Ecology studies the behaviour of systems formed by living beings that interact with their
environment. Although this interaction is reciprocal, many studies assume a non-dynamic
environment within which species evolve. In particular situations, this approximation
could be good enough. However, the hypothesis is, in general, not valid. The seminal
work by A. Watson and J. Lovelock considered explicitly this aspect in a model of Earth,
the so called Daisyworld and, in so doing, they opened a new paradigm in Ecology. Since
then, many models coming from Ecology as well as from other disciplines ranging from
Sociology to Engineering include this feedback between species and the environment where
they live.
As a consequence of this approach the evolution of species is not longer independent of
their surrounding. The evolution of the population induces an intrinsic variation in their
own environment. Even in the absent of external perturbations, as the solar radiation in
the Daisyworld, the environment is driven evolution. The fittness landscape is evolving
coupled with the population variation. So, looking for the fittest species in this context
requires of new strategies.
A very efficient class of optimization algorithms mimic biological evolution to seek
optima in complex problems. Standard genetic algorithms simulate the evolution of entities
(strands) that evolve in a non-dynamic competitive ambient. In some examples, the
environment is externally perturbed to enhance the efficiency of the algorithm, but there
is never a feedback from the population. To our knowledge, there is no genetic algorithms
in which species have the capacity of modifying the environment that, in turn, fixes the
criteria of evolution of the entire population.
In this paper, we present a new brand of genetic algorithm that simulates a population
of strands of given length that evolve in a changing environment. At each time step, the
population defines its environment that is taken into account to obtain the next generation
through the reproduction rate of each species. In order to get some insight about this kind
of evolution, we analyzed firstly a toy model in which only two species (of daisies) exist.
Their replication rate depends on a unique parameter (e.g. temperature) that is modified
dierently by each species. This dynamical system is non linear and, interestingly, presents
a stationary state of coexistence for a value of the temperature in tune with the optimal
growth temperatures of the two daisies. At this simple level, the system is already able
of self-regulates and hence to bring about optimal conditions for living.