AbstractParasitic and symbiotic relationships govern vast nutrient and energy flows1,2, but controversy surrounds their longevity. Enduring relationships may engender parallel phylogenies among hosts and parasites3,4, but so may more ephemeral relationships when parasites disproportionately colonize related hosts5. When considering these relationships’ temporal durability, it would be useful to understand whether parasite and host populations have grown and contracted in concert. Here, we devised methods to compare demographic histories, derived from genomic data6. We used these methods to compare the historical growth of the agent of severe human malaria, Plasmodium falciparum, to human and primate histories7,8 and to that of their mosquito vector Anopheles gambiae9, thereby discerning long-term parallels and anthropogenic population explosions10,11. The growth history of Trichinella spiralis, a zoonotic parasite disseminated by swine domestication12,13, proved regionally-specific, paralleling distinctive growth histories for wild boar in Asia and Europe14. Parallel histories were inferred for an anemone and its algal symbiont (Aiptasia pallida15 and Symbiodinium minutum16). Concerted growth in potatoes and the agent of potato blight (Solanum tuberosum17 and Phytophthora infestans18) did not commence until the age of potato domestication, helping date the acquisition of this historically consequential fungal plant pathogen. Therefore, comparative historical demography provides a powerful new means by which to interrogate the history of myriad ecological relationships, enriching our understanding of their origins and durability.