Elsevier

Ecological Modelling

Volume 221, Issues 13–14, 10 July 2010, Pages 1702-1709
Ecological Modelling

On the reasons of hyperbolic growth in the biological and human world systems

https://doi.org/10.1016/j.ecolmodel.2010.03.028Get rights and content

Abstract

Macroevolution of the biological and human world systems in the aspect of time-dependence of their sizes is studied. These systems are considered as ‘civilizations’, which are defined here in a generalized sense as the systems having memory and producing knowledge (vital information) necessary for survival. Sizes of three types of memory – genetic, neural, and external – are estimated. Dominating one of them leads to the development of an appropriate type of civilization. The rise and development of the genetic memory was accompanied with the formation of the biota (which can be tractable as a biological civilization) and a hyperbolic growth of its biodiversity. The prevailing development of the neural memory in one of the taxa of biota led to the rise of the human civilization and to a hyperbolic growth of its population. The development of the external memory will probably lead to the extraction of a taxon (probably, a pool of countries) from the human world community, with a hyperbolic growth of the taxon's memory and fund of knowledge but without a pronounced growth of its population.

Introduction

Demographic data show that, at least several tens of thousands of years, almost up to the end of XX century, human population growth followed a hyperbolic law (von Foerster et al., 1960, von Hoerner, 1975). Moreover, it appears that a similar hyperbolic law is also inherent in the diversity of different taxa in the biological world system, indicated by the growth of the number of families and genera in the marine and continental biota (separately and as a whole) during the Phanerozoic (Markov and Korotayev, 2007, Markov and Korotayev, 2008, Markov and Korotayev, 2009, Grinin et al., 2009). The similarity of growth laws suggests that in both cases there is a universal mechanism bringing such different systems to the same regime of growth. In the cited works on biodiversity, the hyperbolic growth law is associated with an increase in life span of taxa (families or genera; data on species are not reliable). However, life span itself depends on the fit of taxa to ambient conditions and therefore is determined by the content of valuable information accumulated in genomes. Finally, it turns out that there are informational reasons for inducing the biodiversity growth. Similar reasons are responsible for the hyperbolic growth of human population; this growth is a result of the accumulation of valuable information in the genetic memory and, in a much more rapidly way, in the neural one (Dolgonosov and Naidenov, 2006, Dolgonosov, 2009). Thus, it can be hypothesized that similar informational mechanisms regulate sizes of both world systems – the number of humans and the number of taxa in the biota.

In the literature there is another interpretation of the hyperbolic growth of human population (Kremer, 1993, Cohen, 1995, Kapitza, 1996, Johansen and Sornette, 2001, Podlazov, 2004, Tsirel, 2004). Kapitza (1996) looks the reason of the hyperbolic growth in the pair interactions with information exchange between people. Kremer (1993), in one of his models, proceeds from the assumption that the rate of technological progress is proportional to population size and to the current technological level meaning this level as the amount of available resources. Supposing that population size follows the technological level (proportionally to it), Kremer comes to the hyperbolic law. A similar model is developed by Podlazov (2004), though his model considers vital technologies instead of the amount of resources. A generalization of these models is given in the series of works (Korotayev, 2005, Korotayev, 2006, Korotayev, 2007, Korotayev and Khaltourina, 2006, Korotayev et al., 2006a, Korotayev et al., 2006b).

From the informational viewpoint, civilization represents a system having memory and producing knowledge necessary for survival. In spite of that this definition seems counterintuitive and controversial to common definitions of civilization, this is not so. One of the main philosophers on the concept of civilization – Albert Schweitzer – outlined the idea that there are dual opinions within society; one regarding civilization as purely material and another, as both ethical and material (Tariq, 2009). Schweitzer (1923) defined civilization, saying: “It is the sum total of all progress made by man in every sphere of action and from every point of view in so far as the progress helps towards the spiritual perfecting of individuals as the progress of all progress”. Meanwhile, both material and ethical can be consolidated in the concept of knowledge, and such a consolidation is quite natural because knowledge can be both about material objects and processes and about ethical norms assisting the spiritual perfecting of individuals. Therefore, the definition of civilization as a system producing knowledge includes common notions and even broadens them embracing not only the humanity but also the biota. Thus, this understanding of civilization is suited for systems of any origin, because the presence of memory equipped with a processor for extracting valuable information from incoming signals is a feature of not only humans but every biological species. In this connection, the question rises how memory type influences the type of civilization.

Along with the genetic and neural memory, there is an external memory. The first two types of memory are an internal property of the biological units constituting civilization. The external memory is inherent in the human civilization, where this memory type is realized in the form of different external carriers of information: physical samples, books, films, computer carriers, etc. The genetic memory dominates in the biota providing accumulation of valuable information and its inheritance. Thus, the biota demonstrates the above-mentioned attributes of civilization that allows it to be named the biological one. The human civilization, grown from it, had used advantages of the neural memory (primarily, speed of processing information), whose size on a definite stage of the phylogenesis achieved the size of genetic memory and then surpassed it providing an accelerated development of this phyletic branch. The further evolution of the humanity had led to a gradual development of the external memory, which became dominant in our time due to the fast perfection of computer carriers.

Let us consider the macroevolution of civilization under the domination of a definite memory type and what happens when the dominant changes. A key role pertains here to the compression of the incoming information in its processing into knowledge.

Section snippets

Compression of information

Each type of memory is provided with a processor, which transforms an unconditional (primary) information R, perceived through signals from the outer world, into a conditional (useful, valuable, vital) information q that represents knowledge (Fig. 1). As measures of the quantities R and q, we can take the memory sizes needed for storing the corresponding information. The primary, unconditional information requires too large memory size to store it completely and, moreover, cannot be used

Memory sizes

Memory of any type must give a possibility to reflect complex structures of the outer world in appropriate patterns of the memory itself. For this purpose it is necessary for the memory to have: a large set of elements; means for linking elements and assembling diverse patterns; a sufficient speed of restructuring patterns for fitting to the changing environment. The information content of memory (involving all the existing patterns) cannot surpass the potential memory capacity. Because the

Informational origins of the hyperbolic law

All the long-term evolution preceding the informational epoch is characterized by domination of the internal memory, whose size R is the sum of the memory size m of each of the N individuals yielding R = mN. Assuming that the minimum memory R = 1 (in relative units) inherent in the incipient civilization corresponds to an initial population size N0, we obtain m = 1/N0 and hence R = N/N0. Appealing to R = eq, we obtain N = N0eq. It means that, in the evolution, both the size of recognizable primary

Hyperbolic growth of biodiversity

Biodiversity of a community is adopted to estimate by Shannon's entropyH=i=1Nninlog2nin,where N is the number of taxa, ni is the ith taxon abundance, n is the total community abundance, n = n1 +⋯+ nN. Entropy achieves its maximum value H = log2N at equal abundances of taxa ni = const. It is seen that the maximum entropy depends only on the number of taxa. The stated interpretation of the biodiversity suffers from the shortcoming that equilibrium abundances of taxa cannot in reality be equal because

Transitions with changing of dominant memory type

The hyperbolic growth of biodiversity had continued until there appeared a taxon in the biosphere who could develop its neural memory, became to use it actively for producing and accumulating knowledge, and, due to that, acquired monopolistic positions in the biosphere (we mean, of course, humans).

Transition from the domination of genetic memory in the biota to that of neural memory in one of the taxa led to a qualitative change in the evolutionary process: to the beginning of hyperbolic growth

Acknowledgements

I wish to thank my anonymous reviewers for their analysis of the paper and valuable comments.

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