Temporal patterns in species occupancy and geographic range size are a major topic in evolutionary ecology research. Here we investigate these patterns in Pliocene to Recent large mammal species and genera in Western Eurasia. By using an extensively sampled fossil record including some 700 fossil localities, we found occupancy and range size trajectories over time to be predominantly peaked among both species and genera, meaning that occupancy and range size reached their maxima midway along taxon existence. These metrics are strongly correlated with each other and to body size, after phylogeny is accounted for by using two different phylogenetic topologies for both species and genera. Phylogenetic signal is strong in body size, and weaker but significant in both occupancy and range size mean values among genera, indicating that these variables are heritable. The intensity of phylogenetic signal is much weaker and often not significant at the species level. This suggests that within genera, occupancy and range size are somewhat variable. However, sister taxa inherit geographic position (the center of their geographic distribution). Taken together, the latter two results indicate that sister species occupy similar positions on the earth's surface, and that the expansion of the geographic range during the existence of a given genus is driven by range expansion of one or more of the species it includes, rather than simply being the summation of these species ranges.