We present a genetic model based on simulated recombination of fixed sequences of quaternary genes (assuming four distinct forms, or alleles). States and dynamics of the infinite population genetic system, represented by the model, are derived for quadratic fitness functions. The bivariate marginal distribution genetic algorithm, devised to simulate the system, is experimentally compared with the univariate marginal distribution genetic algorithm with bit-based simulated crossover (in the case of infinite populations) for the MAX - CUT problem. Categories and Subject Descriptors I.6.5 [Computing Methodologies]: Simulation and Modeling, Model Development General Terms Algorithms Keywords Marginal Distribution Genetic Algorithms