Stephen Parnell

Thirteen challenges in modelling plant diseases

The underlying structure of epidemiological models, and the questions that models can be used to address, do not necessarily depend on the host organism in question. This means that certain preoccupations of plant disease modellers are similar to those of modellers of diseases in human, livestock and wild animal populations. However, a number of aspects of plant epidemiology are very distinctive, and this leads to specific challenges in modelling plant diseases, which in turn sets a certain agenda for modellers. Here we outline a selection of 13 challenges, specific to plant disease epidemiology, that we feel are important targets for future work.

Large-Scale Fungicide Spray Heterogeneity and the Regional Spread of Resistant Pathogen Strains

ABSTRACT Most models for the spread of fungicide resistance in plant pathogens are focused on within-field dynamics, yet regional invasion depends upon the interactions between field populations. Here, we use a spatially implicit metapopulation model to describe the dynamics of regional spread, in which subpopulations correspond to single fields. We show that the criterion for the regional invasion of pathogens between fields differs from that for invasion within fields. That is, the ability of a fungicide-resistant strain of a pathogen to invade a field population does not necessarily imply an ability to spread through many fields at the regional scale. This depends upon an interaction between the fraction of fields that is sprayed and the reproductive capacity of the pathogen. This result is of practical significance and indicates that resistance management strategies which currently target within-field processes, such as the use of mixtures and alternations of fungicides, may be more effective if between-field processes also were targeted; for example, through the restricted deployment of fungicides over large areas. We also show that the fraction of disease-free fields is maximized when the proportion of fields that is sprayed is just below the threshold for invasion of the resistant strain.

Small-Scale Fungicide Spray Heterogeneity and the Coexistence of Resistant and Sensitive Pathogen Strains

ABSTRACT Empirical evidence indicates that fungicide-resistant and sensitive strains can coexist for prolonged periods. Coexistence has important practical implications, for example, for the posttreatment recovery of sensitivity and consequently the life expectancy of fungicide products. Despite this, the factors influencing coexistence remain relatively unexplored. Ecological studies have shown that environmental heterogeneity can facilitate the coexistence of different species and subspecific groups. Here we use a simple differential equation model and show that fungicide spray heterogeneity per se is not sufficient for coexistence but that the outcome depends crucially on the competitive relationship between resistant and sensitive strains. The model incorporates the competition between resistant and sensitive pathogen strains for a limited supply of susceptible host tissue on a crop which has received an incomplete coverage of fungicide. We use a combination of invasibility analysis and model simulations to explore the conditions under which coexistence can occur. We further show that the maximum density of healthy host tissue isrealized when resistant and sensitive pathogen strains coexist. A set of key influencing parameters are identified and analyzed, and the consequences of the results for disease and resistance management are discussed.

Optimal Strategies for the Eradication of Asiatic Citrus Canker in Heterogeneous Host Landscapes

ABSTRACT The eradication of nonnative plant pathogens is a key challenge in plant disease epidemiology. Asiatic citrus canker is an economically significant disease of citrus caused by the bacterial plant pathogen Xanthomonas citri subsp. citri. The pathogen is a major exotic disease problem in many citrus producing areas of the world including the United States, Brazil, and Australia. Various eradication attempts have been made on the disease but have been associated with significant social and economic costs due to the necessary removal of large numbers of host trees. In this paper, a spatially explicit stochastic simulation model of Asiatic citrus canker is introduced that describes an epidemic of the disease in a heterogeneous host landscape. We show that an optimum eradication strategy can be determined that minimizes the adverse costs associated with eradication. In particular, we show how the optimum strategy and its total cost depend on the topological arrangement of the host landscape. We discuss the implications of the results for invading plant disease epidemics in general and for historical and future eradication attempts on Asiatic citrus canker.

Some Consequences of Using the Horsfall-Barratt Scale for Hypothesis Testing

Comparing treatment effects by hypothesis testing is a common practice in plant pathology. Nearest percent estimates (NPEs) of disease severity were compared with Horsfall-Barratt (H-B) scale data to explore whether there was an effect of assessment method on hypothesis testing. A simulation model based on field-collected data using leaves with disease severity of 0 to 60% was used; the relationship between NPEs and actual severity was linear, a hyperbolic function described the relationship between the standard deviation of the rater mean NPE and actual disease, and a lognormal distribution was assumed to describe the frequency of NPEs of specific actual disease severities by raters. Results of the simulation showed standard deviations of mean NPEs were consistently similar to the original rater standard deviation from the field-collected data; however, the standard deviations of the H-B scale data deviated from that of the original rater standard deviation, particularly at 20 to 50% severity, over which H-B scale grade intervals are widest; thus, it is over this range that differences in hypothesis testing are most likely to occur. To explore this, two normally distributed, hypothetical severity populations were compared using a t test with NPEs and H-B midpoint data. NPE data had a higher probability to reject the null hypothesis (H0) when H0 was false but greater sample size increased the probability to reject H0 for both methods, with the H-B scale data requiring up to a 50% greater sample size to attain the same probability to reject the H0 as NPEs when H0 was false. The increase in sample size resolves the increased sample variance caused by inaccurate individual estimates due to H-B scale midpoint scaling. As expected, various population characteristics influenced the probability to reject H0, including the difference between the two severity distribution means, their variability, and the ability of the raters. Inaccurate raters showed a similar probability to reject H0 when H0 was false using either assessment method but average and accurate raters had a greater probability to reject H0 when H0 was false using NPEs compared with H-B scale data. Accurate raters had, on average, better resolving power for estimating disease compared with that offered by the H-B scale and, therefore, the resulting sample variability was more representative of the population when sample size was limiting. Thus, there are various circumstances under which H-B scale data has a greater risk of failing to reject H0 when H0 is false (a type II error) compared with NPEs.

Bayesian inference for an emerging arboreal epidemic in the presence of control.

Significance Fast-moving and destructive emerging epidemics are seldom left to run their course because of the imperative to control further spread. Contemporaneous control measures, however, greatly complicate the characterization of the disease transmission process and the extraction of the epidemiological parameters of interest. The spread of Huanglongbing on orchard scales is used as a case study for modeling an emerging epidemic in the presence of control. We show that even with missing and censored data, and with seasonal and host age dependencies, it is possible to infer the parameters of a fully spatiotemporal stochastic model of disease spread. The value of the fitted model is to provide an engine for simulation studies of the costs and benefits of proposed disease control strategies. The spread of Huanglongbing through citrus groves is used as a case study for modeling an emerging epidemic in the presence of a control. Specifically, the spread of the disease is modeled as a susceptible-exposed-infectious-detected-removed epidemic, where the exposure and infectious times are not observed, detection times are censored, removal times are known, and the disease is spreading through a heterogeneous host population with trees of different age and susceptibility. We show that it is possible to characterize the disease transmission process under these conditions. Two innovations in our work are (i) accounting for control measures via time dependence of the infectious process and (ii) including seasonal and host age effects in the model of the latent period. By estimating parameters in different subregions of a large commercially cultivated orchard, we establish a temporal pattern of invasion, host age dependence of the dispersal parameters, and a close to linear relationship between primary and secondary infectious rates. The model can be used to simulate Huanglongbing epidemics to assess economic costs and potential benefits of putative control scenarios.

Estimating the incidence of an epidemic when it is first discovered and the design of early detection monitoring

The early detection of an invading epidemic is crucial for successful disease control. Although models have been used extensively to test control strategies following the first detection of an epidemic, few studies have addressed the issue of how to achieve early detection in the first place. Moreover, sampling theory has made great progress in understanding how to estimate the incidence or spatial distribution of an epidemic but how to sample for early detection has been largely ignored. Using a simple epidemic model we demonstrate a method to calculate the incidence of an epidemic when it is discovered for the first time (given a monitoring programme taking samples at regular intervals). We use the method to explore how the intensity and frequency of sampling influences early detection. In particular, we find that for epidemics characterised by high population growth rates it is most effective to spread sampling resources evenly in time. In addition we derive a useful approximation to our method which results in a simple equation capturing the relation between monitoring and epidemic dynamics. Not only does this provide valuable new insight but it provides a simple rule of thumb for the design of monitoring programmes in practice.

Early detection surveillance for an emerging plant pathogen: a rule of thumb to predict prevalence at first discovery

Emerging plant pathogens are a significant problem for conservation and food security. Surveillance is often instigated in an attempt to detect an invading epidemic before it gets out of control. Yet in practice many epidemics are not discovered until already at a high prevalence, partly due to a lack of quantitative understanding of how surveillance effort and the dynamics of an invading epidemic relate. We test a simple rule of thumb to determine, for a surveillance programme taking a fixed number of samples at regular intervals, the distribution of the prevalence an epidemic will have reached on first discovery (discovery-prevalence) and its expectation E(q*). We show that E(q*) = r/(N/Δ), i.e. simply the rate of epidemic growth divided by the rate of sampling; where r is the epidemic growth rate, N is the sample size and Δ is the time between sampling rounds. We demonstrate the robustness of this rule of thumb using spatio-temporal epidemic models as well as data from real epidemics. Our work supports the view that, for the purposes of early detection surveillance, simple models can provide useful insights in apparently complex systems. The insight can inform decisions on surveillance resource allocation in plant health and has potential applicability to invasive species generally.

The Effect of Farmers’ Decisions on Pest Control with Bt Crops: A Billion Dollar Game of Strategy

A farmer’s decision on whether to control a pest is usually based on the perceived threat of the pest locally and the guidance of commercial advisors. Therefore, farmers in a region are often influenced by similar circumstances, and this can create a coordinated response for pest control that is effective at a landscape scale. This coordinated response is not intentional, but is an emergent property of the system. We propose a framework for understanding the intrinsic feedback mechanisms between the actions of humans and the dynamics of pest populations and demonstrate this framework using the European corn borer, a serious pest in maize crops. We link a model of the European corn borer and a parasite in a landscape with a model that simulates the decisions of individual farmers on what type of maize to grow. Farmers chose whether to grow Bt-maize, which is toxic to the corn borer, or conventional maize for which the seed is cheaper. The problem is akin to the snow-drift problem in game theory; that is to say, if enough farmers choose to grow Bt maize then because the pest is suppressed an individual may benefit from growing conventional maize. We show that the communication network between farmers’ and their perceptions of profit and loss affects landscape scale patterns in pest dynamics. We found that although adoption of Bt maize often brings increased financial returns, these rewards oscillate in response to the prevalence of pests.

The Effect of Horsfall-Barratt Category Size on the Accuracy and Reliability of Estimates of Pecan Scab Severity

Pecan scab (Fusicladium effusum) is a destructive pecan disease. Disease assessments may be made using interval-scale-based methods or estimates of severity to the nearest percent area diseased. To explore the effects of rating method-Horsfall-Barratt (H-B) scale estimates versus nearest percent estimates (NPEs)-on the accuracy and reliability of severity estimates over different actual pecan scab severity ranges on fruit valves, raters assessed two cohorts of images with actual area (0 to 6, 6+ to 25%, and 25+ to 75%) diseased. Mean estimated disease within each actual disease severity range varied substantially. Means estimated by NPE within each actual disease severity range were not necessarily good predictors of the H-B scale estimate at <25% severity. H-B estimates by raters most often placed severity in the wrong category compared with actual disease. Measures of bias, accuracy, precision, and agreement using Lins concordance correlation depended on the range of actual severity, with improvements increasing with actual disease severity category (from 0 to 6 through 25+ to 75%); however, the improvement was unaffected by the H-B assessments. Bootstrap analysis indicated that NPEs provided either equally good or more accurate and precise estimate of disease compared with the H-B scale at severities of 25+ to 75%. Inter-rater reliability using NPEs was greater at 25+ to 75% actual disease severity compared with using the H-B scale. Using NPEs compared with the H-B scale will more often result in more precise and accurate estimates of pecan scab severity, particularly when estimating actual disease severities of 25+ to 75%.