We use a model of social evolution to explore how i) the finiteness of populations, then ii) their subdivision affect the potential for evolutionary diversification (evolutionary branching). We borrow tools from adaptive dynamics, evolutionary quantitative genetics and evolutionary game theory, and we show that both finite sizes and subdivision hinder diversification compared to what happens in well-mixed populations of infinite size. This work is in collaboration with S.P. Otto (finite populations) and P.D. Taylor (subdivided populations).