Amoebae are commonly studied to understand embryogenesis, and the best-characterized amoebozoan species is Dictyostelium discoideum (Dd). Dd has a very simple life cycle with a range of developmental stages, among which we are most interested in the stage of a migrating slug. It has been observed that different sizes of Dd slugs maintain a proportional distribution of prestalk cells and prespore cells: prestalk cells occupy the anterior 20% of the slug, while prespore cells occupy the posterior 80%. However, it remains unknown how the migrating slug forms and preserves this anterior-posterior proportional pattern under so many different dynamics including cell movement, signaling, and cell differentiation. Therefore, we constructed a mathematical model to simulate the cell movement and chemical distribution during slug migration, and we conducted numerical experiments to explore possible factors for this pattern. In particular, we divided the problem of interest into the following three parts to be investigated. (1) differential motion: the ability of prestalk cells to move through all the prespore cells and stay in the anterior region of the slug; (2) signaling: how cells of different types produce, receive, and respond to the signals in the environment; (3) cell differentiation: how prestalk and prespore cells differentiate into each other under the regulation of signaling. We finally combined and balanced these mechanisms appropriately to achieve the desired patterns observed in migrating slugs.