Response models and minimal designs for mixtures of n of m items useful for intercropping and other investigations

Abstract

Suppose that n of m cultivars are grown together in a mixture such as that found in intercropping investigations. Response model equations for n = 2 are formulated in a manner akin to that found for a diallel crossing experiment in genetics. This situation varies considerably from diallel crossing in that n ≥ 2 and yields may or may not be available for each member of the mixture. Response model equations are formulated and then minimal treatment designs obtained to derive least-squares solutions for the parameters of the model. This is done both when individual member yields are available and when they are not. Variances of estimable contrasts are also given. Applications to other areas of investigation are given with examples.