How can spatiotemporal population data be used for modeling migration?

I have a dataset that contains the population of butterflies(5 species) for 15 years for different locations. I want to model it against the climate index collected for same time period and location. The objective is to find how early the migration species migration starts before the onset of a dry period? My idea was to understand all the spatial locations around the dry place and see if the populations have changed over time in the neighbourhood which can indicate a migration, thereby can deduce the time the butterfly realizes before the dry season onset. What type of technique can be used to predict the migration pattern? Does this come under graph theory? If so can someone guide me in a right research direction, what algorithm has to be looked at?