On the use of response models in mixture experiments

Summary

Methods for assessing mixtures and their dynamic interaction over time are proposed, based on response functions relating biomass yield of each species to the densities of the component species. This approach allows a number of different facets of mixtures to be studied in a common framework. Two examples are given. Substitution rates between species and perceived densities for individuals in mixture are defined. These measure the impact of their environment on individuals. The relative resource total (RRT), is suggested as an index of whether species are capturing the same resource amount in mixture as in pure stand. Two indices of the comparative performance of species over time are proposed. The two examples, one with cattle and sheep and the other a plant mixture diallel with 6 genotypes illustrate the use of the methods. In the animal example the maximum yield mixture was calculated, the species perceptions of each other assessed and it is shown that mixing increased the resource capture by up to 17%. In general, the smaller species performed relatively better in mixture over the experimental period. In the plant example, individual plant size varied considerably over genotypes and this was reflected in their perceptions of each other, but not in their pure stand or mixed crop yield potential. Most genotype pairs showed antagonistic behaviour, whether measured by crop yield potential or by the index of resource capture. These conclusions are contrasted with those from an analysis of the data using substitutive methods.