Spatio-temporal associations in beetle and virus count data

This paper analyzes two insect-related sets of agricultural field data. Both comprise spatially referenced count data sampled on a series of occasions. One concerns carabids (ground beetles) in cereals, the other the incidence and spread of an aphid-vectored virus disease of lupins. For both sets, the major objective was to describe and quantify the stability through time of the spatial patterns found for each occasion; this was measured by the spatial association between successive samples. Traditional methods for analyzing count data focus on properties of the frequency distribution of the counts and use little or none of the spatial information in the sample. We used methods that utilized all the spatial information and that, by conditioning on the observed data, provided complementary inferences to the other methods. Our analyses are based on a class of methods termed spatial analysis by distance indices (SADIE). These methods provide indices and formal randomization tests, both for the spatial pattern in a single population and for the spatial association when the patterns of two populations are compared. Our analyses showed considerable aggregation for both the beetles and the infected lupin plants. Furthermore, both populations displayed positive association between successive samples that declined as the temporal lag increased. The beetles were affected greatly by the harvest of the cereal crop. The lupin infections showed maximal association for a 1-week lag despite the fact that the latent period of the virus was a fortnight; it was inferred that the observed pattern of new infections was probably tracking the pattern of the aphid vectors 2 weeks previously.