The analysis of the dynamic behavior of cells in time-lapse microscopy sequences requires the development of reliable and automatic tracking methods capable of estimating individual cell states and delineating the lineage trees corresponding to the tracks. In this paper, we propose a novel approach, i.e., an ant colony inspired multi-Bernoulli filter, to handle the tracking of a collection of cells within which mitosis, morphological change and erratic dynamics occur. The proposed technique treats each ant colony as an independent one in an ant society, and the existence probability of an ant colony and its density distribution approximation are derived from the individual pheromone field and the corresponding heuristic information for the approximation to the multi-Bernoulli parameters. To effectively guide ant foraging between consecutive frames, a dual prediction mechanism is proposed for the ant colony and its pheromone field. The algorithm performance is tested on challenging datasets with varying population density, frequent cell mitosis and uneven motion over time, demonstrating that the algorithm outperforms recently reported approaches.