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IPSIM-Wheat-Brown Rust is based on the DEX method, and was implemented with the software DEXi based on DEX methodology. IPSIM-Wheat-Brown Rust is therefore a hierarchical and qualitative model, allowing the prediction of Brown Rust injury according to various factors in interaction.

1 - IPSIM-Wheat-Brown Rust was designed in 3 steps: (1) identification and organisation of the attributes, (2) definition of attribute scales, and (3) definition of aggregative tables.

• Identification and organisation of the attributes

IPSIM-Wheat-Brown Rust aims at predicting the severity of Brown Rust on Wheat in a given field according to a set of input variables describing the cropping practices and the production situation.

The hierarchical structure presented in figure below represents the breakdown of factors affecting Brown Rust final severity into specific explanatory variables, represented by lower-level attributes. This figure represents the adaptation to Brown Rust of the model structure . All the attributes have been chosen using the knowledge available in the international literature.

In all, IPSIM-Wheat-Brown Rust has 16 attributes, of which 10 are basic (i.e. input variables) and 6 aggregated. The 10 basic attributes are presented as the terminal leaves of the tree and their levels are aggregated into higher levels according to aggregative tables.

• Definition of attribute scales

The second step in the design of a DEXi model is the choice of ordinal or nominal scales for basic and aggregated attributes. Sets of discrete values were defined for all attributes of the model and described by symbolic value scales defined by words. These values were defined according to the knowledge available in the international literature and some expertise when needed. IPSIM-Wheat-Brown Rust uses at most a four-grade value scale.

All the scales in figure below are ordered from values favourable to the disease (i.e. detrimental to the crop) on the left-hand side to values detrimental to the disease on the right-hand side (i.e. favourable to the crop). In the DEXi software, this difference is clearly visible because, by convention, values beneficial to the user are coloured in green, detrimental in red, and neutral in black.

• definition of aggregative tables

The third step in the design of a DEXi model is the choice of aggregative tables that define attribute aggregation throughout the attribute tree. The rules that correspond to a single aggregated attribute are gathered together and conveniently represented in tabular form. In this way, each aggregative table defines a mapping of all value combinations of lower-level attributes into the values of the aggregate attribute. The figure below shows the aggregative table that corresponds to the "mitigation through crop status" aggregated attribute and defines the value of this attribute for the 18 possible combinations of three cultivar choices, two levels of fertilisation and 3 sowing densities.

All aggregative tables are available below.

2 -  Evaluation of the predictive quality of IPSIM brown rust

The ordinal final attribute value (final severity of Brown Rust) is calculated by DEXi. The calculation consists in computing all aggregated attribute values according to: (i) the structure of the tree; (ii) a set of input variables (basic attribute values) defining a simulation unit; and (iii) the aggregative tables. An example of output results obtained for three simulation units is provided in figure below. They represent basic input attributes and aggregated attribute values for an organic,a conventional and a high-input wheat field.

In all, 1740 site-years (commercial or experimental fields) were used for the evaluation of the predictive quality of the model. They are composed of a large number of combinations of cropping practices and production situations (13 French cereal-growing regions over 15 years).

The model was assessed for its ability to predict severity classes. In order to do so, quantitative observed data were transformed into ordinal values, using the same discretization as the model (i.e. 0-5%, 5-10%, 10-20%, 20-50%, 50-100%).

The confusion matrix of the model was calculated and the associated accuracy (proportion of correctly predicted situations) along with the Cohen’s quadratic weighted Kappa, the Kendall’s τ_b and the Spearman’s rank correlation coefficient ρ_S. These calculations were performed with Mathematica 10.1.0.0.

The calculated accuracy of the confusion matrix (Figure below) indicates that the model correctly predicted most of the observations (84.5%). The quadratic weighted Kappa criterion indicated that the model explained ca. 68% of the variability in the dataset. The Kendall’s τ_b and the Spearman’s rank correlation coefficient ρ_S were respectively 0.59 and 0.61. The overall predictive quality of IPSIM-Wheat-brown rust was therefore judged satisfactory. The predictive quality was good for the lowest class (the most frequent observed class in the dataset): 82% of the observed values between 0 and 5% were correctly simulated. The model slightly overestimated final severities for observed severities higher than 5%.