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Biological evolution is a very
complex process. Using mathematical modeling, one can try to
clarify its features. But to what extent can that be done? For
the case of evolution, it seems unrealistic to develop a detailed
and fundamental description of phenomena as it is done in
theoretical physics. Nevertheless, what can we do? Can
mathematical models help us to systemize our knowledge about
evolution? Can they provide us with more a profound understanding
of the particularities of evolution? Can we imagine (using
mathematical representation) some hypothetical stages of
evolution? Can we use mathematical models to simulate some kind
of artificial "evolution"?
In order to clarify such
questions, it is natural to review the already developed models
in a systematic manner. In evolutionary modeling one can
distinguish the following branches:
of molecular-genetic systems origin have been constructed in
connection with the origin of life problem. Quasispecies and hypercycles by M. Eigen and P. Schuster and sysers by V.A. Ratner and V.V. Shamin are
the best known. These models describe mathematically some
hypothetical evolutionary stages of prebiological
self-reproducing macromolecular systems.
- Artificial life evolutionary
models are aimed at
understanding of the formal laws of life and evolution.
These models analyze the evolution of artificial
organisms, living in computer-program worlds.
- Applied evolutionary models are computer algorithms, which
use evolutionary methods of optimization to solve
practical problems. The
genetic algorithm by
J.H. Holland and the evolutionary programming, initiated
by L. Fogel et al., are well-known examples of these
The analysis, accomplished in the
child nodes, demonstrates that the relations between evolutionary
models and experiments are rather abstract. The evolutionary
models are mainly intended to describe general features of
evolution process rather then concrete experiments. Only
particular models (e.g. some models of mathematical genetics) are
used to interpret certain experimental data. Moreover, some
branches of evolutionary modeling (life origin models, artificial
life evolutionary models) go
to more abstract level and describe imaginary evolutionary
processes: not the processes as-we-know-them, but the processes
This abstractness is
understandable: because the biological world is very complex and
diversified, we firstly try to generalize a lot of experiments
and only then we interpret this generalized representation in
Historically, the profound
experimental researches have stimulated the creation of
evolutionary theories. For example, the
mathematical theories of population genetics by R.A. Fisher, J.B.S. Haldane, and S.
Wright were based on experimental genetic investigations,
performed in the first half of the 20-th century. The outstanding
achievements of the molecular biology, which were attained in the
1950-1960s, constituted the underlying background for the life
origin models by M. Eigen et al and the models of regulatory
genetic systems by S.A. Kauffman.
Currently, the evolutionary
models are intensively developed in close connection with
computer science researches, especially in Artificial Life
investigations. There is an obvious tendency towards modeling of
evolution of cybernetic, computer-like, intelligent features of
biological organisms. Current evolutionary models are actively
incorporating such notions as learning, neural networks, adaptive
behavior. Nevertheless, a lot of problems, concerning the
evolution of animal cognition abilities, have to be investigated.
Lets outline these problems briefly.
Biological evolution was able to
create complex, harmonic, and very effective biocybernetic
control systems, which govern the animal behavior. But how do
these cybernetic systems operate? How did they
emerge through evolution? What kinds of information processing and memory structures
are used in animal control systems? How did animal cognitive
abilities evolve? What kinds of "internal models" of the
environment emerge in the animal "minds"? How are these
"models" used in animal behavior? What were the
transitional stages between animal cognitive abilities and human
In order to investigate such a
wide spectrum of problems, it is natural to use a certain
evolutionary strategy and to analyze the animal control systems
and emergence of animal "intelligent" features step by
step, considering the biological evolutionary process as
underlying background. Such a field of investigations can be
called "Evolutionary biocybernetics". The conceptual
background for the investigations of the evolution of animal
cognition abilities was described in the first chapters of "The Phenomenon of Science" by V.F. Turchin . Some
approaches towards the developments of the evolutionary
biocybernetics were outlined in the paper .
mathematical modeling of evolution was profoundly elaborated in
several directions: life origin models, mathematical population
genetics, models of evolution of genetic regulatory systems,
artificial life evolutionary models. These models provide us with
better understanding of biological evolutionary phenomena; they
also give generalized descriptions of biological experiments.
Some models provide us with more abstract pictures they
describe artificial evolutionary processes: not the processes
as-we-know-them, but the processes as-they-could-be. Thus,
mathematical modeling of evolution is profound, well-elaborated,
intensively developing field of theoretical investigations.
Nevertheless, there are serious problems to be analyzed: the
problems of evolution of cybernetic, computer-like,
"intelligent" features of biological organisms. The
theoretical investigations of these problems could constitute the
subject of a future scientific discipline "Evolutionary
1. Turchin, V. F. The Phenomenon of Science. A Cybernetic
Approach to Human Evolution.
Columbia University Press, New York, 1977.
2. Red'ko, V.G. Towards
the evolutionary biocybernetics // Proceedings of The Second International
Symposium on Neuroinformatics and Neurocomputers, Rostov-on-Don,
1995, pp. 422-429.