François Brun

Modelling and mapping potential epidemics of wheat diseases—examples on leaf rust and Septoria tritici blotch using EPIWHEAT

Policy makers and researchers need to develop long-term priorities using reliable, quantitative tools to assess the risks associated with plant diseases over a range of plant pathogens and over space. EPIWHEAT is a generic simulation model designed to analyse potential disease epidemics in wheat, i.e., epidemics that depend only on the physical environment, and that are not constrained by any disease control. The model is developed on a core structure involving healthy, latent, infectious, and removed sites, and accounts for lesion expansion. It simulates in a simple way host dynamics (growth and senescence). The model involves as few parameters as possible, and a few driving functions. Here, EPIWHEAT is populated with parameters for brown rust (leaf rust; Puccinia triticina) and Septoria tritici blotch (Zymoseptoria tritici). Simulated epidemics are compared to observations at the field, national (France), and European scales. The model appears to represent a sound basis for predicting potential epidemics of wheat foliar diseases at large scales. Areas for model development are documented and discussed. EPIWHEAT appears to provide a simple, generic, transparent, flexible, and reliable platform to modelling potential epidemics caused by leaf pathogens of wheat.

Uncertainty and Sensitivity Analysis

Uncertainty analysis consists of quantitatively evaluating uncertainty in model components (input variables, parameters, equations) for a given situation, and deducing an uncertainty distribution for each output variable rather than a single value. Uncertainty analysis is a key component of model-based risk analysis and decision making because it provides risk assessors and decision makers with information about the accuracy of model outputs. The aim of sensitivity analysis is to determine how sensitive the output of a model is with respect to elements of the model which are subject to uncertainty. Sensitivity analysis may be used to study relationships between model outputs and model inputs, and to identify which input factors have a small or a large influence on the output. This chapter presents the main steps of uncertainty and sensitivity analysis, and then describes in detail several methods that can be easily implemented with R. All methods are illustrated with several case studies using epidemiological and weed population models.

Predictive systems models can help elucidate bee declines driven by multiple combined stressors

Bee declines are driven by multiple combined stresses, making it exceedingly difficult to identify experimentally the most critical threats to bees and their pollination services. We highlight here the too often ignored potential of mechanistic models in identifying critical stress combinations. Advanced bee models are now available as open access tools and offer an unprecedented opportunity for bee biologists to explore bee resilience tipping points in a variety of environmental contexts. We provide general guidelines on how to run bee models to help detect a priori critical stress combinations to be targeted in the field. This so-called funnel analysis should be performed in tight conjunction with the recent development of large-scale field monitoring programs for bee health surveillance.

Basics of Agricultural System Models

Agricultural systems are complex combinations of various components. These components contain a number of interacting biological, physical, and chemical processes that are manipulated by human managers to produce the most basic of human needs–food, fiber, and energy. In this chapter, we present concepts of system models with examples, along with methods for developing system models. System models can be viewed in two different, yet complementary ways. First, a model can be treated as a system of differential or difference equations that describe the dynamics of the system. Second, the model can be treated as a set of static equations that describe how responses of interest at particular times depend on explanatory variables. We present and discuss these two viewpoints in this chapter. As we shall see, the different methods described in this book may call for one or the other of these viewpoints. In this chapter, we start by presenting general systems concepts and definitions that are needed for modeling systems. Then we go through the process of developing a model of a system using an example with two simple interacting components that will help give students an intuitive understanding of the system modeling process. Example system models are presented for several important agricultural system components, demonstrating some of the key features and relationships used in model development.

Assessing plant health in a network of experiments on hardy winter wheat varieties in France: patterns of disease-climate associations

A data set generated by a multi-year (2003–2010) and multi-site network of experiments on winter wheat varieties grown at different levels of crop management is analysed in order to assess the importance of climate on the variability of wheat health. Wheat health is represented by the multiple pathosystem involving five components: leaf rust, yellow rust, fusarium head blight, powdery mildew, and septoria tritici blotch. An overall framework of associations between multiple diseases and climate variables is developed. This framework involves disease levels in a binary form (i.e. epidemic vs. non-epidemic) and synthesis variables accounting for climate over spring and early summer. The multiple disease-climate pattern of associations of this framework conforms to disease-specific knowledge of climate effects on the components of the pathosystem. It also concurs with a (climate-based) risk factor approach to wheat diseases. This report emphasizes the value of large scale data in crop health assessment and the usefulness of a risk factor approach for both tactical and strategic decisions for crop health management.

Putting It All Together in a Case Study

In the previous chapters, methods for working with dynamic system models were presented using various examples, chosen to illustrate the principles of the methods. What is missing there is the way that the methods interact within a single modeling project. In fact, there is to a large extent a logical progression in a modeling project, from an exploration of the data, to a preliminary test of the model, to uncertainty analysis and sensitivity analysis, to model calibration, then to another round of evaluation, and finally to application of the model. In many cases, one step uses information from the previous steps. It is this progression and interaction that we illustrate in this chapter. Doing a case study also requires us to choose, when several different approaches are possible. This may also be helpful, since each modeler will be faced with similar choices. The case study uses the simple maize model, and has as its objective to map maize yield and inter-annual variability over Europe. Only the most important parts of the R code to apply the methods are shown. The main results are shown and discussed. All the steps can be easily re-run using demonstration R scripts (demos) in the R package ZeBook.

Parameter Estimation with Bayesian Methods

Bayesian methods are becoming increasingly popular for estimating parameters of complex mathematical models because the Bayesian approach provides a coherent framework for dealing with uncertainty. To start with, the principle is a prior probability distribution of the model parameters describing our belief about the parameter values before we use the set of measurements. The Bayesian methods then tell us how to update this belief using the measurements to give the posterior parameter density. In the Bayesian approach, the parameters are defined as random variables and the prior and posterior parameter distributions represent our belief about parameter values before and after using observed data to improve estimates. This approach has several advantages: i) parameters can be estimated from different types of information (data, literature, expert knowledge); ii) the posterior probability distribution can be used to implement uncertainty analysis methods; iii) the posterior probability distribution can be used for optimizing decisions in the face of uncertainty. This chapter presents the basic principles of the Bayesian approach and describes several algorithms to calculate posterior parameter distributions. These algorithms are illustrated in several applications on yield and soil carbon estimation.

Modelling pesticides leaching in cropping systems: Effect of uncertainties in climate, agricultural practices, soil and pesticide properties

Abstract Modelling of pesticide leaching is paramount to managing the environmental risks associated with the chemical protection of crops, but it involves large uncertainties in relation to climate, agricultural practices, soil and pesticide properties. We used Latin Hypercube Sampling to estimate the contribution of these input factors with the STICS-MACRO model in the context of a 400 km2 catchment in France, and two herbicides applied to maize: bentazone and S-metolachlor. For both herbicides, the most influential input factors on modelling of pesticide leaching were the inter-annual variability of climate, the pesticide adsorption coefficient and the soil boundary hydraulic conductivity, followed by the pesticide degradation half-life and the rainfall spatial variability. This work helps to identify the factors requiring greater accuracy to ensure better pesticide risk assessment and to improve environmental management and decision-making processes by quantifying the probability and reliability of prediction of pesticide concentrations in groundwater with STICS-MACRO.

Estimating the incidence of Septoria leaf blotch in wheat crops from in-season field measurements

Septoria leaf blotch is a widespread disease caused by the fungus Zymoseptoria tritici (formely known as Mycosphaerella graminicola). It causes yield losses in winter wheat crops (Triticum aestivum L.) in many European countries. In this study, we aimed to develop statistical models for estimating regional and site-specific incidence of Septoria leaf blotch from in-season field measurements. Four generalised linear models and four generalised linear mixed-effect models were fitted to six years of data collected from a major wheat-producing area of France, using frequentist and Bayesian methods. We compared the abilities of these models to predict S. tritici incidence over different time scales. We found that the best models were those that included site-year effects and disease risk ratings based on sowing dates and cultivar resistance levels. These models can be used to estimate the dynamics of disease incidence from observations collected in regional surveys and, as such, could help regional extension services evaluate current disease incidence at the regional scale. The proposed models could also be adjusted to make use of site-specific in-season field measurements for the estimation of site-specific disease incidence. With the current survey design, site-specific estimates are more accurate than regional estimates after mid-May. Such estimates could be used to help farmers adapt their control strategies locally during the growing season.

Statistical Notions Useful for Modeling

We first define the notion of a random variable, and then the notion of a probability distribution function. Then we consider multiple random variables, and the ways of describing distributions in this case. We are particularly interested in conditional distributions, since a regression model is in fact an approximation to the conditional expectation of the response variable, given the explanatory variables. Next we consider sampling and samples. Since our information about the random variables of interest comes from sampling, it is essential to show how sampling quantities are related to population quantities. We discuss simple random sampling and also sampling schemes more relevant in agronomy. Next we present regression models. The last section is a brief introduction to Bayesian statistics.