Response-Surface Analysis of Two-Species Competition: An Experiment on Phleum Arenarium and Vulpia Fasciculata

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Abstract
(1) The outcome of competition between two species can be analysed in terms of the changes in their population densities over time, as the species interact with one another. The changes in population density depend on the manner in which the per capita rate of increase of each species is moulded by the population densities of both species. (2) Results of a competition experiment on two winter-annual species of grass, Phleum arenarium and Vulpia fasciculata, are given; the experiment included wide ranges of densities of both species, so that the dependence of their per capita rates of increase on population density could be determined. This contrasts with traditional plant competition experiments that either hold the density of one species constant while varying the other (additive experiments), or hold the sum of both densities constant while varying the proportion (substitutive experiments). (3) Eight models of competition were fitted to the data. A satisfactory fit was achieved only when a model with density-dependent competitive abilities and non-linear isoclines was used. This model predicts the outcome of competition both qualitatively (eradication of P. arenarium) and quantitatively (the changes in population density through time from given initial values) with assumed seed mortality rates. (4) In contrast, additive competition experiments provide no information about the long-term outcome of competition, and substitutive experiments provide qualitative information only. These qualitative insights may themselves be misleading if an inappropriate density is chosen for the substitutive experiment.