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«The Final Appeal to Mankind» by Nicolai Levashov

            Given extensive breeding, equation (3) is less than one (1).

            Extensive breeding occurs when the vegetative biomass produced by photosynthesis
            has not been completely consumed by the herbivorous animals.


            Equation (3) represents the system in balance. Fluctuations in the population density
            can be represented in the following form:

                                            (-)
                     (+)
            m(t) / N  m(n) < 1 < m(t) / N  m(n)                  (4)
            What, then, happens within the population that brings equation (4) to (the status of)
            equations (5) and (6)?

                      (+)
            m(t) / [N – (β ± Δn)] m(n) → 1                        (5)
                      (-)
            m(t) / [N – (p ± Δn)] m(n) → 1                        (6)
            Let us now try to provide a logical explanation for this phenomenon.

            Each individual  in the species  generates a psi-field; the psi-field  generated by  one
            individual is ω. Psi-fields generated by individuals in the population interact with one
            another and affect the processes occurring in their organisms. Let us assume that there
            is a certain optimum density of the aggregate psi-field of the population which ensures
            optimum conditions of existence for each individual.


                    W = ∫ ∫k(N;s)ωdsdN                                (7)
                            n s

            where:

            W — is the aggregate psi-field of the population .

            S — is the area of the population's habitat.

            ω — is the psi-field generated by one individual of the species.


            k(N, S) — is the factor representing the mutual effect of the influence of psi–fields
            within a population.

            Let us introduce a new parameter:

            Pw = [ ∫ ∫k(N;s)ωdsdN] / ∫ds = W/S                 (8)
                         n s                                  s

            where:

            Pw — is the optimum density of the aggregate psi–field per unit of surface area given
            an optimum population.


            In the same way that we obtained equation (4) we can arrive at the following equations:

                    [ ∫ ∫k(N;s)ωdsdN] / ∫ds < W/S                     (9)
                      (-)
                      N s                         s


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