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.

Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension

“…We are locking, according to pattern diversity, in such a way that some equivalent structures, eventually, are not eliminated (viability) in open systems. This process of selection can include intraspecific competition [ 33 ] for chemical resources or “depredation” [ 34 ].…”

Indirect Effects, Biotic Inferential Interactions and Time Functions in H-Semiotic Systems: Ecosystems Case

“…Although in the study of ecosystems the relationships between the variables can be measured, and the effects, direct and indirect, can be compared between different species, as in the case of relations of predation and competition [10,11], there has not been a profound development in the broader context of General Systems Theory. The problems to be solved by this Theory include the question of quantifying the relationships between variables (objects or attributes) of a system, or in the more general case of a system with its subsystems, or of a multilevel system [12].…”