Spatially resolved transcriptomics (SRT) measures mRNA transcripts at thousands of locations within a tissue slice, revealing spatial variations in gene expression and distribution of cell types. In recent studies, SRT has been applied to tissue slices from multiple timepoints during the development of an organism. Alignment of this transcriptomics data can provide insights into the gene expression programs governing the growth and differentiation of cells over space and time. We introduce DeST-OT (velopmental patioemporal ptimal ransport), a method to align SRT slices from pairs of developmental timepoints using the framework of optimal transport (OT). DeST-OT uses optimal transport to precisely model cellular growth, death, and differentiation processes that are not well-modeled by existing alignment methods. We demonstrate the advantage of DeST-OT on simulated slices. We further introduce two metrics to quantify the plausibility of a spatiotemporal alignment: a which quantifies the discrepancy between the inferred and the true cell type growth rates, and a which quantifies the distance traveled between ancestor and descendant cells. DeST-OT outperforms existing methods on these metrics in the alignment of spatiotemporal transcriptomics data from the development of axolotl brain.