Comparing quadrat-based methods to
characterize spatial patterns of plant diseases

Renato Ribeiro de LIMA[1]

Clarice Garcia Borges DEMÉTRIO[2]

Paulo Justiniano RIBEIRO JUNIOR[3]

Martin Spencer RIDOUT[4]

§    ABSTRACT: Information about the spatial-temporal dynamics is of fundamental importance in epidemiological studies for describing and understanding the development of diseases, for developing efficient sampling plans, for planning controlled experiments, for evaluating the effect of different treatments, and for determining crop losses. Several different methods have been used to characterize spatial aggregation, such as the computation of dispersion index, intraclass correlation, and the use of spatial autocorrelation techniques. These methods consider count data from quadrats, which are sample units. With these methods one obtains a direct measure of heterogeneity of disease incidence, which is a function of the spatial interaction of the plants that are inside the quadrats. Some problems were identified by using data simulations, and we can conclude that the characterization of spatial patterns using the indexes considered here must be interpreted with caution, in particular if only one is adopted for a particular data analysis. There are discrepancies between results and their behavior under effects of different quadrat sizes and levels of incidence of the diseases.

§    KEYWORDS: Dispersion index; intraclass correlation; simulation; spatial autocorrelation; spatial pattern.

[1] Departamento de Ciências Exatas, Universidade Federal de Lavras, Caixa Postal 3037, CEP: 37200-000, Lavras, MG, Brasil, E-mail:

[2] Departamento de Ciências Exatas, Escola Superior de Agricultura ``Luiz de Queiroz'', ESALQ, Universidade de São Paulo, Caixa Postal 9, CEP: 13418-900, Piracicaba, SP, Brasil, E-mail:

[3] Laboratório de Estatística e Geoinformação, Universidade Federal do Paraná -- UFPR, Caixa Postal 19,081, CEP: 81531-990, Curitiba, PR, Brasil, E-mail:

[4] Institute of Mathematics, Statistics and Actuarial Science, University of Kent, CT2 7NF, Canterbury, Kent, United Kingdom, E-mail: