This paper explores the spatio-temporal narratives embedded within human population genomic science. Evolution is often represented by a spatio-temporal genealogical tree, which provides specific affordances for conceptualizing sameness and difference. An alternative metaphor is based on the reticulated net or rhizome, which provides different affordances. The tree model implies one version of human “unity in diversity”, in which unity derives from common origin. The net/rhizome model derives unity from constant flows across space and time. These spatio-temporal narratives about the past impinge on genomics’ promise to deliver greater health for all. While the tree model affords ideas of genetic unity, which implies an anti-racism based on downplaying difference, it also affords ideas of deeply-rooted genetic difference between continental populations, which implies recognizing (and geneticizing) “racial” difference, which can underwrite racism. Health inequalities seen to be due to environmental influences (interacting with genomes) invoke the shallower timeframes of the network model. Attention to the various spatio-temporal models underlying different approaches to understanding genetic variation helps us to be mindful of their political and ethical implications.