Whole-genome duplication (WGD, polyploidization) has been identified as a driver of genetic and phenotypic novelty, having pervasive consequences for the evolution of lineages. While polyploids are widespread, especially among plants, the long-term establishment of polyploids is exceedingly rare. Genome doubling commonly results in increased cell sizes and metabolic expenses, which may be sufficient to modulate polyploid establishment in environments where their diploid ancestors thrive. We developed a mechanistic simulation model of photosynthetic individuals to test whether changes in size and metabolic efficiency allow autopolyploids to coexist with, or even invade, ancestral diploid populations. Central to the model is metabolic efficiency, which determines how energy obtained from size-dependent photosynthetic production is allocated to basal metabolism as opposed to somatic and reproductive growth. We expected neopolyploids to establish successfully if they have equal or higher metabolic efficiency as diploids or to adapt their life history to offset metabolic inefficiency. Polyploid invasion was observed across a wide range of metabolic efficiency differences between polyploids and diploids. Polyploids became established in diploid populations even when they had a lower metabolic efficiency, which was facilitated by recurrent formation. Competition for nutrients is a major driver of population dynamics in this model. Perenniality did not qualitatively affect the relative metabolic efficiency from which tetraploids tended to establish. Feedback between size-dependent metabolism and energy allocation generated size and age differences between plants with different ploidies. We demonstrated that even small changes in metabolic efficiency are sufficient for the establishment of polyploids.