Some implications of a first-order model of inter-plant competition for the means and variances of complex mixtures.

Factorial models commonly used in the analysis of overall and component yields of binary mixtures of genotypes are generalised to include mixtures of any number of components (size, m) and the form of an analysis of variance for fitting such a model to tertiary mixtures is outlined. Such a model contains main effects and interactions up to the mth order, and is specific to the size of mixture so that no equivalence necessarily exists between similar parameter sets for different sized mixtures. Monocultures can be regarded as a special case of the general model.A simple model of intra-and inter-component competition is defined which assumes that plants do not interact in their competitive effects on others, a condition which is equivalent to an absence of second and higher order interactions in statistical analyses of mixtures of any size. Simple scaling tests involving the yields of components or whole mixtures of different sizes can also be used to test the adequacy of the model. This competition model least to a linear relationship between the mean yield of a mixture and the reciprocal of the number of components it contains, and thus allows the prediction of means and other statistical parameters for mixtures of one size from those of others.