Ecoinformatics and Soil-Plant Formations - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 647

Each plant or some totality of plants N interacts with the environment
H (including other plants) exchanging some amount of resources V N for an obtained
volume of resources W N . The structure |N| and the behavior N of plants or their
communities are in an equilibrium state with the structure |H| and behavior H of the
environment, and this state is described by a minimax criterion:

W N ; opt ¼ max
j ; N

W N V N ;

ð

j ;

;

j ;

Þ

min
j ; H

N H

fg fg

W H V N ;

ð

j ;

;

j ;

Þ

W H ; opt ¼ max

j ; H

min
j ; N

N H

fg fg

The goals N S and H S of vegetation continuum N and environment H, respec-
tively, can be opposite, partially coinciding, or indifferent. Due to the developed
optimal strategy, plants of different kinds adjust to the levels of (V, W)-exchange,
which are possible on a given territory. Thus, because of differentiation of niches,
there are multi-level vegetation communities, for instance, in the forest the factor of
niches differentiation is many-sided. It covers such special features of various kinds
of plants as the location of roots at different depths, different periods of blossoming,
different response of plants to climate changes, different need of species for mineral
nutrition, etc. In general, a plant

'

s niche can vary in time both due to the dynamics
of the plant itself and in connection with the drifting of the adjacent niches. The
diversity of possible situations brings forth series of models of the functioning of
vegetation communities.
One of the characteristic examples of the models of vegetation communities is a
discrete model by Galitsky (1985). Let us consider it in detail. The equation that
describes a change of the plant ' is biomass B is written as

c B f a

B k B k

dB = dt ¼ k ðÞða þ B = B f

where k(t) = min{A/Af f (t), 1} is the indicator of the plant ' is provision with a territory,

A is the size of the available territory for the plant s growth, A f is the size of the

territory needed for free growth; Bf f is the biomass of a freely growing plant;

'

is the
characteristic of the item of expenditure in the balance (on the biomass mainte-
nance);

ʱ

cit of territory.
The gist of the Galitsky model

ʳ is the index of the de

'

is functioning is that the biomass of each plant
located in a cell of its own in a common mosaic, changes independent of other
plants of the community until either this plant or any of its neighbors dies for lack
of territory. At the moment of dying the adjacent plants rush to distribute the vacant
territory, and after changing the parameter A, the equation of the model is valid
again. As a result, as individual plants die, the original mosaic changes on a local
scale, gradually covering larger areas. The criterion of dying off is simple: a plant is
considered dead if

its biomass becomes below some threshold level B dead

(B dead (t)= ʵ B f (t), 0 < ʵ < 1).