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Here, we use spatially explicit coalescence simulations to explore the properties of the island and the two\u2010dimensional stepping stone models under a wide range of scenarios with spatio\u2010temporal variation in deme size. We avoid the simulation of genetic data, using the fact that under the studied models, summary statistics of genetic diversity and divergence can be approximated from coalescence times. We perform the simulations using <jats:italic>gridCoal<\/jats:italic>, a flexible spatial wrapper for the software <jats:italic>msprime<\/jats:italic> (Kelleher et al., 2016, <jats:italic>Theoretical Population Biology<\/jats:italic>, <jats:italic>95<\/jats:italic>, 13) developed herein. In <jats:italic>gridCoal<\/jats:italic>, deme sizes can change arbitrarily across space and time, as well as migration rates between individual demes. We identify different factors that can cause a deviation from theoretical expectations, such as the simulation time in comparison to the effective deme size and the spatio\u2010temporal autocorrelation across the grid. Our results highlight that <jats:italic>F<\/jats:italic><jats:sub><jats:italic>ST<\/jats:italic><\/jats:sub>, a measure of the strength of population structure, principally depends on recent demography, which makes it robust to temporal variation in deme size. In contrast, the amount of genetic diversity is dependent on the distant past when <jats:italic>N<\/jats:italic><jats:sub><jats:italic>e<\/jats:italic><\/jats:sub> is large, therefore longer run times are needed to estimate <jats:italic>N<\/jats:italic><jats:sub><jats:italic>e<\/jats:italic><\/jats:sub> than <jats:italic>F<\/jats:italic><jats:sub><jats:italic>ST<\/jats:italic><\/jats:sub>. Finally, we illustrate the use of <jats:italic>gridCoal<\/jats:italic> on a real\u2010world example, the range expansion of silver fir (<jats:italic>Abies alba<\/jats:italic> Mill.) since the last glacial maximum, using different degrees of spatio\u2010temporal variation in deme size.<\/jats:p>","DOI":"10.1111\/1755-0998.13676","type":"journal-article","created":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T06:23:25Z","timestamp":1656483805000},"page":"2941-2955","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Using <scp><i>gridCoal<\/i><\/scp> to assess whether standard population genetic theory holds in the presence of spatio\u2010temporal heterogeneity in population size"],"prefix":"10.1111","volume":"22","author":[{"given":"Enik\u0151","family":"Sz\u00e9p","sequence":"first","affiliation":[{"name":"IST Austria (Institute of Science and Technology Austria)  Klosterneuburg 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