The evolutionary transition towards multicellular life often involves growth in groups of undifferentiated cells followed by differentiation into soma and germ-like cells. Theory predicts that germ soma differentiation is facilitated by a convex trade-off between survival and reproduction. However, this has never been tested and these transitions remain poorly understood at the ecological and genetic level. Here, we study the evolution of cell groups in ten isogenic lines of the unicellular green algae Chlamydomonas reinhardtii with prolonged exposure to a rotifer predator. We confirm that growth in cell groups is heritable and characterized by a convex trade-off curve between reproduction and survival. Identical mutations evolve in all cell group isolates; these are linked to survival and reducing associated cell costs. Overall, we show that just 500 generations of predator selection were sufficient to lead to a convex trade-off and incorporate evolved changes into the prey genome.