disrupts the
uniformity of individual fitness across the population. Whether this process
displays SOC
remains unclear.
There are those who claim that SOC is demonstrated by the available fossil
data[31]
with a power law
distribution on the lifetimes of genera drawn from fossil records, and
artificial life
simulations[1]
with a power law distribution on the lifetimes of competing species. On the
other
hand, there are
those who feel that the fossil data is inconclusive, and the artificial life
simulations
do not show SOC,
because the key power law behaviour in both can be generated by models
without
SOC[23].
SOC has nothing to say about the organisation of the population at the critical
state, only
the organisation
of the events, avalanches, which moves the population temporarily away, and
then
back to the
critical state.
One possibility
for determining the organisational complexity (organisation) of the population
of
agent-chains
would be the application of the Minimum Description Length(MDL) principle[7]
to
the executable
components of the agent-chains in the population. The best model, among a
collection
of tentatively
suggested ones, is the one that gives the smallest stochastic complexity to the
given
data. However,
the MDL principle has nothing to say about how to select the family of model
classes
to be applied
for determining the stochastic complexity. In fact, this problem cannot be
adequately
formalised[28].
In practice, their selection is based on human judgement and prior knowledge of
the
kinds of models
that have been used in the past. This limitation would make it impossible to
automate
the
organisational complexity estimation process, due to the necessity of human
intervention at model
selection for
every different user request.
Mean Field
Theory (MFT) requires a neighbour model to describe the interactions
between
neighbours in
the systems it is applied to, and is therefore easily applied to Cellular
Automata[19].
The main concept
in MFT is that, for a single particle, the most important contribution to
its
interactions
comes from its neighbouring particles, and therefore its behaviour can be
approximated
by relying upon
the mean field caused by its neighbouring particles. MFT application to the
evolution
of a
population[16]
requires a neighbour model, which in actual biological systems is a
reasonable
assumption.
agent populations lack neighbour models based on a 2D or 3D metric space. The
only
available
neighbour model becomes a distance measure on a parameter space measuring
dissimilarity.
However, such a
neighbourhood model cannot represent the information-based interactions
between
individuals of a
population of agent-chains.
In Replicator
dynamics, of evolutionary game theory, agents of a population play a game and
do
not optimise
over strategic alternatives, but inherit a fixed strategy and then replicate
depending on
the strategys
payoff (fitness)[15].
An equilibrium, a stable steady state, can be reached in which all
the
strategies have
the same expected payoff. It is called a stable steady state, because if pushed
slightly
off, it returns
back to the equilibrium of the stable steady state. An evolutionarily stable
strategy
(ESS) is an
equilibrium strategy that can overcome the presence of a small number of
invaders, so
it is an
asymptotically stable steady state, which is a more stringent stable equilibrium
concept[33],
than a stable
steady state. The self-organisation found in replicator dynamics is not the
composition
of the
population directly, but the presence of stable steady states, in which the
genotype frequencies
of the
population cease to change from one generation to the next. The composition of
the resulting
population can
even be randomly distributed, but stable. This self-organisation measure is
more
relevant to the
genetic stability of the population from one generation to the next, rather than
the
organisational
complexity (organisation).
Kolmogorov-Chaitin(KC)
complexity measures the complexity of binary sequences by the
smallest
possible Universal Turing Machine (UTM), algorithm (program and input), that
produces
9