Modelling and simulation are tools that can be used to help the adequate management of natural forests, aiming conservation or production, and may be considered as additional techniques to help the decision making process. Among the modelling and simulation processes, the diffusion method, which applies a model composed by Fokker-Planck or Kolmogorov differential equations, is not yet fully studied and applied in simulating natural forests dynamics. The main goal of the present research work was to use and to test the diffusion method for simulating dynamics and growth of a mixed araucaria-hardwood forest. Data used came from a continuous forest inventory belonging to the Long Term Ecological Program (PELD), taken at the São João do Triunfo Experimental Station, located in Paraná State, Southern of Brazil. Data were collected from four plots, during a ten-year period, including all trees with DBH equal or larger than 10 cm. The dynamics modeling was performed by the diffusion method, which is characterized by the integration of recruitment, growth and mortality as a function of time and individuals measures. For modeling diametric growth, twelve equations were fitted and tested, with annual diameter increment as the dependent variable and DBH and Kohyama’s competition index as the independent variables. Values of annual rates of recruitment and mortality were also considered, for each period of time analyzed. The measurements intervals varied from one to four years, adding up to 14 periods, for whose the dynamics of two sets of distinct data were projected. One data set was composed by all species while the other comprised only araucaria species. The simulated projections aiming validation and auto calibration, as well as sensibility analysis of the implemented system, were performed for several cycles and were compared statistically with the observed abundance values by the Chi-Square test. All simulations were done using the computerized system (SISDIF) developed and implemented for such objectives. The results showed that non linear equations fitted including the Kohyama’s competition index were more efficient. Exponential equation showed good fitting for predicting mortality in all measurements periods. The graphical method for modeling recruitment was very efficient, being the two calculating process for recruitment and mortality non significant different for projecting the results. The set of data including only the araucaria species showed results closer to the observed values than the set that included all species. The validation process for a one-year period and long-term projections, for 2020 and 2040, showed the best results for simulating diametric distribution behavior. Multiple projections, with a larger number of simulation cycles, induced an increase in the differences between the projected and observed values. Increasing the rate of recruitment and mortality showed greater influence in the projected values, according to the sensibility analysis performed for the developed system. The developed computerized system, using the diffusion method, revealed to be practical and efficient for simulating and projecting the forest dynamics, in spite of the heavy dependence it has on the performance of the fitted equations and data available.
