A joint model for plot yield in response to fertility trends and interplot competition is described. The
model combines the mixed model representation of a cubic smoothing spline to model fertility and
a regression model with auto-regressive terms to model competition. Estimation is based on a
generalization of residual maximum likelihood. The methods were applied to a series of 70 sugar beet
trials conducted by the Plant Breeding Institute, Cambridge, UK, and the results summarized.