How do the 3 parts of the "evolution recipe" work together to evolve species and increase biodiversity?

According to the evolution theory, the organisms that are better adapted have more chances to survive and to reproduce, thereby they also have more chance to perpetuate their own genes in the next generation. This statement can be divided into three properties. First, the adaptation (or adaptive fitness) of one organism is the ability to make use of the available resources in particular environmental conditions. Second, survival is defined as the ability to identify dangerous (environmental) conditions. Finally, reproduction can be defined as the ability to leave descendants (i. e., own offspring). The most important evolutionary forces that drive this process are mutations and recombination that generate biodiversity, these forces are capable of increasing the adaptive fitness in the next generation and generating speciation.