Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-08T03:30:12.751Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of novel and standard methods for analysing patterns of plant death in designed field experiments

Published online by Cambridge University Press:  04 July 2011

L. D. B. SURIYAGODA ,
M. H. RYAN ,
H. LAMBERS  and
M. RENTON
L. D. B. SURIYAGODA*
Affiliation:
School of Plant Biology and Institute of Agriculture, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia Future Farm Industries Cooperative Research Centre, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia Faculty of Agriculture, University of Peradeniya, Peradeniya, 20400, Sri Lanka
M. H. RYAN
Affiliation:
School of Plant Biology and Institute of Agriculture, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia Future Farm Industries Cooperative Research Centre, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
H. LAMBERS
Affiliation:
School of Plant Biology and Institute of Agriculture, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
M. RENTON
Affiliation:
School of Plant Biology and Institute of Agriculture, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia Future Farm Industries Cooperative Research Centre, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia CSIRO Ecosystem Sciences, Floreat, WA 6014, Australia
*
*To whom all correspondence should be addressed. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

The present paper compares standard and novel methods for analysing aggregated patterns of plant death in designed field experiments; these methods include binomial (BN), beta-binomial (BBN), logistic-normal-binomial (LNB), BN models with random blocks, BN models with smooth-scale spatial components and principal coordinates of neighbour matrices (PCNM). PCNM is a relatively new technique used in ecology to determine how much observed variability can be explained by spatial and environmental variables, and has not yet been applied to agricultural studies. The survival data of two pasture species, collected from a designed field experiment that was replicated at multiple locations, were used. First, the occurrence of overdispersion was tested using the BN and BBN distributions. Goodness-of-fit tests proved that the BBN model provided a better description (better fit) of the observed data in some cases than did the BN distribution, indicating overdispersion was present. When overdispersion was not present, the BN distribution was adequate to describe the data, and the use of the BBN distribution was superfluous. It is then shown that the PCNM approach, the BN model with smooth-scale spatial components and the LNB model were able to account for some of the variation as spatial variability, thus reducing the species effect compared with that explained under the standard BN model. The amount of variation among species according to the BN model and the BN model with random blocks was similar. Therefore, it is argued that the novel PCNM approach warrants further testing when exploring the spatial variability in designed experiments in agriculture and using LNB, PCNM and BN with smooth-scale spatial components may provide better predictions of species effects than do other, more conventional, approaches.

Type
Crops and Soils Research Paper
Information
The Journal of Agricultural Science , Volume 150 , Issue 3 , June 2012 , pp. 319 - 334
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aitchison, J. & Shen, S. M. (1980). Logistic-normal distributions: some properties and uses. Biometrika 67, 261–272.CrossRefGoogle Scholar
Anderson, D. R., Burnham, K. P. & White, G. C. (1994). AIC model selection in overdispersed capture–recapture data. Ecology 75, 1780–1793.CrossRefGoogle Scholar
Borcard, D. & Legendre, P. (1994). Environmental control and spatial structure in ecological communities: an example using oribatid mites (Acari, Oribatei). Environmental and Ecological Statistics 1, 37–61.CrossRefGoogle Scholar
Borcard, D. & Legendre, P. (2002). All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling 153, 51–68.CrossRefGoogle Scholar
Borcard, D., Legendre, P. & Drapeau, P. (1992). Partialling out the spatial component of ecological variation. Ecology 73, 1045–1055.CrossRefGoogle Scholar
Brockhoff, P. B. (2003). The statistical power of replications in difference tests. Food Quality and Preference 14, 405–417.CrossRefGoogle Scholar
Burnham, K. P. & Anderson, D. R. (2002). Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach, 2nd edn. New York: Springer-Verlag.Google Scholar
Campbell, C. L. & Noe, J. P. (1985). The spatial analysis of soilborne pathogens and root diseases. Annual Review of Phytopathology 23, 129–148.CrossRefGoogle Scholar
Chen, J., Shiyomi, M., Hori, Y. & Yamamura, Y. (2008). Frequency distribution models for spatial patterns of vegetation abundance. Ecological Modelling 211, 403–410.CrossRefGoogle Scholar
Cox, D. R. & Snell, E. J. (1989). Analysis of Binary Data, 2nd edn. Monographs on Statistics and Applied Probability Vol. 32. London: Chapman and Hall.Google Scholar
Dray, S., Legendre, P. & Peres-Neto, P. R. (2006). Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecological Modelling 196, 483–493.CrossRefGoogle Scholar
Dutilleul, P. (1993). Modifying the t test for assessing the correlation between two spatial processes. Biometrics 49, 305–314.CrossRefGoogle Scholar
Engle, R. F. (1984). Wald, likelihood ratio, and Lagrange multiplier tests in econometrics. In Handbook of Econometrics II (Eds Intriligator, M. D. & Griliches, Z.), pp. 776–826. Amsterdam: Elsevier.Google Scholar
Garrett, K. A., Madden, L. V., Hughes, G. & Pfender, W. F. (2004). New applications of statistical tools in plant pathology. Phytopathology 94, 999–1003.CrossRefGoogle ScholarPubMed
Gotway, C. A. & Stroup, W. W. (1997). A generalized linear model approach to spatial data and prediction. Journal of Agricultural, Biological, and Environmental Statistics 2, 157–187.CrossRefGoogle Scholar
Griffiths, D. A. (1973). Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease. Biometrics 29, 637–648.CrossRefGoogle Scholar
Hughes, G. & Madden, L. V. (1993). Using the beta-binomial distribution to describe aggregated patterns of disease incidence. Phytopathology 83, 759–763.CrossRefGoogle Scholar
Hughes, G., Munkvold, G. P. & Samita, S. (1998). Application of the logistic-normal-binomial distribution to the analysis of Eutypa dieback disease incidence. International Journal of Pest Management 44, 35–42.CrossRefGoogle Scholar
Kleinman, J. C. (1973). Proportions with extraneous variance: Single and independent sample. Journal of the American Statistical Association 68, 46–54.Google Scholar
Legendre, P. (1990). Quantitative methods and biogeographic analysis. In Evolutionary Biogeography of the Marine Algae of the North Atlantic. NATO ASI Series G 22 (Eds Garbary, D. J. & South, R. G.), pp. 9–34. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Legendre, P., Dale, M. R. T., Fortin, M.-J., Gurevitch, J., Hohn, M. & Myers, D. (2002). The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25, 601–615.CrossRefGoogle Scholar
Legendre, P. & Legendre, L. (1998). Numerical Ecology. 2nd edn. Amsterdam, The Netherlands: Elsevier Science.Google Scholar
Legendre, P. & Troussellier, M. (1988). Aquatic heterotrophic bacteria: modeling in the presence of spatial autocorrelation. Limnology and Oceanography 33, 1055–1067.CrossRefGoogle Scholar
Li, G. D., Lodge, G. M., Moore, G. A., Craig, A. D., Dear, B. S., Boschma, S. P., Albertsen, T. O., Miller, S. M., Harden, S., Hayes, R. C., Hughess, S. J., Snowball, R., Smith, A. B. & Cullis, B. C. (2008). Evaluation of perennial pasture legumes and herbs to identify species with high herbage mass and persistence in mixed farming zones in southern Australia. Australian Journal of Experimental Agriculture 48, 449–466.CrossRefGoogle Scholar
Lin, X. & Breslow, N. E. (1996). Analysis of correlated binomial data in logistic-normal models. Journal of Statistical Computation and Simulation 55, 133–146.CrossRefGoogle Scholar
Madden, L. V. (1989). Dynamic nature of within-field disease and pathogen distributions. In Spatial Components of Plant Disease Epidemics (Ed. Jeger, M. J.), pp. 96–126. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
Madden, L. V. & Hughes, G. (1995). Plant disease incidence: Distributions, heterogeneity, and temporal analysis. Annual Review of Phytopathology 33, 529–564.CrossRefGoogle ScholarPubMed
McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models. London: Chapman and Hall.CrossRefGoogle Scholar
Moore, D. F. (1987). Modelling the extraneous variance in the presence of extra-binomial variation. Applied Statistics 36, 8–14.CrossRefGoogle Scholar
Oksanen, J., Kindt, R., Legendre, P. & O'Hara, R. B. (2007). Vegan: community ecology package. R package version 1.9–25. Available online at: http://r-forge.r-project.org/projects/vegan/ (verified 9 June 2011).Google Scholar
Peres-Neto, P. R. & Legendre, P. (2010). Estimating and controlling for spatial structure in the study of ecological communities. Global Ecology and Biogeography 19, 174–184.CrossRefGoogle Scholar
Peres-Neto, P. R., Legendre, P., Dray, S. & Borcard, D. (2006). Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87, 2614–2625.CrossRefGoogle ScholarPubMed
R Development Core Team (2007). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available online at: http://www.R-project.org (verified 26 May 2011).Google Scholar
Richards, S. A. (2008). Dealing with overdispersed count data in applied ecology. Journal of Applied Ecology 45, 218–277.CrossRefGoogle Scholar
SAS Institute (2010). SAS/STAT(R) 9.2 User's Guide, 2nd Edn. Cary, NC: SAS Institute Inc.Google Scholar
Schabenberger, O. & Pierce, F. J. (2002). Contemporary Statistical Models for the Plant and Soil Sciences. Boca Raton, FL: CRC Press.Google Scholar
Skellam, J. G. (1948). A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society, Series B (Methodological) 10, 257–261.CrossRefGoogle Scholar
Smith, D. M. (1983). Maximum likelihood estimation of the parameters of the beta-binomial distribution. Applied Statistics 32, 192–204.CrossRefGoogle Scholar
Thuiller, W., Araújo, M. B. & Lavorel, S. (2003). Generalized models vs. classification tree analysis: Predicting spatial distributions of plant species at different scales. Journal of Vegetation Science 14, 669–680.CrossRefGoogle Scholar
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439–447.Google Scholar
Williams, D. A. (1975). The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics 31, 949–952.CrossRefGoogle ScholarPubMed
Williams, D. A. (1982). Extra-binomial variation in logistic linear models. Applied Statistics 31, 144–148.CrossRefGoogle Scholar