Estimation of economically optimum seed rates for winter wheat from series of trials

The results of recent trials for winter wheat (Triticum aestivum L.) have influenced farming practice in the UK by encouraging the use of lower seed rates. Spink et al. (2000) have demonstrated that, particularly if sown early, wheat can compensate for reduced plant populations by increased tiller production. Results from seed-rate trials are usually analysed separately for each environment or each combination of environment and variety, and not combined into a single model. They therefore address the question of what the best seed rate would have been for each combination, rather than answer themore relevant question of what rate to choose for a future site. The current paper presents a Bayesian method for combining data from seed-rate trials and choosing optimum seed rates: this method can incorporate information on seed and treatment costs, crop value and covariates. More importantly, for use as an advisory tool, it allows incorporation of expert knowledge of the crop and of the target site. The method is illustrated using two series of trials : the first, carried out at two sites in 1997–99, investigated the effects of sowing date and variety in addition to seed rate. The second was conducted at seven sites in 2001–03 and included latitude and certain management factors. Recommended seed rates based on these series vary substantially with sowing date and latitude. Two non-linear dose-response functions are fitted to the data, the widely used exponential-pluslinear function and the inverse-quadratic function (Nelder 1966). The inverse-quadratic function is found to provide a better fit to the data than the exponential-plus-linear and the latter function gives estimated optimum rates which are as much as 40% lower. The economic consequences of using one function rather than the other are not great in these circumstances. The method is found to be robust to changes in the prior distribution and to other changes in the model used for dependence of yield on sowing date, latitude, variety and management factors.