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Chapter 15
Evolutionary Models for Simple Biosystems
Franco Bagnoli
Department of Energy and CSDC, University of Florence
Via S. Marta, 350139 Firenze, Italy
Also INFN, sez. Firenze
franco.bagnoli@uni.it
The concept of evolutionary development of structures constituted a real rev-
olution in biology: it was possible to understand how the very complex struc-
tures of life can arise in an out-of-equilibrium system. The investigation of such
systems has shown that indeed, systems under a ux of energy or matter can
self-organize into complex patterns, think for instance to Rayleigh-Bernard con-
vection, Liesegang rings, patterns formed by granular systems under shear. Fol-
lowing this line, one could characterize life as a state of matter, characterized
by the slow, continuous process that we call evolution. In this paper we try to
identify the organizational level of life, that spans several orders of magnitude
from the elementary constituents to whole ecosystems.
Although similar structures can be found in other contexts like ideas (memes)
in neural systems and self-replicating elements (computer viruses, worms, etc.)
in computer systems, we shall concentrate on biological evolutionary structure,
and try to put into evidence the role and the emergence of network structure in
such systems.
15.1. Introduction
The study of evolution has been largely aided by theoretical and computer models.
First, it is hard to perform experiments in evolution, although some of them have
been carried out. As a consequence, one cannot observe the dynamics of an evo-
lutionary phenomenon, but only a (partial) snapshot of some phases. In general,
there are many dynamics compatible with these observations, and therefore it is
not easy to decide among the possible \sources" of an observed behavior. The deci-
sion is often quantitative: many hypotheses can in principle originate an observed
evolutionary feature, and one has not only to decide which one is compatible with
other characteristics, but also which is the more robust, i.e., which requires less
parameters (that in general are poorly known) and less tuning.
An unique characteristic of evolution is its historical character. The genotypic
space is so large and ddled with \holes" (corresponding to non-viable phenotypes),
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