In many evolutionary algorithms, crossover is the main operator used in generating new
individuals from old ones. However, the usual mechanism for generating offsprings in spatially
structured evolutionary games has to date been clonation. Here we study the effect of
incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's
Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in
the clonal process can explain the emergence of cooperation from a non-cooperative initial
state. First, we show that this only occurs for particular regimes of low costs of cooperation.
Then, we display how crossover gets greater the range of scenarios where cooperative mutants
can invade selfish populations. In a social context, where crossover involves a general rule of
gradual learning, our results show that the less that is learnt in a single step, the larger the
degree of global cooperation finally attained. In general, the effect of step-by-step learning can
be more efficient for the evolution of cooperation than a full blast one
