Trend surface analysis of a Douglas-fir provenance–progeny transfer test

Spatial variability in heights of 8-year-old Douglas-fir in a IUFRO provenance–progeny transfer test was analyzed using trend surface analysis to differentiate genetic and environmental effects on tree height. The test installation was located in the University of British Columbia Research Forest, and was a randomized incomplete block design with three replications. Only the 25 provenances that were replicated in each block and had a balanced data set (eight families, five trees per family) were used. Trends were fitted to the average height of each replicate of each provenance, and also to the average size of the largest and smallest families per replicate. Interpretation was based on the assumption that the effects of microsite (mainly grass invasion of one block) were defined by the trend surface, while genetic effects were represented by the residuals from the trend. The data had previously been analyzed by ANOVA methods and these results were contrasted with the results using trend surface analysis. Trend surface analysis generally gave results similar to ANOVA, but in some cases resulted in different conclusions. Additional insights into the interaction of genotype and environment were obtained. Trend surface analysis is proposed as a useful supplement to analysis of variance in provenance transfer studies. Potential problems in using the method are discussed.