Descriptions of population dynamics in submerged cultures are important when studying the mechanisms of growth and fragmentation of filamentous microorganisms. Population models are traditionally formulated as population balance equations. Population models of filamentous morphology are difficult to solve because of random fragmentation, which introduces an integral term into the population balance equations. Balances for the systemic properties, e.g. concentration of hyphal elements, substrate concentration, average total hyphal length, and average number of growing tips, are set up. Based on these balances one can solve the inverse problem, i.e. determination of kinetic parameters directly from measurements of the hyphal morphology. Both a Monte Carlo method and a discretization method have been used to calculate the steady-state population distribution. The two methods are compared and the Monte Carlo method is shown to be superior with respect to versatility. With measurements of 100 hyphal elements to represent a steady state and using the Monte Carlo method and a statistical test it is shown that one can discriminate between four models of hyphal fragmentation in submerged cultures.