Interactive competition models explicitly consider the interaction between competitor population levels and the levels of their resources. By assuming that the time scale of the resource dynamics is much shorter than that of the competitor dynamics, it is possible to investigate the shape of competitor isoclines. Two models are considered, representing opposite extremes of a continuum. The additive resource model is based upon the assumption that the competitive community is regulated by the availability of a single factor, but that this factor can be obtained from a variety of resources. At the other extreme, the multiplicative resource model assumes that regulation is mediated via a number of factors, each factor being available from only one resource. Analysis of the additive model shows that if type-3 (sigmoid) functional responses determine the competitor-resource interactions and the resource levels are generally held below the point of infection of the responses, then concave competitor isoclines are to be expected. In particular, if resource levels are kept sufficiently low by the competitors, so that self- regulation can be ignored, then a consequence of the isocline curvature is that species poor communities will generally maintain a higher "biomass" than comparable species rich communities. This has relevance to the phenomenon of excess density compensation. Biomass per se can over estimate the effect of larger species in this comparison. Ideally species numbers should be weighted by the inverse of their carrying capacities, but it is suggested that w2 3is a suitable conversion factor, where w is the individual weight of a species. Increasing the number of resource dimensions acts to decrease the likelihood of concave isoclines, so that the possibility of the simultaneous regulation of competitive communities by more than one resource dimension must be borne in mind in any analysis of community structure. © 1981.
Nunney, L. (1981). Interactive competition models and isocline shape. Mathematical Biosciences, 56(1–2), 77–110. https://doi.org/10.1016/0025-5564(81)90029-8