Abstract
Anyone with an interest in precision agriculture has already formed a hypothesis that the field is a sub-optimum management unit for cropping. The role of experimentation is to test this hypothesis. Geostatistics can play an important role in analysing experiments for site-specific crop management: put simply, spatial autocorrelation must be accounted for if one is to draw valid inferences. We provide here some background to the basic concepts of agronomic experimentation. We then consider two broad classes of experimental design for precision agriculture (management-class experiments and local-response experiments), and show, with the aid of case studies, how each may be analysed geostatistically. Ultimately though, if farmers are compelled to use relatively simple designs and less formal analyses, then researchers must follow and adapt their geostatistical analyses accordingly.
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References
Anselin, L. (1988).Spatial econometrics: methods and models. Dordrecht, The Netherlands: Kluwer.
Anselin, L., Bongiovanni, R., & Lowenberg-DeBoer, J. (2004). A spatial econometric approach to the economics of site-specific nitrogen management in corn production.American Journal of Agricultural Economics,86, 675–687.
Beckett, P. H. T., & Webster, R. (1971). Soil variability: a review.Soils and Fertilizers,34, 1–15.
Besag, J., & Higdon, D. (1999). Bayesian analysis of agricultural field experiments.Journal of the Royal Statistical Society, Series B: Statistical Methodology,61, 691–746.
Bishop, T. F. A., & Lark, R. M. (2006). The geostatistical analysis of experiments at the landscape-scale.Geoderma,133, 87–106.
Bishop, T. F. A., & Lark, R. M. (2007). A landscape-scale experiment on the changes in available potassium over a winter wheat cropping season.Geoderma,141, 384–396.
Boyd, D. A., Yuen, Lowsing, T. K., & Needham, P. (1976). Nitrogen requirement of cereals. 1. response curves.Journal of Agricultural Science, Cambridge,87, 149–162.
Bramley, R. G. V., Cook, S. E., Adams, M. L., & Corner, R. J. (1999).Designing your own experiments: how precision agriculture can help. Canberra, Australia: Grains Research and Development Corporation.
Brus, D. J., & de Gruijter, J. J. (1997). Random sampling or geostatistical modelling? Choosing between design-based and model-based sampling strategies for soil (with Discussion).Geoderma,80, 1–44.
Bruulsema, T. W., Malzer, G. L., Robert, P. C., Davis, J. G., & Copeland, P. J. (1996). Spatial relationships of soil nitrogen with corn yield response to applied nitrogen. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision Agriculture: Proceedings of the 3rd International Conference (pp. 505–512). Madison, WI: ASA, CSSA, SSSA.
Christakos, G. (2000).Modern spatiotemporal geostatistics. New York: Oxford University Press.
Christakos, G., & Li, X. (1998). Bayesian maximum entropy analysis and mapping: a farewell to kriging estimators.Mathematical Geology,130, 435–462.
Cook, S. E., & Bramley, R. G. V. (2000). Coping with variability in agricultural production-implications for soil testing and fertiliser management.Communications in Soil Science and Plant Analysis,31, 1531–1551.
Cook, S. E., Adams, M. L., & Corner, R. J. (1999). On-farm experimentation to determine site-specific responses to variable inputs. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision Agriculture: Proceedings of the 4th International Conference (pp. 611–621). Madison, WI: ASA, CSSA, SSSA.
Davis, J. G., Malzer, G. L., Copeland, P. J., Lamb, J. A., & Robert, P. C. (1996). Using yield variability to characterize spatial crop response to applied N. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision Agriculture: Proceedings of the 3rd International Conference (pp. 513–519). Madison, WI: ASA-CSSA-SSSA.
de Gruijter, J. J., Brus, D. J., Bierkens, M. F. P., & Knotters, M. (2006).Sampling for natural resource monitoring. Berlin: Springer.
Diggle, P. J., & Ribeiro, Jr, P. J. (2007).Model-based geostatistics. New York: Springer.
Doerge, T. A., & Gardner, D. L. (1999). On-farm testing using the adjacent strip comparison method. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision Agriculture: Proceedings of the 4th International Conference (pp. 603–609). Madison, WI: ASA, CSSA, SSSA.
Gomez, K. A., & Gomez, A. A. (1984).Statistical procedures for agricultural research. New York: Wiley.
Goovaerts, P. (1997).Geostatistics for natural resource evaluation. New York, NY: Oxford University Press.
Hurlbert, S. H. (1984). Pseudoreplication and the design of ecological field experiments.Ecological Monographs,54, 187–211.
Hurley, T. M., Oishi, K., & Malzer, G. L. (2005). Estimating the potential value of variable rate nitrogen applications: a comparison of spatial econometric and geostatistical models.Journal of Agricultural and Resource Economics,30, 231–249.
Lambert, D. M., Lowenberg-DeBoer, J., & Bongiovanni, R. (2004). Comparison of four spatial regression models for yield monitor data: a case study from Argentina.Precision Agriculture,5, 579–600.
Lark, R. M., & Cullis, B. R. (2004). Model-based analysis using REML for inference from systematically sampled data on soil.European Journal of Soil Science,55, 799–813.
Lark, R. M., & Wheeler, H. C. (2003). A method to investigate within-field variation of the response of combinable crops to an input.Agronomy Journal,95, 1093–1104.
McBratney, A. B. (1985). The role of geostatistics in the design and analysis of field experiments with reference to the effect of soil properties on crop yield. In D. R. Nielsen, & J. Bouma (Eds.),Soil Spatial Variability: Proceedings of a Workshop of the ISSS and the SSSA. Las Vegas, USA. 30th November–1st December 1984 (pp. 3–8). Wageningen, The Netherlands: Pudoc.
Mercer, W. B., & Hall, A. D. (1911). The experimental error of field trials.Journal of Agricultural Science, Cambridge,4, 107–127.
Minasny, B., & McBratney, A. B. (2007). Spatial prediction of soil properties using EBLUP with the Matérn covariance function.Geoderma,140, 324–336.
Pannell, D. J. (1998). On the estimation of on-farm benefits of agricultural research.Agricultural Systems,61, 123–134.
Panten, K., Bramley, R. G. V., Lark, R. M., & Bishop, T. F. A. (2010). Enhancing the value of field experimentation through whole-of-block designs.Precision Agriculture,11, 18–213.
Papritz, A. (2008). Standardised vs. customary ordinary cokriging: some comments on the article “The geostatistical analysis of experiments at the landscape-scale” by T.F.A. Bishop and R.M. Lark.Geoderma,146, 391–396.
Pardo-Igúquiza, E., & Dowd, P.A. (1997). AMLE3D: A computer program for the inference of spatial covariance parameters by approximate maximum likelihood estimation.Computers & Geosciences,23, 793–805.
Pardo-Igúzquiza, E., & Dowd, P. A. (1998). Maximum likelihood inference of spatial covariance parameters of soil properties.Soil Science,163, 212–219.
Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal.Biometrika,58, 545–554.
Peace, G. S. (1993).Taguchi methods. Boston, MA: Addison-Wesley.
Petersen, R. G. (1994).Agricultural field experiments: design and analysis. New York, NY: Marcel Dekker.
Pringle, M. J., McBratney, A. B., & Cook, S. E. (2004). Field-scale experiments for site-specific crop management. Part II: a geostatistical analysis.Precision Agriculture,5, 625–645.
R Development Core Team. (2008).R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing (URL:http://www.R-project.org; last accessed 19.8.2009).
Reetz, H. F. (1996). On-farm research opportunities through site-specific management. In P. C. Robert, R. H. Rust, & W. E. Larson (Eds.),Precision Agriculture: Proceedings of the 3rd International Conference (pp. 1173–1176). Madison, WI: ASA-CSSA-SSSA.
Ribeiro, Jr, P. J., & Diggle, P. J. (2001). geoR: A package for geostatistical analysis.R-NEWS, 1, 15–18 (URL:http://cran.r-project.org/doc/Rnews/Rnews_2001--2.pdf; last accessed 19.8.2009).
Russell, E. W. (1976).Soil conditions and plant growth (10th ed.). London, UK: Longman.
Stein, M. L., Chi, Z., & Welty, L. J. (2004). Approximating likelihood methods for large spatial data sets.Journal of the Royal Statistical Society, Series B: Statistical Methodology,66, 275–296.
Taylor, J. A., McBratney, A. B., & Whelan, B. M. (2007). Establishing management classes for broadacre agricultural production.Agronomy Journal,99, 1366–1376.
Van Groenigen, J. W., & Stein, A. (1998). Constrained optimization of spatial sampling using continuous simulated annealing.Journal of Environmental Quality,27, 1078–1086.
Webster, R., & Oliver, M. A. (2007).Geostatistics for environmental scientists (2nd ed.). Chichester, UK: Wiley.
Whelan, B. M., & McBratney, A. B. (2002). A parametric transfer function for grain-flow within a conventional combine harvester.Precision Agriculture,3, 123–134.
Whelan, B. M., McBratney, A. B., & Stein, A. (2003). On-farm field experiments for precision agriculture. In J. V. Stafford, & A. Werner (Eds.),Precision Agriculture: Papers from the 4th European Conference on Precision Agriculture, Berlin, Germany, 15–19 June 2003 (pp. 731–737). Wageningen, the Netherlands: Wageningen Academic Publishers.
Acknowledgements
Thanks to Mr. Michael Ledingham, ‘Merinda’, NSW, for the data for Rosewood field. The contribution of RML is part of the programme in Mathematical and Computational Biology at Rothamsted Research, funded by the UK Biotechnology and Biological Sciences Research Council (BBSRC). The analyses for Bypass field were undertaken as part of a project funded by BBSRC Grant D20191, using data collected in another BBSRC-funded project (Grant 204/11563). Thanks also to Dr Rob Bramley for providing the comments that helped shape the final version.
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Pringle, M.J., Bishop, T.F.A., Lark, R.M., Whelan, B.M., McBratney, A.B. (2010). The Analysis of Spatial Experiments. In: Oliver, M. (eds) Geostatistical Applications for Precision Agriculture. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9133-8_10
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DOI: https://doi.org/10.1007/978-90-481-9133-8_10
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