Adaptive Dynamics is a mathematical framework that has been developed to capture how the phenotypic distribution of biological populations is shaped by ecological interactions together with environmental variability. In the past, it has been successful e.g in showing how speciation could be triggered by competition mechanisms. We aim at further developing this framework to understand how the interplay between those mechanisms, combined with complex landscapes structures, can explain biodiversity patterns that have emerged over deep evolutionary times. This is a big challenge, as the mathematical model describing the processes involves heavy computations. In order to overcome the problem of high dimensionality, we are developing cutting edge algorithms based on deep learning techniques, to approximate the solution of this equation. Eventually, we hope that these models will allow a better understanding of the role of allopatric versus sympatric speciation in promoting biodiversity.