Looking at how species may have evolved over time is not usually considered an area where GIS might be applied. However, studies have used spatial modeling and GIS approaches to understanding species evolution.
In one study, the authors studied the evolution of two rodent species by changing the environmental conditions in a given region and studying how that would affect the distribution of rodents based on varied scenarios. The application of spatial models with different initial conditions that produce outcomes are then matched with empirical evidence from the biological record to determine which model conditions best match the distribution for the rodents.[1]
Another study looking at pelobatoid frogs analyzed GIS-based climatic data, with published life-history data of the frogs. The approach utilized a time-calibrated phylogeny. However, the results did not show climate as a major factor in the evolution of the frogs, rather small genome sizes and phylogeny affected by spatial factors were more of a contributing factor to noticeable evolution.[2]

Other studies are utilizing similar methods, such as in studying amphibians, that take advantage of the presence of GIS-based climate data for understanding evolutionary change where climate and phylogenic trait within geographic locations are potentially important factors.[3] Another similar approach was applied on Malagasy primates, where generalized linear models looking at climate and resource-related variables that also accounted for phylogenetic history and spatial autocorrelation determined that a strong phylogenetic effect, once again, had the most influence in evolutionary change, where the effects of space and location were relevant for the specie’s genetic development.[4] These examples demonstrate that spatial modeling and GIS can be used to explain how species evolution has occurred, helping to explain distribution of species in ways that have provided new insights to evolutionary biologists.
References
[1] For more on the application of modeling to understand rodent species’ distribution, see: Anderson, R. P., & Raza, A. (2010). The effect of the extent of the study region on GIS models of species geographic distributions and estimates of niche evolution: preliminary tests with montane rodents (genus Nephelomys) in Venezuela: Effect of study region on models of distributions. Journal of Biogeography, 37(7), 1378–1393.
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[2] For more on the evolution of pelobaoid frogs and their evolution using GIS, see: Zeng, C., Gomez-Mestre, I., & Wiens, J. J. (2014). Evolution of Rapid Development in Spadefoot Toads Is Unrelated to Arid Environments. PLoS ONE, 9(5), e96637. https://doi.org/10.1371/journal.pone.0096637
[3] For more on the study looking at amphibians, see: Bonetti, M. F., & Wiens, J. J. (2014). Evolution of climatic niche specialization: a phylogenetic analysis in amphibians. Proceedings of the Royal Society B: Biological Sciences, 281(1795), 20133229–20133229. https://doi.org/10.1098/rspb.2013.3229
[4] For more on Malagasy primates and studying their evolution using spatial methods, see: Kamilar, J. M., Muldoon, K. M., Lehman, S. M., & Herrera, J. P. (2012). Testing Bergmann’s rule and the resource seasonality hypothesis in Malagasy primates using GIS-based climate data. American Journal of Physical Anthropology, 147(3), 401–408. https://doi.org/10.1002/ajpa.22002