We apply a comparative framework to test for concerted demographic changes in response to climate shifts in the neotropical lowland forests, learning from the past to inform projections of the future. Using reduced genomic (SNP) data from three lizard species codistributed in Amazonia and the Atlantic Forest ( Anolis punctatus , Anolis ortonii , and Polychrus marmoratus ), we first reconstruct former population history and test for assemblage-level responses to cycles of moisture transport recently implicated in changes of forest distribution during the Late Quaternary. We find support for population shifts within the time frame of inferred precipitation fluctuations (the last 250,000 y) but detect idiosyncratic responses across species and uniformity of within-species responses across forest regions. These results are incongruent with expectations of concerted population expansion in response to increased rainfall and fail to detect out-of-phase demographic syndromes (expansions vs. contractions) across forest regions. Using reduced genomic data to infer species-specific demographical parameters, we then model the plausible spatial distribution of genetic diversity in the Atlantic Forest into future climates (2080) under a medium carbon emission trajectory. The models forecast very distinct trajectories for the lizard species, reflecting unique estimated population densities and dispersal abilities. Ecological and demographic constraints seemingly lead to distinct and asynchronous responses to climatic regimes in the tropics, even among similarly distributed taxa. Incorporating such constraints is key to improve modeling of the distribution of biodiversity in the past and future.