Abstract
In this study, starting with a newly introduced concept of data complexity ("empirical data complexity"), we specify the concept of complexity more concretely in relation to mathematical modeling and introduce "model-based complexity (MBC)". Inductive inference based on the minimum model-based complexity method is then applied to the reconstruction of molecular evolutionary tree from DNA sequences. We find that minimum MBC method has good asymptotic property when DNA sequence lengths approach to infinite and compensates the bias of maximum likelihood method due to the difference of tree topology complexity. The efficiency of minimum MBC method for reconstruction of molecular tree is studied by computer simulation, and results suggest that this method is superior to the traditional maximum likelihood method or its modification by Akaike's AIC.