The effect of mixture on productivity has been widely studied for applications related to agriculture but results in forestry are scarce due to the difficulty of conducting experiments. Using a modeling approach, we analyzed the effect of mixture on the productivity of forest stands composed of sessile oak and Scots pine. To determine whether mixture had a positive effect on productivity and if there was an optimum mixing proportion, we used an aggregation technique involving a mean-field approximation to analyze a distance-dependent individual-based model. We conducted a local sensitivity analysis to identify the factors that influenced the results the most. Our model made it possible to predict the species proportion where productivity peaks. This indicates that transgressive over-yielding can occur in these stands and suggests that the two species are complementary. For the studied growth period, mixture does have a positive effect on the productivity of oak-pine stands. Depending on the plot, the optimum species proportion ranges from 38 to 74% of oak and the gain in productivity compared to the current mixture is 2.2% on average. The optimum mixing proportion mainly depends on parameters concerning intra-specific oak competition and yet, intra-specific competition higher than inter-specific competition was not sufficient to ensure over-yielding in these stands. Our work also shows how results obtained for individual tree growth may provide information on the productivity of the whole stand. This approach could help us to better understand the link between productivity, stand characteristics, and species growth parameters in mixed forests.