A mathematical model of weight loss under total starvation: evidence against the thrifty-gene hypothesis

Abstract

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.

Fig. 2.

The trajectories of weight loss in a hypothetical 100 kg female subject starving to death, using three different models each with slightly different assumptions. See Table 1 for the model assumptions.

Fig. 3.

Energy utilisation from fat and protein, and weight loss during a hypothetical fast to death. (A) The modelled energy contributions by fat (blue) and protein (red) oxidation throughout a hypothetical 268-day fatal fast by a 100 kg female. Throughout the entire fast the majority of energy is supplied each day by fat oxidation, but this contribution by fat gets progressively smaller, whereas that from protein remains almost constant. (B) The modelled contributions to weight loss (green indicates total weight loss per day) by fat (blue) and protein (red) for the same fast. Until about half way through the fast, weight loss was predominantly fat, but in the second half of the fast it was predominantly protein.

Fig. 1.

Empirical relationships showing the proportion of body that is fat (pFAT) in relation to body weight (BW) and the relationship between basal energy expenditure (BEE) and lean tissue weight (LTW). (A) The proportion of fat in the body across a cohort of 592 individual adults aged between 18 and 93 years in relation to sex and body weight. Body composition was determined by DXA. The y-axis (pFAT weight) is the proportion of fat in the body by weight and the x-axis is the log_n body weight in kg. Males are shown as black dots and females as red squares. (B) For the same individuals, the relationship between basal energy expenditure (E_bee) and log_e lean tissue weight (LTW).

Fig. 4.

The differences between the predicted weight loss and the observed weight loss during complete starvation in humans. Predictions from three models are presented and compared with actual fasts. Points show the average discrepancies and the error bars show the standard deviations. The fitted lines show third-order polynomial best-fit regressions (r²>0.98 in all three cases).

Fig. 5.

The predicted effect of body fatness on survival time under complete starvation for females and males carrying different amounts of body fat. The lines reflect the second-order polynomial equations that are shown in the plots.

Fig. 6.

The modelled spread of an allele due to a random mutation conferring an effect of storing an extra 80 g of fat on an individual already storing 30 kg of body fat. The allele is assumed to increase survival during famines by 0.25% [hence, survival during famine of AA (wild-type homozygote)=0.68, of Aa (heterozygote)=0.6825 and for aa (mutant homozygote)=0.685]. The allele moves from being a mutation in a single individual to complete fixation in the entire population after about 6000 selection events (famines).

Fig. 7.

The relationship between effect size and prevalence for 32 SNPs identified by Speliotes et al. as being significantly linked to BMI. r²=0.4, P=0.78 (Speliotes et al., 2010).