Mathematical Modeling of Biological and Social Evolutionary Macrotrends

Leonid Grinin (1) , Alexander V Markov , Andrey Korotayev (1)

1 RAS - Russian Academy of Sciences [Moscow]

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically.

Keywords: social evolution; biological evolution; mathematical model; Biodiversity; population growth; positive feedback; hyperbolic growth

Domains: History, Philosophy and Sociology of Sciences; History; Philosophy

Leonid Grinin, Alexander V Markov, Andrey Korotayev. Mathematical Modeling of Biological and Social Evolutionary Macrotrends. Leonid Grinin, Andrey V. Korotayev History & Mathematics: Trends and Cycles., Uchitel, pp.9-48, 2014, 978-5-7057-4223-3. ⟨hprints-01863038⟩