Analyzing the Spread of Beech Canker

Abstract

Abstract We investigate the spread of Nectria canker of beech, which is a fungal chronic disease caused by Nectria ditissima Tul. et C. Tul. Data are available from a beech provenance trial. A possible influential factor on the proportion of infected trees per plot is the wind dispersal zone(s) (wdz), a categorical variable describing the distance and wind direction from diseased shelterwood, the source of infection. We investigate the effect of wdz and whether the disease incidence in the regeneration can be explained alone by the wdz using different approaches accounting for spatial correlation in the data. One method uses generalized estimating equations (GEE) where, through specification of a general variance–covariance matrix allowing for nonindependence, spatial correlation can be accounted for in the model. The second method uses generalized additive models (GAM) and the spatial autocorrelation is dealt with by modeling it as a spatial trend. The third method uses generalized linear mixed models (GLMM) with a random effect accounting for spatial correlation and heterogeneity. We show that, in the beech data, some spatial correlation is present that is over and above that accounted for by the wdz. Therefore, methods not accounting for this correlation are inappropriate. The GLMM is the most appropriate model because it manages to model the biological process best: It explains the variation in disease incidence by the wdz and by secondary infection. Hence it yields the most precise estimates. FOR. SCI. 51(5):438–448.