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In Article I we showed the effects of phenotypic robustness on evolutionary dynamics, in particular that there is a critical level of phenotypic robustness required for adaptation to occur. This was shown through the analysis of deterministic models, thus our results hold under the assumption of a non-stochastic scenario. However, evolutionary processes are a combination of deterministic and stochastic mechanisms and virtually every aspect of evolution is somehow affected by randomness. Accounting for stochasticity in evolutionary models have been shown to be crucial for a better and more comprehensive understanding of evolutionary dynamics citep{rice2008stochastic}. This is the case for example of the genetic drift model citep{ohta1992nearly}, in which is shown that the effect of random sampling can produce non-adaptive directional evolutionary changes. As a first attempt, we tried to consider stochastic evolutionary models in our analysis, in particular we focused on the diffusion approximation model citep{ohta1992nearly}, which is the most powerful method devised for combining different deterministic and stochastic mechanisms citep{rice2004evolutionary}. However, we realized that even this model lack of sufficient generality for two main reasons. First, the diffusion approximation model is a closed system with non-changing parameters. This means that stochasticity on parameters is non taken into account. Second, it has very narrow boundary condition limits: in fact to be mathematically tractable the model assumes that three main evolutionary forces, migration, selection and mutation are of similar magnitude and sufficiently weak that allele frequencies are not likely to change by more than the amount of 1/2N per generation citep{ohta1992nearly, rice2004evolutionary}. Since our boundary conditions are more extended, virtually to all possible parameter values, we decided to study the evolutionary consequences of stochasticity through evolutionary computer simulations. Computer simulations have become a useful tool for the mathematical modeling of many natural systems including biological, and more specifically, evolutionary systems.A simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics, behaviors and functions of the selected physical or abstract system or process. The model represents the system itself, whereas the simulation represents the operation of the system over time. We first developed a model representing the stochastic and the deterministic processes occurring each generation, thus it can be seen as a stochastic-deterministic dynamical system. Model rules and functions define the relationships between elements of the modeled system. The main elements of the model are internal variables and parameters. An internal variable is a changing variable during time according to the internal model rules or to external inputs, while a parameter is defined as a non-changing value of the model. When parameters can change during time they actually become variables. In this case the dynamical system is defined as “non-sufficient”, meaning that is no more mathematically tractable during time or at best only instantaneously (this is indeed why we need computer simulations). At the beginning of each simulation, initialization parameters and variables must be specified, corresponding to the definition of the initial conditions. At each time point, the dynamical system can be defined by the so called state variables. A state variable is a value describing a particular aspect of the system during time and is usually calculated with specific rules from parameters and internal variables. Finally, the observed behaviors are emergent properties of the dynamical system.