### Models and Simulations in Systems Biology

Joao Carlos Marques Magalhaes^{1}, Cedric Gondro^{2}

^{1}jcmm@bio.ufpr.br, Federal University of Parana; ^{2}cgondro@pobox.une.edu.au, University of New England

From logics standpoint a model is an interpretation of the formal treatment of a theory, in the sense of the set of objects and relations that behave as expected by the axioms of the theory. There are few examples of axiomatic theories in biology and these are rarely used in applied science. Informally a model can be seen as a representation analogous to real systems; it consists of a set of objects that hold relations to the parts and interactions of the modelled system. Biological systems are complex dynamic systems that transform a great number of variables. Realistic models of these processes can encompass many variables and generate complex systems for which adequate mathematical handling may not be available thus limiting the use of analytical models. An example of this scenario is the interaction of just two loci with two alleles each. Research indicates that depending on the adaptive values of the genotypes, small shifts in the initial allelic frequencies can evolve into chaotic dynamics making the system unpredictable. Extending such a model to thousands of loci renders the analytical approach untenable. Under these circumstances computational models that simulate complex adaptive systems offer an alternative approach. A relatively small set of objects and simple rules, computationally implemented via techniques as genetic algorithms or genetic programming can within the limits of the model replicate the complexity of biological systems in a controlled environment. The main argument to this approach is that even if the simulation reflects biological theory nothing beyond what has been modelled can be detected, meaning that unknown mechanisms operating in biological systems can not be detected. Alternatively what can be of interest should result from unknown interactions between the modelled elements and those for which analytical tools have not yet been developed. Thus computational modelling of complex systems can assist in bridging the gap between experimentation and theory. A simple implementation of this approach is freely available for download from http://www.sigex.com.br/genetics.