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Alexandr N. Tetearing
THEORY of POPULATIONS


Alexandr N. Tetearing. Theory of Populations


 
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Alexandr N. Tetearing

THEORY of POPULATIONS


ISBN 978-5-600-00753-6


The book is devoted to the theory of development of the biological systems.

The fundamental equation of life of a biological population, based on the general physical principles, allows us to get all the basic equations of population dynamics, describing the development of the populations under various environmental conditions.

The equations describe the population transition that occurred in our human population in the late 20-th century. This transition may indicate the fact that the human population consists of two super-races – the old ”slow” race, and new fast-growing human race that appeared on Earth relatively recently.

The separate chapter presents the base classification of predator-prey systems. The classification consists of ninety-six different equation systems.

The book is addressed to a broad auditorium of biologists, ecologists, and demographers, as well as readers, interested in the development of the biological populations.

Translated from Russian


Contents


Part I

Introduction to the theory of populations
  • Chapter 1.
    Definition of a biological population
  • Chapter 2.
    Equation of life. General form of fundamental equation of development of a biological population
  • Chapter 3.
    Derivation of the equation of unlimited growth of a biological population. Malthus law
  • Chapter 4.
    Growth of a biological population under conditions of limited food resource
  • Chapter 5.
    Transition from the stage of unlimited growth of a population to the stage with limited food resource. Two-stage scenario of the development of a population


Part II

Equation of life of a population with taking into account the energy expenses on searching for food resource
  • Chapter 6.
    Development of persons in the personal areas
    • 6.1   Full-fed existence of persons in the personal areas
    • 6.2   Hungry existence of persons in the personal areas
  • Chapter 7.
    Development of persons in the common territory
    • 7.1   Full-fed existence of persons in the common territory
    • 7.2   Hungry existence of persons in the common territory
    • 7.3   Transition of a population from the mode of a full-fed existence to the mode of a hungry existence


Part III

Equation of life with taking into account the mortality in the population
  • Chapter 8.
    Equation of life under conditions of a full-fed existence of persons in the personal areas with taking into account the mortality in population
    • 8.1   Equations of life of a biological population under conditions of full-fed existence of persons in the personal areas
    • 8.2   Parameter of birth rate
    • 8.3   Solution in the form M(t)=const
    • 8.4   About existing polynomial solutions
    • 8.5   Exponential solution of equation of life with taking into account the mortality in the population under conditions of a full-fed existence of persons in the personal areas
    • 8.6   Law on restriction of birth rate for exponential solution
    • 8.7   Solution of equation of life in the form of a piecewise function
    • 8.8   Two-exponent solution of equation of life under conditions of a full-fed existence of persons in the personal areas
    • 8.9   Remarks to the race theory of mankind
    • 8.10   Periodic solutions of equation of life under conditions of a full-fed existence of persons in the personal areas
    • 8.11   Damped periodic solutions of equation of life under conditions of a full-fed existence of persons in the personal areas
    • 8.12   General form of solution of equation of life for a biological population under conditions of a full-fed existence of persons in the personal areas
    • 8.13   About observation of the periodic oscillations in population size in the laboratory
  • Chapter 9.
    Hungry existence in the personal areas with taking into account the mortality in the population
    • 9.1   Conditions of a hungry existence of persons in the personal areas
    • 9.2   General solution of equation of life under conditions of a hungry existence in the personal areas with taking into account the mortality in the population
  • Chapter 10.
    Transition of a population to a hungry existence
    • 10.1   Problem about decrease in food resource
    • 10.2   Parameter of stability of a population
  • Chapter 11.
    Full-fed existence of mortal persons in the common territory
    • 11.1   General form of equation of life under conditions of a full-fed existence of persons in the common territory with taking into account the mortality in the population
    • 11.2   Solution in the form M(t)=const
  • Chapter 12.
    Hungry existence of mortal persons in the common territory
    • 12.1   General form of life equation under conditions of a hungry existence in the common territory with taking into account the mortality of persons
    • 12.2   Solution in the form M(t)=const
    • 12.3   Linear and polynomial solutions
    • 12.4   Limited solution
    • 12.5   Periodic solutions of equation of life under conditions of a hungry existence of persons in the common territory with taking into account the mortality in the population
    • 12.6   Damped periodic solutions of equation of life under conditions of a hungry existence of persons in the common territory with taking into account the mortality in the population
    • 12.7   General solution of equation of life under conditions of a hungry existence of persons in the common territory with taking into account the mortality in the population
  • Chapter 13.
    Two-mode scenario of population development
    • 13.1   Transition of a population from the per- sonal areas to the common territory under conditions of a hungry existence of persons with taking into account the mortality in the population
    • 13.2   Successful scenario of transition of a population from the personal area to the common territory under conditions of a hungry existence of persons with taking into account the mortality in the population
    • 13.3   Catastrophic transition of a population from the personal areas to the common territory
    • 13.4   Numerally solving the life equations
  • Chapter 14.
    Three-mode scenario of population development
    • 14.1   Transition of full-fed mortal population from the personal areas to the common territory and subsequent transition to a hungry existence
    • 14.2   Catastrophic scenario of the three-mode development of a population. Transition of full-fed persons from the personal areas to the common territory with subsequent transition to a hungry existence
    • 14.3   Problem about climate changes (periodic variations in food resource) s
    • 14.4   Historical sequence of the populations
  • Chapter 15.
    Base octet of equations of population development
    • 15.1   Full-fed persons in the personal areas without mortality in the population
    • 15.2   Hungry persons in the personal areas without mortality in the population
    • 15.3   Full-fed persons in the common territory without mortality in the population
    • 15.4   Hungry persons in the common territory without mortality in the population
    • 15.5   Full-fed mortal persons in the personal areas
    • 15.6   Hungry mortal persons in the personal areas
    • 15.7   Full-fed mortal persons in the common territory
    • 15.8   Hungry mortal persons in the common territory
    • 15.9   Transitive conditions for various modes of existence of the population


Part IV

Predator-prey population systems
  • Chapter 16.
    Classification of predator-prey systems
  • Chapter 17.
    Predator-prey equations systems
    • Class I  
      • Group I-A
        • I-A-1-a-1
        • I-A-1-a-2   Lotka-Volterra equations
        • I-A-1-b-1
        • I-A-1-b-2
        • I-A-2-a-1
        • I-A-2-a-2   Lotka-Volterra equations
        • I-A-2-b-1
        • I-A-2-b-2
      • Group I-B
        • I-B-1-a-1
        • I-B-1-a-2
        • I-B-1-b-1
        • I-B-1-b-2
        • I-B-2-a-1
        • I-B-2-a-2
        • I-B-2-b-1
        • I-B-2-b-2
      • Class II  
        • Group II-A
          • II-A-1-a-1
          • II-A-1-a-2
          • II-A-1-b-1
          • II-A-1-b-2
          • II-A-2-a-1
          • II-A-2-a-2
          • II-A-2-b-1
          • II-A-2-b-2
        • Group II-B
          • II-B-1-a-1
          • II-B-1-a-2
          • II-B-1-b-1
          • II-B-1-b-2
          • II-B-2-a-1
          • II-B-2-a-2
          • II-B-2-b-1
          • II-B-2-b-2
      • Class III  
        • Group III-A
          • III-A-1-a-1
          • III-A-1-a-2
          • III-A-1-a-3
          • III-A-1-a-4
          • III-A-1-b-1
          • III-A-1-b-2
          • III-A-1-b-3
          • III-A-1-b-4
          • III-A-2-a-1
          • III-A-2-a-2
          • III-A-2-a-3
          • III-A-2-a-4
          • III-A-2-b-1
          • III-A-2-b-2
          • III-A-2-b-3
          • III-A-2-b-4
        • Group III-B
          • III-B-1-a-1
          • III-B-1-a-2
          • III-B-1-a-3
          • III-B-1-a-4
          • III-B-1-b-1
          • III-B-1-b-2
          • III-B-1-b-3
          • III-B-1-b-4
          • III-B-2-a-1
          • III-B-2-a-2
          • III-B-2-a-3
          • III-B-2-a-4
          • III-B-2-b-1
          • III-B-2-b-2
          • III-B-2-b-3
          • III-B-2-b-4
      • Class IV  
        • Group IV-A
          • IV-A-1-a-1
          • IV-A-1-a-2
          • IV-A-1-a-3
          • IV-A-1-a-4
          • IV-A-1-b-1
          • IV-A-1-b-2
          • IV-A-1-b-3
          • IV-A-1-b-4
          • IV-A-2-a-1
          • IV-A-2-a-2
          • IV-A-2-a-3
          • IV-A-2-a-4
          • IV-A-2-b-1
          • IV-A-2-b-2
          • IV-A-2-b-3
          • IV-A-2-b-4
        • Group IV-B
          • IV-B-1-a-1
          • IV-B-1-a-2
          • IV-B-1-a-3
          • IV-B-1-a-4
          • IV-B-1-b-1
          • IV-B-1-b-2
          • IV-B-1-b-3
          • IV-B-1-b-4
          • IV-B-2-a-1
          • IV-B-2-a-2
          • IV-B-2-a-3
          • IV-B-2-a-4
          • IV-B-2-b-1
          • IV-B-2-b-2
          • IV-B-2-b-3
          • IV-B-2-b-4
    • Chapter 18.
      Food chains
    • Chapter 19.
      Practical simulation of predator-prey systems
      • 19.1   Simulation of I-st class problems
      • 19.2   Simulation of IV-st class problems
      • 19.3   Simulation of IV-st class problems with quasi-sinusoidal prehistory function of the prey


    Part IV

    Functions of age distribution
    • Chapter 20.
      Functions of age distribution of population mass. Basic definitions
    • Chapter 21.
      Use of age distribution functions in the life equations
    • Chapter 22.
      Calculation of the function of numerical age distribution
      • 22.1   Calculation of the function of numerical age distribution for a known function M(t)
      • 22.2   Calculation of the function of numerical age distribution for an exponential function
      • 22.3   Calculation of the function of numerical age distribution using the Fourier transform
      • 22.4   Calculation of the functions of numerical age distribution using the Laplace transform
      • 22.5   Summary table of the functions of numerical age distribution for some functions of changes in population mass
      • 22.6   Some remarks about interpretation of demographic data
      • 22.7   Development of a population with taking into account the losses from external action. Problem about the fishermen
      • 22.8   Modi cation of equations of the population development taking into account an arbitrary function of losses from external influence
    • Chapter 23.
      Equation of life in general case with unknown function M(t) and unknown function of numerical age distribution Ng(t)
    • Chapter 24.
      Function of age distribution of birth rate
      • 24.1   General form of function of age distribution of birth rate
      • 24.2   Numerical simulation of population devel- opment using the function of age distribu- tion of birth rate


    Part IV

    Growth equation
    • Chapter 25.
      Growth equations
      • 25.1   Equation of growth of a biological organism
      • 25.2   Solution in the form L(t)=const
      • 25.3   Bertalanffy equation as a special case of the growth equation
      • 25.4   Physical meaning of the "coefficient of anabolism" and "coefficient of catabolism" in the Bertalanffy equation
      • 25.5   Solving the growth equation using the nu- merical methods
      • 25.6   Equation of growth under conditions of limitation in food resource
      • 25.7   Two-stage scenario of organism growth
      • 25.8   Dendrochronological equation


    Author's afterword


    List of symbols



ISBN 978-5-600-00753-6

600 pages



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