Use of Substitution Rates to Describe Competition in Mixed Plant Populations

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Abstract
A competition model for mixed populations is presented. The model is a combination of (1) a yield density relationship and (2) a density model. The yield density relationship is given by w = A/[1+(A/B) (N—N 0)] where w is the mean plant dry weight and N is the perceived plant density. Parameter A is the mean plant weight at density N 0 and B is the potential yield per unit area. The density model estimates the perceived density of a species, which is the monoculture density where the dry weight per plant is the same as that observed in the mixed population. For each species, the density is added to the density of the competing species converted into a corresponding number of monoculture plants, giving the perceived density. Data of 21 observation times covering two years' results of barley and oilseed rape grown under both greenhouse and field conditions were tested for deviations from an asymptotic yield density relationship, and for density dependence of the substitutions rates. The results showed no deviations from an asymptotic relationship between biomass yield per unit area and density, but in more than half of the observation times the substitutions rates were dependent on the density of the competing species. The perceived density of species 1 was therefore N = N 1 + c(1 + qN 2)N 2 where N is the perceived plant density and N 1 and N 2 are the observed densities of the two species in the mixed population. The substitution rate, c(1 + qN 2), was linearly related to the density of the competing species. In the barley populations, the substitution rates of oilseed rape were negatively related to increased densities of oilseed rape. In the oilseed rape populations, the substitution rates of barley were positively related to increased densities of barley. Barley was generally a better competitor than oilseed rape.