Physical Oceanography, Vol. 13, No.
SIMULATION OF THE PROCESSES OF ADAPTATION IN ECOLOGICAL SYSTEMS
E. M. Igumnova and I. E. Timchenko
The method of adaptive balance of causes (ABC method) is used for the simulation of the pro-
cesses of adaptation of ecosystems to the environmental conditions. We present the foundations
of this method and show that the ABC model gives a more realistic description of the processes
of adaptation in modeling the “prey–predator” ecosystem than the Lotka–Volterra model. We
study the problem of identification of the coefficients of the ABC models of ecosystems by
means of the reanalysis of adaptive scenarios of their development and present an example of ap-
plication of the equations of optimal interpolation to the evaluation of the coefficients of a model
biogeocenosis. The ABC method proves to be quite promising for the construction of model
ecosystems according to the expert and archival data on the scenarios of their development.
The property of adaptation of living organisms (elements of ecological systems) to variable environmental
conditions is an inherent characteristic feature of the living matter. This means that organisms are able to rebuild
the processes running in them or to change their behavior with an aim to restore the existing balance with the en-
vironment on a new level guaranteeing their survival. The processes of adaptation in ecosystems are quite
complicated. Therefore, they are extensively studied on the genetic level, on the level of species, and on the
level of ecosystems . As follows from the results of investigations, a new method for modeling complex
systems called the ABC (adaptive balance of causes) method may turn into a promising approach to the solution
of the problem of adaptation . In the present work, we study some features of this method on the level of eco-
The ABC method allows one to represent the entire complex of nonlinear relationships between the natural
processes running in an ecosystem in the form of a simpler combination of local dynamic balances described by
standard modules. The equations for these modules have the same general form and include functions reflecting
the influence of the other modules on a given module. These functions can be chosen in the form of arbitrary
monotonically increasing functions, i.e., their derivatives must be nonnegative. Thus, in particular, they can be
regarded as linear functions with variable coefficients depending on time. In this case, the model of an ecosys-
tem remains relatively simple but can describe complex processes of internal adaptation, i.e., reproduce the state
of dynamic balance under the conditions of variable links in the system.
We now study the applicability of the ABC method to the construction of model ecosystems formed by in-
teracting populations of organisms. Thus, it is of interest to use the ABC method for the simulation of the pro-
cesses of adaptation of phyto- and zooplankton in marine media. The analysis of the indicated ecosystems in-
cludes the classical “predator–prey” problem described by the Lotka–Volterra equations and studied in biooce-
anography in detail . As compared with traditional approaches, the ABC method gives a simpler and more re-
alistic solution of this problem.
As an important practical problem of ecological simulation, one can mention the evaluation of the coeffici-
ents on the right-hand sides of the evolutionary equations for model ecosystems. In what follows, we present the
solution of this problem by the ABC method. In this case, we use the system of equations of optimal interpola-
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
46–57, January–February, 2003. Original article submitted May 31, 2001.
0928-5105/03/1301–0041 $25.00 © 2003 Plenum Publishing Corporation 41