Archaeobotanical evidence for Near Eastern einkorn wheat, barley, and Chinese rice suggests that the fixation of key domestication traits such as non-shattering was slower than has often been assumed. This suggests a protracted period of pre-domestication cultivation, and therefore implies that both in time and in space the initial start of cultivation was separated from eventual domestication, when domesticated and wild populations would have become distinct gene pools. Archaeobotanical evidence increasingly suggests more pathways to cultivation than are represented by modern domesticated crop lines, including apparent early experiments with cultivation that did not lead to domestication, and early domesticates, such as two-grained einkorn and striate-emmeroid wheats, which went extinct in prehistory. This diverse range of early crops is hard to accommodate within a single centre of origin for all early Near Eastern cultivars, despite suggestions from genetic datasets that single origins from a single centre ought to be expected. This apparent discrepancy between archaeobotany and genetics highlights the need for modelling the expected genetic signature of different domestication scenarios, including multiple origins. A computer simulation of simple plant populations with 20 chromosomes was designed to explore potential differences between single and double origins of domesticated populations as they might appear in genomic datasets millennia later. Here we report a new simulation of a self-pollinating (2% outbreeding) plant compared to panmictic populations, and find that the general outcome is similar with multiple starts of cultivation drifting towards apparent monophyly in genome-wide phylogenetic analysis over hundreds of generations. This suggests that multiple origins of cultivation of a given species may be missed in some forms of modern genetic analysis, and it highlights the need for more complex modelling of population genetic processes associated with the origins of agriculture.