Looks to me that people use a wide variety of software tool chains ( https://scholar.google.com/scholar?hl=en&as_sdt=0%252C48&q=Spatio-temporal+Analysis+of+Herpetofaunal+software ). Usually my preference would be to use something similar to whichever Community of Practice is using, and / or what aligns with whatever GIS / statistical software you already are familiar with, if not, which is prevalent in your local academic or professional community so you have help nearby and close. And then other factors such as open source, etc. I say 'Tool chain' because it is often the case one uses a GIS for the data wrangling and clipping to the Area of Interest, etc., then might need some specialized algorithms in a package like R-Spatial, and then might have to write custom Python code in an Anaconda Notebook if you come up with your innovative algorithms.
Might be worth wile to use your own search terms in Google Scholar, my quick look showed 1100 papers on the topic, you don't have to look at all those just find ones that are in your domain to get some ideas.
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