The thrifty-gene hypothesis (TGH) posits that the modern genetic predisposition to obesity stems from a historical past where famine selected for genes that promote efficient fat deposition. It has been previously argued that such a scenario is unfeasible because under such strong selection any gene favouring fat deposition would rapidly move to fixation. Hence, we should all be predisposed to obesity: which we are not. The genetic architecture of obesity that has been revealed by genome-wide association studies (GWAS), however, calls into question such an argument. Obesity is caused by mutations in many hundreds (maybe thousands) of genes, each with a very minor, independent and additive impact. Selection on such genes would probably be very weak because the individual advantages they would confer would be very small. Hence, the genetic architecture of the epidemic may indeed be compatible with, and hence support, the TGH. To evaluate whether this is correct, it is necessary to know the likely effects of the identified GWAS alleles on survival during starvation. This would allow definition of their advantage in famine conditions, and hence the likely selection pressure for such alleles to have spread over the time course of human evolution. We constructed a mathematical model of weight loss under total starvation using the established principles of energy balance. Using the model, we found that fatter individuals would indeed survive longer and, at a given body weight, females would survive longer than males, when totally starved. An allele causing deposition of an extra 80 g of fat would result in an extension of life under total starvation by about 1.1-1.6% in an individual with 10 kg of fat and by 0.25-0.27% in an individual carrying 32 kg of fat. A mutation causing a per allele effect of 0.25% would become completely fixed in a population with an effective size of 5 million individuals in 6000 selection events. Because there have probably been about 24,000 famine events since the evolution of hominins 4 million years ago, there has been ample time even for genes with only very minor impacts on adiposity to move to fixation. The observed polymorphic variation in the genes causing the predisposition to obesity is incompatible with the TGH, unless all these single nucleotide polymorphisms (SNPs) arose in the last 900,000 years, a requirement we know is incorrect. The TGH is further weakened by the observation of no link between the effect size of these SNPs and their prevalence, which would be anticipated under the TGH model of selection if all the SNPs had arisen in the last 900,000 years.