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In order to clarify the theoretical relationship between individual behavior and population-level competition between two species with spatial correlation, this paper describes how discrete-time competition equations for the two species can be derived from local resource competition among individuals. Competition type of each species is either scramble, contest, or modified contest, and for various combinations of two competition types, different competition models are derived. Simple competition models that can approximate the above models when competition is weak are also derived. Furthermore, the derived models are used to investigate how coexistence conditions and coexistence probability depend on spatial correlation and aggregation of individuals. For the weak competition models, spatial aggregation and non-correlation, in terms of measures adopted here, play exactly symmetric roles in promoting coexistence. In contrast, for the fully developed models, spatial aggregation generally exerts stronger effects than non-correlation on coexistence. Coexistence probability also depends greatly on competition types. For example, two species are generally more likely to coexist when they are of the same competition type than of different competition types. Coexistence probabilities from the mathematical analysis are in good agreement with those from individual-based simulations.

This paper demonstrates how discrete-time models describing population dynamics of two competing species can be derived in a bottom-up manner by considering competition for resources among individuals and the spatial distribution of individuals. The competition type of each species is assumed to be either scramble, contest, or an intermediate between them. Individuals of two species are distributed over resource sites or patches following one of three distribution functions. According to the combination of competition types of the two species and the distribution of individuals, various interspecific competition models are derived. Furthermore, a general interspecific competition model that includes various competition models as special cases is derived for each distribution of individuals. Finally, this paper examines dynamics of some of the derived competition models and shows that the likelihood of coexistence of the two species varies greatly, depending on the type of spatial distribution of individuals.