Is there a computational method/method/way to predict if a cell population in a tissue immigrated or is enriched locally?
This may not be a viable answer for all experimental contexts, but you can compare expression profiles of individual cells against datasets that contain known reference cell types (migratory and not). We have recently published a web-based tool called CIPR (cluster identity predictor) that helps with cluster annotations in scRNAseq experiments. There are various reference datasets available, but you can also provide a custom reference by preparing data from databases like GEO.
You can read the manuscript for more information about how the algorithm works, but in a nutshell, it compares differentially expressed genes or global expression patterns within your data to known reference datasets and creates quick visual outputs. If your reference contains both migratory and non-migratory cell types, maybe CIPR can help differentiate them. For other identity prediction tools, check out this article is a good resource that compares different cluster calling algorithms.