Automated cell tracking in populations is important for research and discovery in biology and medicine. In this paper, we propose a cell tracking method based on global spatio-temporal data association which considers hypotheses of initialization, termination, translation, division and false positive in an integrated formulation. Firstly, reliable tracklets (i.e., short trajectories) are generated by linking detection responses based on frame-by-frame association. Next, these tracklets are globally associated over time to obtain final cell trajectories and lineage trees. During global association, tracklets form tree structures where a mother cell divides into two daughter cells. We formulate the global association for tree structures as a maximum-a-posteriori (MAP) problem and solve it by linear programming. This approach is quantitatively evaluated on sequences with thousands of cells captured over several days.