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Conceived and designed the experiments: KDH CCC. Performed the experiments: KDH CCC. Analyzed the data: KDH JG MD CCC. Contributed reagents/materials/analysis tools: KDH CCC. Wrote the paper: KDH CCC.

The authors have declared that no competing interests exist.

Food waste contributes to excess consumption of freshwater and fossil fuels which, along with methane and CO_{2} emissions from decomposing food, impacts global climate change. Here, we calculate the energy content of nationwide food waste from the difference between the US food supply and the food consumed by the population. The latter was estimated using a validated mathematical model of metabolism relating body weight to the amount of food eaten. We found that US per capita food waste has progressively increased by ∼50% since 1974 reaching more than 1400 kcal per person per day or 150 trillion kcal per year. Food waste now accounts for more than one quarter of the total freshwater consumption and ∼300 million barrels of oil per year.

Recent spikes in food prices have led to increasing concern about global food shortages and the apparent need to increase agricultural production

Energy from ingested food supports basal metabolism and physical activities, both of which are functions of body weight. Surplus ingested energy is stored in the body and is reflected by a change of body weight. Because the average body weight of the US population has been increasing over the past 30 years, it is not immediately clear how much of the increased food supply was ingested by the population. Quantifying the food intake underlying an observed change of body weight requires knowing the energy cost of tissue deposition and the increased cost of physical activity and metabolic rate with weight gain. Here, we develop and validate a mathematical model of human energy expenditure that includes all of these factors and used the model to calculate the average increase of food intake underlying the observed increase of average adult body weight in the US since 1974 as measured by the US National Health and Nutrition Examination Survey (NHANES)

(A) The average adult body weight (Δ) as measured by the National Health and Nutrition Examination Survey. (B). Per capita U.S. food availability unadjusted (○) and adjusted for wastage (▪) according to the United States Department of Agriculture (USDA). The solid curve represents the mathematical model prediction of average food intake change (dashed curves indicate±95% confidence intervals). (C) Energy content of per capita U.S. food waste predicted using our mathematical model (solid curve, left axis). The right axis plots the per capita annual mass of municipal solid food waste (▴). (D) Percentage of available food energy wasted as calculated by previous USDA estimates (▪) and predicted using our mathematical model (solid curve).

The calculated progressive increase of food waste suggests that the US obesity epidemic has been the result of a “push effect” of increased food availability and marketing with Americans being unable to match their food intake with the increased supply of cheap, readily available food. Thus, addressing the oversupply of food energy in the US may help curb the obesity epidemic as well as decrease food waste, which has profound environmental consequences.

Assuming that agriculture utilizes about 70% of the freshwater supply _{2}

Our food waste estimate resulted from subtracting the calculated average food energy intake from the food supply of the US population. Thus, there are two potential sources of error in our food waste estimate. First, the FAO food balance sheets were the source of our estimate of the US food supply

The second source of error in our calculation of food waste results from our mathematical model estimates of average food intake. The fact that average body weight of the US population has increased in parallel with the increasing food supply raises the question of how much of the additional available food was actually ingested by the population. Without an accurate mathematical model of human metabolism, we could not determine how increasing food intake quantitatively translates into a change of body weight.

(A) The experimentally imposed increases of food intake during controlled over-feeding experiments (black bars) along with model predicted values (white bars) calculated using the measured body weight changes. (B) Model predicted relationship between changes of 24 hour energy expenditure and body weight change after 3.6 years of over- and under-feeding (♦) along with the best-fit regression line determined from longitudinal measurements in a cohort of Pima Indians followed for the same average time interval. (mean±SD).

Our estimates of food waste likely represent lower bounds since we did not simulate the effects of a progressive decrease of physical activity that may have contributed to the US obesity epidemic

Our calculation of food wasted by the US population does not rely on direct measurements of waste produced by small groups that often know they are being investigated

The principle of energy conservation implies that the energy content of food is closely related to the energy requirements for agricultural production as well as the methane and CO_{2} emissions produced by decomposition of wasted food. Thus, the energy content of wasted food may be a more important environmental index than the mass of wasted food as determined by more traditional methods. Nevertheless, traditional methods of measuring food waste provide important information about the types of foods wasted and the relative contribution of waste along various points of the supply chain from farm to fork. Because our methodology calculates food intake by the population and tracks food energy and not food types, we cannot address such issues. Nevertheless, the progressive deviation of our calculated wasted food energy compared with the USDA adjustment for wastage suggests that traditional methods are increasingly missing large quantities of food waste in America.

The basis of our mathematical model is the energy balance equation where the rate of change in stored body energy is given by the difference between the metabolizable energy intake rate _{FFM}_{F}

Consider a population where each individual's weight change obeys equation (1) with their own individual intake and expenditure functions. We take a sample sum over (1) to obtain

Since

For the first NHANES phase from 1971–1974, we assumed that people were approximately weight-stable corresponding to a state of energy balance. Using the fact that

Therefore, assuming that the covariance of physical activity and body weight and the covariance of the parameter

To estimate the rate of change of stored energy we consider fat and fat-free mass changes separately:_{0}

Equation 9 implies that:

Therefore, substituting equations 11 and 12 into equation 7 gives the change of energy intake underlying the observed increase of average body weight:

Using the nominal parameter values and assuming no change of physical activity, equation 13 can be represented as:

The first term of equation 14 evaluates to <10 kcal/d for the NHANES data since the rate of change of average body weight was only ∼9.5×10^{−4} kg/d. The second term evaluates to ∼220 kcal/d for the NHANES data since the change of average body weight was ∼10 kg between 1974 and 2003.

Our mathematical model was previously demonstrated to give accurate results in situations of underfeeding and body weight loss

While these results give us some confidence in the validity of our model in response to weight gain, we note that the controlled over-feeding experiments were conducted in a small number subjects over a relatively short period of time. We could only find one study that measured longitudinal changes of energy expenditure with weight gain over extended time periods

To calculate the absolute level of energy intake corresponding to the NHANES data, we assumed that the average initial energy intake was

To calculate the confidence intervals of our calculations, each model parameter value was randomly selected from a normal distribution with mean and standard deviations given in ^{5} simulations and report the mean and 95% confidence intervals for the predicted food intake and waste calculations.

_{FFM} |
22±4 kcal/kg/d | Resting metabolic rate coefficient for FFM |

_{F} |
3.6±2 kcal/kg/d | Resting metabolic rate coefficient for F |

7±4 kcal/kg/d | Physical activity coefficient | |

0.24±0.1 | Adaptive thermogenesis parameter | |

_{FFM} |
230±100 kcal/kg | Energy cost for FFM deposition |

_{F} |
180±20 kcal/kg | Energy cost for F deposition |

10.4±5 kg | Forbes body composition parameter | |

2100±100 kcal/d | Average energy intake in 1974 |