Functional symmetry and reproducibility of the evolutionary process

The question on the reproducibility of evolutionary processes is primarily of fundamental importance; however, with the development of methods for modeling evolutionary processes on computer multilevel models, an answer to this question is necessary to clarify the status of the predictions obtained. Experimental obtaining of ensembles of evolutionary outcomes for subsequent statistical processing on real biological systems seems to be impracticable. At the same time, the results obtained on multilevel computer models are difficult to interpret due to their complexity and the dependence of modeling results on a variety of parameters. This work is aimed at identifying common properties of evolving systems using a simple heuristic model based on transparent general principles and ideas about the key properties of biological systems that are important for the evolutionary process. Agents undergoing evolutionary changes are recurrent neural networks with a well-defined structure, a given function, and a specific rule for modifying the structure in the direction of maximum fitness. A separate instance of a neural network formed during the evolutionary process is called neural network model object (NNMO). Computational experiments have been carried out to generate ensembles of NNMO structures performing a given function, and the patterns of NNMO distribution in the structural space have been analyzed. This analysis confirms the presence of functional symmetry in the structure of NNMOs performing the same function. An assessment of the stability and reproducibility of individual evolutionary trajectories has been carried out. It is shown that under certain constraints leading to a reduction of the complexity of the NNMO structure (analogous to a narrow environmental specialization), the final NNMO structures may be close, but not identical. This suggests an inaccurate reproduction of the evolution of the structure with functional equivalence. Nevertheless, it can be argued that in the general case, the very ability for evolutionary change is possible with the redundancy of the potential complexity of the structure over the functional complexity and automatically entails a multiplicity of evolutionary outcomes based on the fact that the same function can be implemented by different, but functionally invariant structures.

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