In this thesis, we explored the evolutionary gene network. we could developed 3 different simple gene network models, and could describe these network by mathematical approach. From the evolutionary view point, we figured out high fitnesses of gene network models, and tracked the fitness to show how gene networks are evolved. We used ordinary differential equations because it is useful to apply evolutionary time. Also, when we simulated to obtain a high fitness of gene networks, we applied simulated annealing algorithm. The simulated annealing algorithm is fit for finding good combinations of parameters that produce the high fitness of the gene network and it is the closest analogy with the shifting balance theory in populations(Kirkpatrick,et al., 1983). It’s not easy to find proper conditions for simulation, but we found empirical value from many simulations.
After we developed the fitness formula, we could expect the results, then we obtain same results with what would be expected from simulation. Thus, we could prove our formula is working well and the simulation is working well from the results.
In summary, 3 different gene network models depicted to ordinary differential equations and simulation applied simulated annealing algorithm. We could show how each model evolve with two environments in evolutionary time, and how the parameters of each model affect to the fitness of the gene network model. Furthermore, this study can be applied to design and optimize other gene networks. Therefore, we think this research can encourage the evolutionary gene network study. Also, we think this research is good start to expand analysis of the evolutionary gene network.
APPENDIX. ADDITIONAL MATERIAL
Track of parameters
We simulated with an initial temperature, 0.4305. First, we simulated with the initial temperature,1 and we choose 38 times fitness point from [ Figure .1 ]. [ Figure .2 ] indicates a result of simulation with the initial temperature 0.4305 and finally it shows the fitness clime up until 0.8414. The previous simulation with the initial temperature, 1 indicates the fitness is 0.8668 at the end of simulation. Both fitnesses are close to each other. Thus, this example also proves we find the properly initial temperature.
There are 3 figures indicate the track of other parameters of 3 different gene network models [ Figure .3, Figure .4, and Figure .5 ].
Figure .6 200 times simulation: Blue line is a simulation with the initial parameters. Red line is other 166 simulation results. the cutoff value is 0.4
200 simulations to show the pattern of parameters
We simulated 200 times and set the cutoff value is 0.4. 0.4 is not big enough but it makes the pattern of parameters is much clearly. [ Figure .6 ] shows same pattern with [ Figure 2.13 ] .
Also, there are 4 other figures to explain why there are several lines are out of the pattern of parameters in [ Figure .6 ] .
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