Kappa Function as a Unifying Framework for Discrete Population Modeling

Abstract

Abstract. This paper develops a unified way to describe the various generalized discrete-time nonlinear dynamical models with density dependence, Allee effects, and parasitoids. We show how the kappa function can be used to describe the probabilities involved in intra-or interspecific encounters, namely, (i) the probability of surviving to the next generation in the absence of parasitoids or Allee effects, (ii) the encounter probability associated with Allee effects, and (iii) the probability of escaping parasitism in the presence of parasitoids. Having introduced a phenomenological framework of modeling via the kappa function, we then provide a realistic mechanism through stochastic encounters, responsible for generating the kappa function to any of the three involved probabilities. The unified modeling through the kappa function yields insights into how abundances influence species interactions. It is now straightforward to use this unified modeling to analyze and investigate its consequences in species dynamics.

Statistical analysis of the impact of environmental temperature on the exponential growth rate of cases infected by COVID-19

“…Applied measures could be loosen and shorter! Model (1) originates from the logistic map family (e.g., [7], and references therein; [8]); other complicate versions, such as, the Susceptible-Infectious-Recovered models (e.g., [9]) may be expressed by multi-dimensional differential or difference equations (e.g., [10], and references therein; [11]), but still, the curve flattening is governed by the same features. The two composites, the exponential growth E and the negative feedback I, are just the main and necessary conditions for reproducing the growth-decay phases of the spread curve.…”

High Density Nodes in the Chaotic Region of 1D Discrete Maps

“…Are there the same features of nodes into the 1D Poincare section return maps (e.g., [ 70 , 71 ])? How the nodes and their properties appear in higher dimensions (e.g., [ 72 , 73 ])?…”

Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities

“…The q -exponential distributions are observed quite frequently in nature, and constitute a suitable generalization of the BG exponential distribution. Applications of the q -exponential distribution can be found in a wide variety of topics, among numerous others, are the following: sociology–sociometry: e.g., internet [ 6 ]; citation networks of scientific papers [ 7 ]; urban agglomeration [ 8 ]; linguistics [ 9 ]; economy [ 10 ]; biology: biochemistry [ 11 , 12 ]; ecology [ 13 , 14 ]; statistics: [ 15 , 16 , 17 , 18 ]; physics: e.g., nonlinear dynamics [ 19 , 20 ]; condensed-matter: [ 21 ]; earthquakes [ 22 , 23 , 24 , 25 , 26 ]; turbulence [ 27 , 28 ]; physical chemistry [ 29 ]; and space physics/astrophysics [ 30 , 31 , 32 ]; (a more extended bibliography of q -deformed exponential distributions can be found in [ 14 , 32 , 33 , 34 , 35 , 36 , 37 ]).…”