Related papers: Evolution du Principe d'Exclusion Comp\'etitive : …
I introduce an axiomatic representation, called ecoset, to consider interactions between species in ecological systems. For interspecific competition, the exclusion conjecture (Gause) is put in a symbolic way and used as a basic operational…
There is a growing need to integrate sustainability into tertiary mathematics education given the urgency of addressing global environmental challenges. This paper presents four case studies from Australian university courses that…
The fact that certain "extraordinary" probabilistic phenomena--in particular, macroscopic violations of the second law of thermodynamics--have never been observed to occur can be accounted for by taking hard preclusion as a basic physical…
Explaining biodiversity is a central focus in theoretical ecology. A significant obstacle arises from the Competitive Exclusion Principle (CEP), which states that two species competing for the same type of resources cannot coexist at…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are…
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev.…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
Motivated by the concept of degeneracy in biology (Edelman, Gally 2001), we establish a first connection between the Multiplicity Principle (Ehresmann, Vanbremeersch 2007) and mathematical statistics. Specifically, we exhibit two families…
Consider a population of organisms that harvest free energy from their environment to reproduce. This paper shows that if the organisms' reproductive rates are proportional to the amount of physical free energy that they can convert into…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…
Simplified mechanistic models in ecology have been criticized for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in…
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
We study a spatially homogeneous model of a market where several agents or companies compete for a wealth resource. In analogy with ecological systems the simplest case of such models shows a kind of "competitive exclusion" principle.…
Cooperation is a widespread natural phenomenon yet current evolutionary thinking is dominated by the paradigm of selfish competition. Recent advanced in many fronts of Biology and Non-linear Physics are helping to bring cooperation to its…
Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…