Modelagem Matemática Aplicada a Recomendação de Uso de Sistemas Agroflorestais Multiestratos Sucessionais pelo Pequeno Agricultor no Bioma Cerrado

Abstract

The mathematical modeling of complex productive systems (arrangement of different plant structures), biodiverse and their differentials, both environmental and financial, enables the understanding of the behavior and, consequently, the better implementation and management of these systems. Through knowledge transfer, the rural producer can obtain and apply environmental recovery practices, mainly of soil and water resources. In this study, deterministic mathematical models were developed and tested to obtain arrangements between agricultural, fruit, forage and tree species, in order to assist family farmers in choosing the most appropriate arrangements and with the lowest initial cost for Agroforestry Systems (SAFs) in the Cerrado biome. The thesis is organized into three chapters, the first being a general review of the Cerrado biome, soil classes, species found in this environment and their different applications and use, as well as the SAFs and the processes for their implementation. Systems that combine several strata within the understanding of natural succession were considered in the study, being called here: Successional Multistratum Agroforestry System (SAFms). The second chapter presents the development of a deterministic mathematical model that, through environmental and bromatological data and information, indicates the most viable arrangements, given the environmental data provided, in agroforests already consolidated in different scenarios in the Cerrado biome. In the third chapter, we conclude the study with the development of the model that uses the principles of formation of a SAFms, that is, the stages that contemplate the succession of species and the different strata they have when composing this system at different times within the chronology of the its growth. As “output” the model delivered solutions where the ideal arrangement would have the lowest initial implementation cost of this production system for the small farmer. For the development of the mathematical models, binary integer programming - PIB, implemented with the GLPK package was used. The formation of data sets was based on secondary sources, scientific articles, theses and dissertations, among others, as well as the report of species cultivated in Brazilian states that have the Cerrado biome. It was concluded that deterministic mathematical models, such as GDP, are robust to combine, through decision trees, different species according to the weights of each one of them, following the determination of the objective function of each proposed model. We can say that the mathematical models can show and value particularities of knowledge for dynamic systems such as those of process agriculture. Which was seen and analyzed, mathematically, in its interactions, both internal and with the environment. Deterministic models are able to deliver parameters hitherto not analyzed numerically. For SAFms in the Cerrado biome, implementation arrangements for process agriculture are also presented, with the lowest possible cost.