Bivariate Diagrams for Plant Competition Data: Modifications and Interpretation

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Abstract
Where competition studies are based on binary mixtures, data can be clearly displayed by plotting the yield per unit area of one component against that of the other component; such plots are termed bivariate diagrams. Data from both replacement and additive designs can be displayed in this way. Three modifications of the basic bivariate diagram are described: (i) plotting the relative yield of one component against that of the other; (ii) plotting the log yield per unit area of one component against that of the other; and (iii) plotting the log relative yield of one component against that of the other. Ecological interpretations of these diagrams are considered. In the basic bivariate diagram, a straight line joining the monoculture yields of the two components indicates conditions where the relative yield total (RYT) is 1.0. Lines fanning out from the origin indicate the harvested proportions of the components in the mixture; by comparing the harvested proportion with the expected proportion, calculated from sown proportions and monoculture yields, an indication of the relative competitive abilities of the components can be obtained. Two advantages are obtained if the relative yield of one component is plotted against that of the other: (a) the RYT values of various mixtures, or of a given mixture receiving various treatments, can be more easily compared; and (b) differences in the competitive abilities of components are more easily seen, though still not easily measured. Plotting the log yield per unit area of one component against that of the other has the advantage that it displays proportional differences, rather than arithmetic differences. The resulting logit scale for the composition of mixtures allows easy measurement of competitive ability along one diagonal, while resource complementarity (RYT) can be measured along one diagonal, while resource complementarity (RYT) can be measured along the other diagonal. The severity of competition can also be measured if the yield per plant under conditions of no competition (i.e. wide-spacing) is known. All three measures of competition can be subjected to statistical analysis. Plotting the log relative yield of one component against that of the other has most of the advantages of the two other modifications, allowing easy measurement of competitive ability, resource complemetarity, and severity of competition for various mixtures and treatments.