Abstract
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.
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Acknowledgments
This research was supported by SynOEM - Mieux profiter de la synergie entre réseaux d’observations, expertise et modélisation pour l’élaboration du Bulletin de Santé du Végétal (http://www.modelia.org/moodle/course/view.php?id=55), funded by the French National Agency for Water and Aquatic Environments (ONEMA) under the Ecophyto Plan supported by the French Ministry of Agriculture. This work was cofunded by a PhD grant from the French Association for Technical Research (ANRT).
We are grateful to E. Gourdain, D. Simonneau, V. Bochu, A. Decarrier, D. Gouache, G. Hugerot, and J.Veslot for their comments on our results and to Alex Edelman & Associates for English proofreading.
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Appendix
Appendix
Appendix A. Correspondence between final leaf numbers and observed leaf numbers as a function of wheat stage on the observation date (Simonneau et al. 2009)
Observed leaf number | Zadoks stage (Zadoks et al. 1974) on the observation date | Corresponding final leaf number |
|---|---|---|
1 | Z31 | 4 |
1 | Z32 | 3 |
1 | Z37 | 2 |
1 | Z39 | 1 |
2 | Z31 | 5 |
2 | Z32 | 4 |
2 | Z37 | 3 |
2 | Z39 | 2 |
3 | Z31 | 6 |
3 | Z32 | 5 |
3 | Z37 | 4 |
3 | Z39 | 3 |
Appendix B. R code used to fit a frequentist model including site-year random effects and a covariable describing the level of SLB risk (model 4F)
This model was fitted with the glmer() function (available with the lme4 package version 1.1–6). The SLB incidence data were included in a data.frame object called TAB_glob. The vector feuille_m includes the numbers of infected leaves in samples of 20 leaves. The vector feuille_s is the number of healthy leaves (feuille_m + feuille_s = 20). The variable time_b represents time in days (noted t in “Materials and methods”), risque is a categorical variable indicating levels of SLB risk (high, medium, low) and id_plot is the site-year index variable.
In the glmer() function, the terms on the left of the sign “~” represent the data (cbind(feuille_m,feuille_s)) and the terms on the right describe the fixed effect (time_b + risque) and the random effect ((1 + time_b|id_plot)).
The number of infected leaves was assumed to follow a binomial probability distribution specified as family = binomial.
Model < − glmer(cbind(feuille_m, feuille_s) ~ time_b + risque + (1 + time_b | id_plot), family = binomial, data = TAB_glob)
Appendix C. WinBUGS script used to fit a Bayesian model including site-year random effects and a covariable describing the level of SLB risk (model 4B)
Ndata is the total number of SLB incidence data, Nsiteyear is the number of site-years, y[i] is the ith incidence, theta[] is a vector of random site-year effects, rm[] and rf[] are dummy variables indicating medium and high risk levels respectively, p[] is the probability that one leaf is infected, alpha0, alpha1, betarm and betarf are fixed effects, and lambda is a variable used to ensure that disease incidence is an increasing function of time (time[]).
Appendix D. Estimated parameter values and 95 % confidence intervals (in brackets) obtained for the frequentist models 1F-3F, for the three leaves considered (leaves 1 to 3).
Parameters | Leaf 1 | ||
Model 1F | Model 2F | Model 3F | |
α 0 | −7.223 (−7.403; −7.063) | −15.854 (−17.188; −14.52) | −8.083 (−8.282; −7.884) |
α 1 | 0.110 (0.107; 0.113) | 0.239 (0.214; 0.264) | 0.112 (0.109; 0.116) |
g H | 1.217 (1.108; 1.327) | ||
g M | 0.616 (0.511; 0.721) | ||
Leaf 2 | |||
Model 1F | Model 2F | Model 3F | |
α 0 | −6.083 (−6.201; −5.965) | −11.052 (−11.73; −10.373) | −6.551 (−6.685; −6.416) |
α 1 | 0.094 (0.092; 0.096) | 0.169 (0.155; 0.182) | 0.096 (0.094; 0.099) |
g H | 0.824 (0.747; 0.902) | ||
g M | 0.203 (0.131; 0.276) | ||
Leaf 3 | |||
Model 1F | Model 2F | Model 3F | |
α 0 | −5.121 (−5.212; −5.029) | −8.925 (−9.466; −8.383) | −5.495 (−5.598; −5.391) |
α 1 | 0.075 (0.074; 0.077) | 0.133 (0.123; 0.144) | 0.076 (0.075; 0.078) |
g H | 0.675 (0.613; 0.738) | ||
g M | 0.250 (0.193; 0.308) | ||
Appendix E. Estimated posterior means of the parameters and 95 % credibility intervals (in brackets) obtained for Bayesian models 1B-3B, for the three leaves considered (leaves 1 to 3).
Parameters | Leaf 1 | ||
Model 1B | Model 2B | Model 3B | |
α 0 | -7.235 (-7.408; -7.067) | −15.931 (−16.960; −14.86) | -8.085 (-8.286; -7.894) |
α 1 | 0.110 (0.107; 0.113) | 0.243 (0.223; 0.263) | 0.112 (0.109; 0.115) |
g H | 1.219 (1.111; 1.329) | ||
g M | 0.618 (0.515; 0.722) | ||
Leaf 2 | |||
Model 1B | Model 2B | Model 3B | |
α 0 | -6.084 (-6.203; -5.968) | −11.106 (−11.89; −10.43) | -6.552 (-6.688; -6.418) |
α 1 | 0.094 (0.092; 0.096) | 0.17 (0.158; 0.184) | 0.096 (0.094; 0.098) |
g H | 0.825 (0.749; 0.903) | ||
g M | 0.204 (0.132; 0.276) | ||
Leaf 3 | |||
Model 1B | Model 2B | Model 3B | |
α 0 | −5.121 (-5.212; -5.030) | −8.788 (−9.479; −8.196) | -5.495 (-5.599; -5.393) |
α 1 | 0.075 (0.074; 0.077) | 0.131 (0.119; 0.143) | 0.076 (0.075; 0.078) |
g H | 0.676 (0.614; 0.738) | ||
g M | 0.251 (0.194; 0.301) | ||
Appendix F. Median regional disease incidence (%) estimated for leaf 2 from 2009 to 2015. The medians were calculated across the site-specific disease incidence dynamics estimated with model 4F fitted to 4617 SLB data collected from 2009 to 2015 in the Centre region. Estimates obtained in 2015 (brown line) were derived from data collected before June 10th and extracted from the Vigiculture database. Light brown circles indicate observed data collected in the Centre region in 2015. Circle size is proportional to the number of data.
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Michel, L., Brun, F., Piraux, F. et al. Estimating the incidence of Septoria leaf blotch in wheat crops from in-season field measurements. Eur J Plant Pathol 146, 17–35 (2016). https://doi.org/10.1007/s10658-016-0887-9
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DOI: https://doi.org/10.1007/s10658-016-0887-9