We model the potential range shifts of lion and tiger populations over the Late Pleistocene and Holocene, to shed light on the potential competitive dynamics between these two apex predators through long-term, glacial-interglacial climate cycles. We focus on the Near East and Indian subcontinent, where both species are historically present, however the study incorporates the full distributions of both the lion and tiger throughout Africa and Eurasia. We employ species distribution models (SDMs) with bioclimatic data to model present-day idealised ranges in the absence of non-climatic, principally human, disturbance. We compare these idealised ranges with a statistically derived bioclimatic stratification layer so as to clearly describe the driving conditions behind each species’ distribution. Preferred strata are then considered for time slices at the Last Glacial Maximum and mid Holocene to identify areas of optimal climate for each species. The merits of our approach are considered in relation to the practice of directly projecting models onto past climatic conditions. This novel technique of model explanation allows greater use of expert species knowledge in the evaluation of SDMs, and makes the underlying ecology of the modelling process more explicit. The modelled distributions of lions and tigers throughout the Late-Pleistocene and Holocene are discussed in relation to existing genetic and archaeological literature, to contextualise current knowledge regarding lion and tiger palaeodistributions.