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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

On carrying-capacity construction, metapopulations and density-dependent mortality

Pages: 1099 - 1110, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017054

 
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J. X. Velasco-Hernández - Instituto de Matemáticas, Universidad Nacional Autónoma de México, Boulevard Juriquilla No. 3001, Juriquilla, 76230, Mexico (email)
M. Núñez-López - Departamento de Matemáticas Aplicadas y Sistemas, DMAS, Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, Cuajimalpa de Morelos, 05300, México, D.F., Mexico (email)
G. Ramírez-Santiago - Instituto de Matemáticas, Universidad Nacional Autónoma de Mexico, Boulevard Juriquilla No. 3001, Juriquilla, 76230, Mexico (email)
M. Hernández-Rosales - CONACYT Research Fellow, Instituto de Matemáticas, Universidad Nacional Autónoma de México, Boulevard Juriquilla No. 3001, Juriquilla, 76230, Mexico (email)

Abstract: We present a mathematical model for competition between species that includes variable carrying capacity within the framework of niche construction. We make use the classical Lotka-Volterra system for species competition and introduce a new variable which contains the dynamics of the constructed niche. The paper illustrates that the total available patches at equilibrium always exceeds the constructed niche at equilibrium in the absence of species.

Keywords:  Niche construction, patches, Lotka-Volterra system, coexistence, competitive exclusion.
Mathematics Subject Classification:  Primary: 92D25, 92D40; Secondary: 34D20, 37C75.

Received: September 2015;      Revised: April 2016;      Available Online: January 2017.

 References