Resumen
This publication begins a series of works devoted to the comparison of the results of numerical methods for solving integral equations and the results of computer simulations using Poisson processes. The pros and cons of these two approaches are highlighted. The main subject of study is the model of two-species communities proposed in the works of W. Dickman and R. Lowe. The mathematical formulation of this model for an infinite domain is described. A modification of this model for work in a limited area is given. In the future, this is required for stochastic modeling. Further, the most important moments of the stochastic model are briefly described, and the features of the computer simulations built for it are noted ? the algorithm used is described and the data structures used are noted. At the end of the work is a number of pictures, with the results of the above comparisons. The comparison is made within the framework of two classical scenarios of two-species models -- Competition-colonization trade-off (Bay-Run scenario) and heteromyopia (People-and-Mosquitoes scenario). These drawings show very similar results, as well as some discrepancies. All this allows us to hope that the work in this direction will be very fruitful in the future.