title: Competitive Exclusion and Axiomatic Set-Theory: De Morgan's Laws, Ecological Virtual Processes, Symmetries and Frozen Diversity.
abstract: This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.
authors.affiliation: Instituto de Alta Investigación IAI, Universidad de Tarapacá, Casilla 7-D, Arica, Chile. cflores@uta.cl.
authors.forename: J C
authors.initials: JC
authors.lastname: Flores
mesh_terms: D044822:Biodiversity; D005075:Biological Evolution; D004463:Ecology; D006801:Humans; D008962:Models, Theoretical; D013045:Species Specificity
keywords: Coexistence and competition; Ecologic set; Food web theory; Population dynamics; Symbolic ecology