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Modeling Bromus diandrus Seedling Emergence Using Nonparametric Estimation

  • R. Cao
  • M. Francisco-FernándezEmail author
  • A. Anand
  • F. Bastida
  • J. L. González-Andújar
Original Article

Abstract

Hydrothermal time (HTT) is a valuable environmental index to predict weed emergence. In this paper, we focus on the problem of predicting weed emergence given some HTT observations from a distribution point of view. This is an alternative approach to classical parametric regression, often employed in this framework. The cumulative distribution function (cumulative emergence) of the cumulative hydrothermal time (CHTT) is considered for this task. Due to the monitoring process, it is not possible to observe the exact emergence time of every seedling. On the contrary, these emergence times are observed in an aggregated way. To address these facts, a new nonparametric distribution function estimator has been proposed. A bootstrap bandwidth selection method is also presented. Moreover, bootstrap techniques are also used to develop simultaneous confidence intervals for the HTT cumulative distribution function. The proposed methods have been applied to an emergence data set of Bromus diandrus.

Key Words

Hydrothermal time Interval-censorship Nonparametric distribution estimation Bromus diandrus 

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References

  1. Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. MathSciNetzbMATHGoogle Scholar
  2. Bonferroni, C. E. (1935), “Il Calcolo Delle Assicurazioni Su Gruppi di Teste,” in Studi in Onore del Professore Salvatore Ortu Carboni, Rome, pp. 13–60. Google Scholar
  3. Bradford, K. J. (2002), “Applications of Hydrothermal Time to Quantifying and Modeling Seed Germination and Dormancy,” Weed Science, 50, 248–260. CrossRefGoogle Scholar
  4. Cao, R. (1993), “Bootstrapping the Mean Integrated Squared Error,” Journal of Multivariate Analysis, 45, 137–160. MathSciNetzbMATHCrossRefGoogle Scholar
  5. Cao, R., Cuevas, A., and Fraiman, R. (1995), “Minimum Distance Density-Based Estimation,” Computational Statistics & Data Analysis, 20, 611–631. MathSciNetzbMATHCrossRefGoogle Scholar
  6. Cao, R., Francisco-Fernández, M., and Quinto, E. J. (2010), “A Random Effect Multiplicative Heteroscedastic Model for Bacterial Growth,” BMC Bioinformatics, 11, 77. CrossRefGoogle Scholar
  7. Cao, R., Francisco-Fernández, M., Anand, A., Bastida, F., and Gonzalez-Andujar, J. L. (2011), “Computing Statistical Indices for Hydrothermal Times Using Weed Emergence Data,” Journal of Agricultural Science, Cambridge, 149, 701–712. CrossRefGoogle Scholar
  8. Colbach, N., Dürr, C., Roger-Estrade, J., and Caneill, J. (2005), “How to Model the Effects of Farming Practices on Weed Emergence,” Weed Research, 45, 2–17. CrossRefGoogle Scholar
  9. Davison, A. C., and Hinkley, D. V. (1997), Bootstrap Methods and Their Applications, Cambridge: Cambridge Univ. Press. Google Scholar
  10. Dorado, J., Sousa, E., Calha, I. M., González-Andújar, J. L., and Fernández-Quintanilla, C. (2009), “Predicting Weed Emergence in Maize Crops Under Two Contrasting Climatic Conditions,” Weed Research, 49, 251–260. CrossRefGoogle Scholar
  11. Fernández-Quintanilla, C., Navarrete, L., González-Andújar, J. L., Fernández, A., and Sánchez, M. J. (1986), “Seedling Recruitment and Age-Specific Survivorship and Reproduction in Populations of Avena sterilis ssp. ludoviciana,” Journal of Applied Ecology, 23, 945–955. CrossRefGoogle Scholar
  12. Forcella, F., Benech-Arnold, R. L., Sánchez, R., and Ghersa, C. M. (2000), “Modeling Seedling Emergence,” Field Crops Research, 67, 123–139. CrossRefGoogle Scholar
  13. Gonzalez-Andujar, J. L., Fernandez-Quintanilla, C., Bastida, F., Calvo, R., Gonzalez-Diaz, L., Izquierdo, J., Lezaun, J. A., Perea, F., Sanchez Del Arco, M. J., and Urbano, J. (2010), “Field Evaluation of a Decision Support System for Avena sterilis ssp. ludoviciana Control in Winter Wheat,” Weed Research, 50, 83–88. CrossRefGoogle Scholar
  14. Grundy, A. C. (2003), “Predicting Weed Emergence: A Review of Approaches and Future Challenges,” Weed Research, 43, 1–11. CrossRefGoogle Scholar
  15. Haj Seyed Hadi, M. R. and González-Andújar, J. L. (2009), “Comparison of Fitting Weed Seedling Emergence Models With Nonlinear Regression and Genetic Algorithm,” Computers & Electronics in Agriculture, 65, 19–25. CrossRefGoogle Scholar
  16. Hunter, E. A., Glasbey, C. A., and Naylor, R. E. L. (1984), “The Analysis of Data From Germination Tests,” Journal of Agricultural Science, Cambridge, 102, 207–213. CrossRefGoogle Scholar
  17. Izquierdo, J., González-Andújar, J. L., Bastida, F., Lezaun, J. A., and Sánchez del Arco, M. J. (2009), “A Thermal Time Model to Predict Corn Poppy (Papaver rhoeas) Emergence in Cereal Fields,” Weed Science, 57, 660–664. CrossRefGoogle Scholar
  18. Leblanc, M. L., Cloutier, D. C., Stewart, K., and Hamel, C. (2003), “The Use of Thermal Time to Model Common Lambsquarters (Chenopodium album) Seedling Emergence in Corn,” Weed Science, 51, 718–724. CrossRefGoogle Scholar
  19. Leguizamón, E. S., Fernández-Quintanilla, C., Barroso, J., and González-Andújar, J. L. (2005), “Using Thermal and Hydrothermal Time to Model Seedling Emergence of Avena sterilis ssp. ludoviciana in Spain,” Weed Research, 45, 149–156. CrossRefGoogle Scholar
  20. Lesaffre, E., Komárek, A., and Declerck, D. (2005), “An Overview of Methods for Interval-Censored Data With an Emphasis on Applications in Dentistry,” Statistical Methods in Medical Research, 14, 539–552. MathSciNetzbMATHCrossRefGoogle Scholar
  21. McGiffen, M., Spokas, K., Forcella, F., Archer, D., Poppe, S., and Figueroa, R. (2008), “Emergence Prediction of Common Groundsel (senecio vulgaris),” Weed Science, 56, 58–65. CrossRefGoogle Scholar
  22. Miller, R. G. (1991), Simultaneous Statistical Inference, New York: Springer. Google Scholar
  23. Naylor, R. E. L. (1981), “An Evaluation of Various Germination Indices for Predicting Differences in Seed Vigour in Italian Ryegrass,” Seed Science and Technology, 9, 593–600. MathSciNetGoogle Scholar
  24. Onofri, A., Gresta, F., and Tei, F. (2010), “A New Method for the Analysis of Germination and Emergence Data of Weed Species,” Weed Research, 50, 187–198. CrossRefGoogle Scholar
  25. Parzen, E. (1962), “On Estimation of a Probability Density Function and Mode,” The Annals of Mathematical Statistics, 32, 1065–1076. MathSciNetCrossRefGoogle Scholar
  26. Peto, R. (1973), “Experimental Survival Curves for Interval-Censored Data,” Journal of the Royal Statistical Society, Series C, 22, 86–91. Google Scholar
  27. R Development Core Team (2011), R: A Language and Environment for Statistical Computing, Vienna: R Foundation for Statistical Computing. http://www.R-project.org. Google Scholar
  28. Ritz, C., Pipper, C., Yndgaard, F., and Fredlund, K. (2010), “Modelling Flowering of Plants Using Time-to-Event Methods,” European Journal of Agronomy, 32, 155–161. CrossRefGoogle Scholar
  29. Schutte, B. J., Regnier, E. E., Harrison, S. K., Schmoll, J. T., Spokas, K., and Forcella, F. (2008), “A Hydrothermal Seedling Emergence Model for Giant Ragweed (ambrosia trifida),” Weed Science, 56, 555–560. CrossRefGoogle Scholar
  30. Seber, G. A. F., and Wild, C. J. (2003), Nonlinear Regression, Hoboken: Wiley-Interscience. Google Scholar
  31. Spokas, K., and Forcella, F. (2009), “Software Tools for Weed Seed Germination Modeling,” Weed Science, 57, 216–227. CrossRefGoogle Scholar
  32. Sun, J. (2006), The Statistical Analysis of Interval-Censored Failure Time Data, New York: Springer. zbMATHGoogle Scholar
  33. Titterington, D. M. (1983), “Kernel-Based Density Estimation Using Censored, Truncated or Grouped Data,” Communications in Statistics. Theory and Methods, 12, 2151–2167. MathSciNetzbMATHCrossRefGoogle Scholar
  34. Turnbull, B. (1976), “The Empirical Distribution Function With Arbitrarily Grouped, Censored and Truncated Data,” Journal of the Royal Statistical Society, Series B, 38, 290–295. MathSciNetzbMATHGoogle Scholar
  35. Wand, M. P., and Jones, M. C. (1995), Kernel Smoothing, London: Chapman and Hall. zbMATHGoogle Scholar

Copyright information

© International Biometric Society 2012

Authors and Affiliations

  • R. Cao
    • 1
  • M. Francisco-Fernández
    • 1
    Email author
  • A. Anand
    • 2
  • F. Bastida
    • 3
  • J. L. González-Andújar
    • 4
  1. 1.Faculty of Computer Science, Department of MathematicsUniversity of A CoruñaA CoruñaSpain
  2. 2.Department of MathematicsIndian Institute of TechnologyKharagpurIndia
  3. 3.Polytechnic School, Department of Agroforestry ScienceUniversity of HuelvaPalos de la Frontera (Huelva)Spain
  4. 4.CSICInstitute for Sustainable AgricultureCórdobaSpain

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