Explore deterministic mathematical modeling in ecology through this comprehensive lecture from the Serrapilheira/ICTP-SAIFR Training Program in Quantitative Ecology. Delve into community models, competition dynamics, and predator-prey interactions as presented by Roberto Kraenkel from IFT-Unesp. Examine key concepts such as fixed points, coexistence, equilibrium, and total extinction in ecological systems. Gain insights into community ecology, parameter analysis, and the importance of observation in understanding complex ecological interactions. This in-depth presentation offers valuable knowledge for students and researchers interested in applying mathematical approaches to ecological studies.