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Field data on intensity of plant diseases is very often irregularly spaced (i.e., there are varying amounts of distance between rows, ponds, voids, roads, houses, or other land areas). Typically, this type of data is gridded and the average disease intensity of the plants within the grid is used instead of the original data on each separate plant. This is done because the underlying statistical assumptions in the analysis of spatial data usually require that data be equally spaced. However, a new method of analysis, sometimes called second-generation wavelet analysis, can be used on irregularly spaced spatial data. Wavelet analysis is a method used to analyze variations in scale and position of non-stationary spatial signals (non-stationary for our data means the statistical properties can vary based on location within the orchard), and the second-generation refers to an iterative process, called a lifting scheme (1), which allows for the irregular spacing. Irregular spacing is often found in citrus groves as spacing within and between rows is often not uniform, and on a larger spatial scale, distance between blocks and plantings are not necessarily simple multiples of distances between rows and trees. In addition, there are a number of other issues such as missing trees, the presence of irregular roads, ponds, staging areas, etc., that cause citrus groves to have irregular distances between trees when viewed at the plantation or regional scale. Therefore, to test this new method, we conducted a second-generation spatial wavelet analysis on a large irregularly spaced citrus planting (Southern Gardens) in Florida where over 260,000 trees were assessed for incidence of huanglongbing (HLB) over five sampling times.

Candidatus Liberibacter americanus and Candidatus Liberibacter asiaticus are two bacterial species that cause huanglongbing (HLB) disease in citrus-growing regions of Brazil. A concentrated sampling plan of a grove in Matao, Brazil was initiated to evaluate the spatial and temporal spread of these bacteria. The exact location of each of 8697 trees was recorded, and each symptomatic tree was assessed by PCR for the presence of Ca. L. americanus and Ca. L. asiaticus during 17 different months from April 2006 to May 2008 (Fig. 1). In the first month, only five trees were confirmed to have Ca. L. asiaticus. The first trees with confirmed cases of Ca. L. americanus were not found until February 2007. By the end of the study, 43 trees were confirmed to have Ca. L. americanus, 1164 trees were confirmed to have Ca. L. asiaticus, and three trees were coinfected.