Page 328 - The Final Appeal to Mankind

«The Final Appeal to Mankind» by Nicolai Levashov
Appendix 1. Derivation of the Formula for Species Self-
Regulation

The habitat area (i.e., the area of the territory occupied by the population of a given
species) can support a certain number of animals (n) without disrupting the ecological
balance.

Due to a change in the environment of the habitat, fluctuations in the birth rate
occasionally result in an increase in population equal to:

(+)
N = n + β
where β — eguals the excessive number of individuals responsible for the imbalance

in the ecological equilibrium.

Given the same death rate and the same negative factors in the external environment,
the death rate increases and the number of individuals in the population approximates
a negative value.

(+)
N – (β ± Δn) → n (1)
where Δn — designates an insignificant deviation of the population from the optimum
value.

If, however, the number of members of the population is less than optimum, then given
the same natural conditions, the birth rate will increase and the population approaches
optimum.

(-)
N – (p ± Δn) → n (2)
where:

(–)
N — is less than the optimum number of individuals in the population,
p — is the number of individuals in the species less than optimum in the population.

What, then, is the reason for such a reaction by individuals to fluctuations in their
numbers?

Let us put forward a number of assumptions and analyze them. Consider the equation:

m(t) / m(n)n → 1 (3)
where:

m(t) — is the vegetative biomass growing on the habitat area in a unit of time,

m(n) — is the vegetative biomass necessary to support an herbivorous animal (a rabbit)
at an optimum existence,

n — is the optimum density of a population for the maintenance of ecological
equilibrium.

Given simple reproduction, equation (3) equals one (1).

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