Mathematics of Darwin's Diagram. (28th May 2014)

• Record Type: Journal Article
• Authors: Bessonov, N.; Reinberg, N.; Volpert, V.
• Editors: Morozov, A.
• Is Part Of: Mathematical modelling of natural phenomena. Volume 9:Number 3(2014)
• Page Start: 5
• Page End: 25
• Publication Date: 2014-05-28
• Subjects: speciation, -- evolution, -- nonlocal reaction-diffusion equations; Science -- Mathematical models -- Periodicals; Medicine -- Mathematical models -- Periodicals; Biology -- Mathematical models -- Periodicals; 501.51
• DOI: 10.1051/mmnp/20149302
• Languages: English
• ISSNs: 0973-5348

Abstract

Abstract : Darwin illustrated his theory about emergence and evolution of biological species with a diagram. It shows how species exist, evolve, appear and disappear. The goal of this work is to give a mathematical interpretation of this diagram and to show how it can be reproduced in mathematical models. It appears that conventional models in population dynamics are not sufficient, and we introduce a number of new models which take into account local, nonlocal and global consumption of resources, and models with space and time dependent coefficients.