel second- and third-order moment closure approximations which we apply to the stochastic SI and SIS epidemic models. In the case of the SI model, which has a highly skewed distribution of infection, we develop a second-order approximation based on the beta-binomial distribution. In addition, a closure approximation based on mixture distribution is developed in order to capture the behaviour of the stochastic SIS model around the threshold between persistence and extinction. This mixture approximation comprises a probability distribution designed to capture the quasi-equilibrium probabilities of the system and a probability mass at 0 which represents the probability of extinction. Two third-order versions of this mixture approximation are considered in which the log-normal and the beta-binomial are used to model the quasi-equilibrium distribution. Comparison with simulation results shows: (1) the beta-binomial approximation is flexible in shape and matches the skewness predicted by simulation as shown by the stochastic SI model and (2) mixture approximations are able to predict transient and extinction behaviour as shown by the stochastic SIS model, in marked contrast with existing approaches. We also apply our mixture approximation to approximate a likelihood function and carry out point and interval parameter estimation.

Parasitic helminths present one of the most pervasive challenges to grazing herbivores. Many macro-parasite transmission models focus on host physiological defence strategies, omitting more complex interactions between hosts and their environments. This work represents the first model that integrates both the behavioural and physiological elements of gastro-intestinal nematode transmission dynamics in a managed grazing system. A spatially explicit, individual-based, stochastic model is developed, that incorporates both the hosts' immunological responses to parasitism, and key grazing behaviours including faecal avoidance. The results demonstrate that grazing behaviour affects both the timing and intensity of parasite outbreaks, through generating spatial heterogeneity in parasite risk and nutritional resources, and changing the timing of exposure to the parasites' free-living stages. The influence of grazing behaviour varies with the host-parasite combination, dependent on the development times of different parasite species and variations in host immune response. Our outputs include the counterintuitive finding that under certain conditions perceived parasite avoidance behaviours (faecal avoidance) can increase parasite risk, for certain host-parasite combinations. Through incorporating the two-way interaction between infection dynamics and grazing behaviour, the potential benefits of parasite-induced anorexia are also demonstrated. Hosts with phenotypic plasticity in grazing behaviour, that make grazing decisions dependent on current parasite burden, can reduce infection with minimal loss of intake over the grazing season. This paper explores how both host behaviours and immunity influence macro-parasite transmission in a spatially and temporally heterogeneous environment. The magnitude and timing of parasite outbreaks is influenced by host immunity and behaviour, and the interactions between them; the incorporation of both regulatory processes is required to fully understand transmission dynamics. Understanding of both physiological and behavioural defence strategies will aid the development of novel approaches for control.

Microbial diversity in the human colon is very high with apparently large functional redundancy such that within each bacterial functional group there are many coexisting strains. Modelling this mathematically is problematic since strains within a functional group are often competing for the same limited number of resources and therefore competitive exclusion theory predicts a loss of diversity over time. Here we investigate, through computer simulation, a fluctuation dependent mechanism for the promotion of diversity. A variable pH environment caused by acidic by-products of bacterial growth on a fluctuating substrate coupled with small differences in acid tolerance between strains promotes diversity under both equilibrium and far-from-equilibrium conditions. Under equilibrium conditions pH fluctuations and relative nonlinearity in pH limitation among strains combine to prevent complete competitive exclusion. Under far-from-equilibrium conditions, loss of diversity through extinctions is made more difficult because pH cycling leads to fluctuations in the competitive ranking of strains, thereby helping to equalise fitness. We assume a trade-off between acid tolerance and maximum growth rate so that our microbial system consists of strains ranging from specialists to generalists. By altering the magnitude of the effect of the system on its pH environment (e.g. the buffering capacity of the colon) and the pattern of incoming resource we explore the conditions that promote diversity.

Simple Summary Parasitic helminths represent one of the most pervasive challenges to livestock, and their intensity and distribution will be influenced by climate change. There is a need for long-term predictions to identify potential risks and highlight opportunities for control. We explore the approaches to modelling future helminth risk to livestock under climate change. One of the limitations to model creation is the lack of purpose driven data collection. We also conclude that models need to include a broad view of the livestock system to generate meaningful predictions. Abstract Climate change is a driving force for livestock parasite risk. This is especially true for helminths including the nematodes Haemonchus contortus, Teladorsagia circumcincta, Nematodirus battus, and the trematode Fasciola hepatica, since survival and development of free-living stages is chiefly affected by temperature and moisture. The paucity of long term predictions of helminth risk under climate change has driven us to explore optimal modelling approaches and identify current bottlenecks to generating meaningful predictions. We classify approaches as correlative or mechanistic, exploring their strengths and limitations. Climate is one aspect of a complex system and, at the farm level, husbandry has a dominant influence on helminth transmission. Continuing environmental change will necessitate the adoption of mitigation and adaptation strategies in husbandry. Long term predictive models need to have the architecture to incorporate these changes. Ultimately, an optimal modelling approach is likely to combine mechanistic processes and physiological thresholds with correlative bioclimatic modelling, incorporating changes in livestock husbandry and disease control. Irrespective of approach, the principal limitation to parasite predictions is the availability of active surveillance data and empirical data on physiological responses to climate variables. By combining improved empirical data and refined models with a broad view of the livestock system, robust projections of helminth risk can be developed.

Biological atlases are, for many species, the only source of information on their distribution over large geographical areas, and are widely used to inform models of the environmental distribution of species. Such data are not collected using standardized survey techniques, however, and spatial variations in coverage (the relative extent or completeness of records) may lead to variations in the probability that the species will be recorded at locations where it is present (the ‘‘recording probability’’). If spatial patterns in recording probabilities are correlated with key environmental variables, then biased estimates of the relationships between environmental variables and species distributions may be obtained. We outline a general statistical framework for modelling the environmental distribution of species using, known as Bayesian Image Restoration (BIR). BIR can be used in combination with any species distribution model, but in addition allows us to account for spatial heterogeneity in recording probabilities by utilizing expert knowledge on spatial patterns in coverage. We illustrate the methodology by applying it to maps of the recorded distribution of two plant species in Germany, taken from the German atlas of vascular plants. We find that estimated spatial patterns in recording probabilities for both species are correlated with key environmental variables. Consequently, different relationships between the probability of presence of a species and environmental variables were obtained when the species distribution models were parameterised within a BIR framework. Care must be taken in the application of BIR, since the resulting inferences can depend strongly upon the modelling assumptions that are adopted. Nevertheless, we conclude that BIR has the potential to make better use of uncertain information on species distributions than conventional methods, and can be used to formally investigate the robustness of inferences on the environmental distribution of species to assumptions concerning spatial patterns in recording probabilities.

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process., Author Summary In the midst of increasingly available sequence data of pathogens, a key challenge is to better integrate these data with traditional epidemiological data, with the proximate goal of reliable prediction and the ultimate aim of effective management of disease outbreaks. Although substantial advances have been made for such an integration, and they have improved our understandings of many disease dynamics which are not available otherwise, current methods have relied on fast algorithms, rather than achieving a systematic integration and accurate inference of the joint epidemiological-evolutionary process. Building on methods in current literature, this paper describes a novel Bayesian approach for systematically integrating these two streams of data. We propose a computationally tractable Bayesian inferential algorithm which takes the full joint epidemiological-evolutionary process into account. Using this algorithm, we study systematically the value of genetic data, providing valuable insights into future sampling designs. The algorithm is subsequently applied to real-world dataset describing the spread of animal foot-and-mouth disease in the UK, demonstrating the importance of such a systematic integration achieved with our methodology.

The role of stochasticity and spatial heterogeneity in foraging systems is investigated. We formulate a spatially explicit model which describes the behaviour of grazing animals in response to local information using simple stochastic rules. In particular the model reflects the biology in that decisions to move to a new location are based on visual assessment of the sward height in a surrounding neighbourhood, whilst the decision to graze the current location is based on the residual sward height and olfactory assessment of local faecal contamination. It is assumed that animals do not interact directly, but do so through modification of, and response to a common environment. Spatial heterogeneity is shown to have significant effects including reducing the equilibrium intake rate and increasing the optimal stocking density, and must therefore be taken into account by resource managers. We demonstrate the relationship between the stochastic spatial model and its non-spatial deterministic counterpart, and in the process derive a moment-closure approximation to the full process, which can be regarded as an intermediate, or pseudo-spatial model. The role of spatial heterogeneity is emphasized, and better understood by comparing the results obtained from each approach. The relative efficiency of random and directed searching behaviour in spatially heterogeneous environments is explored for both clean and contaminated pastures, and the impact of faecal avoidance behaviour assessed.

Population reduction is often used as a control strategy when managing infectious diseases in wildlife populations in order to reduce host density below a critical threshold. However, population reduction can disrupt existing social and demographic structures leading to changes in observed host behaviour that may result in enhanced disease transmission. Such effects have been observed in several disease systems, notably badgers and bovine tuberculosis. Here we characterise the fundamental properties of disease systems for which such effects undermine the disease control benefits of population reduction.\ud \ud By quantifying the size of response to population reduction in terms of enhanced transmission within a generic non-spatial model, the properties of disease systems in which such effects reduce or even reverse the disease control benefits of population reduction are identified. If population reduction is not sufficiently severe, then enhanced transmission can lead to the counter intuitive perturbation effect, whereby disease levels increase or persist where they would otherwise die out. Perturbation effects are largest for systems with low levels of disease, e.g. low levels of endemicity or emerging disease.\ud \ud Analysis of a stochastic spatial meta-population model of demography and disease dynamics leads to qualitatively similar conclusions. Moreover, enhanced transmission itself is found to arise as an emergent property of density dependent dispersal in such systems. This spatial analysis also shows that, below some threshold, population reduction can rapidly increase the area affected by disease, potentially expanding risks to sympatric species.\ud \ud Our results suggest that the impact of population reduction on social and demographic structures is likely to undermine disease control in many systems, and in severe cases leads to the perturbation effect. Social and demographic mechanisms that enhance transmission following population reduction should therefore be routinely considered when designing control programmes.

A cardinal challenge in epidemiological and ecological modelling is to develop effective and easily deployed tools for model assessment. The availability of such methods would greatly improve understanding, prediction and management of disease and ecosystems. Conventional Bayesian model assessment tools such as Bayes factors and the deviance information criterion (DIC) are natural candidates but suffer from important limitations because of their sensitivity and complexity. Posterior predictive checks, which use summary statistics of the observed process simulated from competing models, can provide a measure of model fit but appropriate statistics can be difficult to identify. Here, we develop a novel approach for diagnosing mis-specifications of a general spatio-temporal transmission model by embedding classical ideas within a Bayesian analysis. Specifically, by proposing suitably designed non-centred parametrization schemes, we construct latent residuals whose sampling properties are known given the model specification and which can be used to measure overall fit and to elicit evidence of the nature of mis-specifications of spatial and temporal processes included in the model. This model assessment approach can readily be implemented as an addendum to standard estimation algorithms for sampling from the posterior distributions, for example Markov chain Monte Carlo. The proposed methodology is first tested using simulated data and subsequently applied to data describing the spread of Heracleum mantegazzianum (giant hogweed) across Great Britain over a 30-year period. The proposed methods are compared with alternative techniques including posterior predictive checking and the DIC. Results show that the proposed diagnostic tools are effective in assessing competing stochastic spatio-temporal transmission models and may offer improvements in power to detect model mis-specifications. Moreover, the latent-residual framework introduced here extends readily to a broad range of ecological and epidemiological models.

Fasciola hepatica (liver fluke) is a physically and economically devastating parasitic trematode whose rise in recent years has been attributed to climate change. Climate has an impact on the free-living stages of the parasite and its intermediate host Lymnaea truncatula, with the interactions between rainfall and temperature having the greatest influence on transmission efficacy. There have been a number of short term climate driven forecasts developed to predict the following season's infection risk, with the Ollerenshaw index being the most widely used. Through the synthesis of a modified Ollerenshaw index with the UKCP09 fine scale climate projection data we have developed long term seasonal risk forecasts up to 2070 at a 25 km square resolution. Additionally UKCIP gridded datasets at 5 km square resolution from 1970-2006 were used to highlight the climate-driven increase to date. The maps show unprecedented levels of future fasciolosis risk in parts of the UK, with risk of serious epidemics in Wales by 2050. The seasonal risk maps demonstrate the possible change in the timing of disease outbreaks due to increased risk from overwintering larvae. Despite an overall long term increase in all regions of the UK, spatio-temporal variation in risk levels is expected. Infection risk will reduce in some areas and fluctuate greatly in others with a predicted decrease in summer infection for parts of the UK due to restricted water availability. This forecast is the first approximation of the potential impacts of climate change on fasciolosis risk in the UK. It can be used as a basis for indicating where active disease surveillance should be targeted and where the development of improved mitigation or adaptation measures is likely to bring the greatest benefits.