Analysis of Frequency and Density Effects on Growth in Mixtures of Salvia Splendens and Linum Grandiflorum Using Hexagonal Fan Designs

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Abstract
The use of hexagonal fan designs as an efficient method for the analysis of frequency and density effects on growth and survival in 2 component mixtures is illustrated in greenhouse experiments with the annual cultivars S. splendens and L. grandiflorum. Density had a large effect on vegetative and reproductive wt of Salvia, but a lower effect on Linum. These effects were consistent with the dwarf, large-broad-leaved habit of Salvia declined with increasing density but increased in Linum. There were complex density and frequency interactions, with the growth of Salvia at low densities being affected by a higher frequency of Salvia, and at high densities being affected by a higher frequency Linum. At low low densities, mixtures tended to give increased yields at low Salvia frequencies, but lower yields at high Salvia frequencies than in monocultures. The density and frequency responses in the mixed hexagonal fan designs were generally consistent with responses in pure fans, or pure stands at fixed density, although there was evidence that the results in the mixed fans could not solely be accounted for by nearest-neighbor effects. Data from such designs could be used to construct replacement series graphs, and density-frequency response surfaces, and to examine population regulation in 2-spp. mixtures using graphs of population growth given different initial numbers of the 2 components. Complex patterns of population regulation were revealed that did not fit expectations from simple of population regulation were revealed that did not fit expectations from simple 2-spp. competition models. Hexagonal fan designs provided an .apprx. 4-fold economy in seeds and nearly a 10-fold economy in space, compared with separate hexagonal plots providing the same range of frequencies and densities. However, there are considerable statistical problems associated with analysis of such designs. Nevertheless, they promise to be an important exploratory tool for examination of yield and population regulation in 2-spp. mixtures.