The fitness of an evolutionary individual can be understood in terms of its two basic components: survival and reproduction. As embodied in current theory, trade-offs between these fitness components drive the evolution of life-history traits in extant multicellular organisms. Here, we argue that the evolution of germ-soma specialization and the emergence of individuality at a new higher level during the transition from unicellular to multicellular organisms are also consequences of trade-offs between the two components of fitness-survival and reproduction. The models presented here explore fitness trade-offs at both the cell and group levels during the unicellular-multicellular transition. When the two components of fitness negatively covary at the lower level there is an enhanced fitness at the group level equal to the covariance of components at the lower level. We show that the group fitness trade-offs are initially determined by the cell level trade-offs. However, as the transition proceeds to multicellularity, the group level trade-offs depart from the cell level ones, because certain fitness advantages of cell specialization may be realized only by the group. The curvature of the trade-off between fitness components is a basic issue in life-history theory and we predict that this curvature is concave in single-celled organisms but becomes increasingly convex as group size increases in multicellular organisms. We argue that the increasingly convex curvature of the trade-off function is driven by the initial cost of reproduction to survival which increases as group size increases. To illustrate the principles and conclusions of the model, we consider aspects of the biology of the volvocine green algae, which contain both unicellular and multicellular members.