Table 5.
Diet modelling using mathematical programming techniques for the design of optimised diets for health and environmental sustainability
| Health considerations in the diet modelling | Environmental considerations in the diet modelling | ||||||
|---|---|---|---|---|---|---|---|
| Reference | Country | Dietary data | Nutritional constraints using dietary guidelines (i.e. Recommended Dietary Allowance values) | Acceptability constraints with reference to the current diet | Health evaluation of whole diet based on | Food aggregation level* | Environmental indicator |
| Arnoult et al. (2010)( 43 ) | UK | Individual level 2-week diet record (Expenditure and Food Survey 2003–2004) | UK Department of Health 12 nutrients 1 food group | Yes; similar energy and alcohol intake as current diet | Food group | 293 items | Land use†† |
| Macdiarmid et al. (2012)( 44 ) | UK | Individual level 7 d diet record (UK National Diet and Nutrition Survey 2000–2001) | UK dietary guidelines for an adult women Total energy 12 nutrients 3 food groups | No and yes; food quantity limits for each food group|| | Food group Energy Macronutrients Micronutrients | 82 groups | GHGE, to be minimised |
| Thompson et al. (2013)( 45 ) | France Spain Sweden | Individual level 7 d diet record (INCA 2, France, 2007) 3 d diet record (ENIDE, Spain, 2013) 4 d diet record (Riskmaten, Sweden, 1997–1998) | Dietary guidelines from the French Agency for Food, Food circle with Swedish Nutrition Recommendations Objectified | Yes; food quantity limits|| and food popularity¶ | Food group Energy Macronutrients Micronutrients | 68 items for France 277 items for Spain 88 items for Sweden | GHGE, to be reduced by 25 % |
| Wilson et al. (2013)( 56 )† | New Zealand | Individual level 24 h recalls and questionnaire (New Zealand Adult Nutrition Survey 2008–2009) | New Zealand dietary recommendations for men Total energy intake 14 nutrients | Yes; daily maximum limits for flour, pasta and oats, total vegetable intake and added salt | Food group Energy Macronutrients Micronutrients | 76 items | GHGE, to be minimised |
| Jalava et al. (2014)( 27 )‡ | 176 countries | Population level Per country annual food supply data (FAOSTAT 2013) | County-specific dietary guidelines for total energy intake WHO dietary guidelines for macronutrient intake, and fruit and vegetables | Yes; food popularity using a penalty score for any deviation from the original diet | Macronutrients | 13 groups | Consumptive water use at the global level†† |
| Tyszler et al. (2014)( 52 )§ | Netherlands | Individual level 2×24h recalls (Dutch National Food Consumption Survey 2007–2010) | Dutch dietary guidelines for a non-active adult women Total energy All macronutrients All micronutrients Amino acids 2 food groups | Yes; food popularity including portion size by using a penalty score for each change in serving size** | Food group | 207 items | pReCiPe, including GHGE, fossil energy use and land use, to be reduced by 30 % |
| Green et al. (2015)( 46 ) | UK | Individual level 4d diet record (UK National Diet and Nutrition Survey 2010–2011) | WHO dietary guidelines 10 nutrients | Yes; similar energy intake as current diet and similar amount of liquids as current diet | Food group | 42 groups | GHGE, to be gradually reduced by 10 %‡‡ |
| Van Dooren et al. (2015)( 53 ) | Netherlands | Individual level 2×24h recalls (Dutch National Food Consumption Survey 2007–2010) | Dutch dietary guidelines Total energy All macronutrients All micronutrients 1 food group | Yes; food popularity including portion size by using a penalty score for each change in serving size** | Food group Energy Macronutrients Micronutrients | 206 items | GHGE, to be reduced by 20 % |
INCA 2, Individual and National Study on Food Consumption; ENIDE, Spanish National Diet Survey; GHGE, greenhouse gas emissions.
Food aggregation level: the number of food items or groups (depending on author’s terminology) for which environmental sustainability data of food intake was available.
Additional diet models were optimised to meet nutrient requirements and: (i) minimise costs; (ii) minimise costs and GHGE; (iii) be relatively healthy, Mediterranean- and Asian-style; and (iv) include ‘more familiar New Zealand meals’.
Diet was initially optimised in view of dietary recommendations only, thereafter additional diet models were optimised using quadratic programming to meet nutritional constraints along with a forced reduction on the animal-based products, in particular including limits on the protein intake from all animal products and from meat, starting from a limit to 50 % and 16·7 %, respectively, and gradually reducing these to zero.
Additional diet models were optimised to (i) meet nutritional constraints only, and along with forced reductions on animal-based products (ii) excluding meat, (iii) excluding meat and fish, and (iv) excluding meat, fish, dairy and eggs.
Food quantity limits (i.e. upper and/or lower bounds) were set for each group to give standard usable portion sizes (i.e. in whole units or in units in which it is sold).
For France, acceptability constraints on food quantity for each food item included a minimum value equal to the 5th percentile of consumption observed in the population (non-consumers included) and a maximum value equal to the 95th percentile of consumption observed in the population (non-consumers excluded), to ensure that the number of daily portions is acceptable to consumers. For Spain and Sweden, bounds were based on food popularity including minimum portion sizes. Food popularity (that is related to cultural preferences) was based on the current consumption as observed in the dietary surveys and expressed as the percentage of the populating consuming a particular food item. This resulted in the following acceptability constraints: (i) amounts consumed in a particular food group should at least be 60–80 % of the habitual consumption; (ii) popular foods (eaten by at least 50 % of the population) could be increased by up to four times, but not decreased by 30 % of the habitual consumption; (iii) unpopular foods (eaten by less than 25 % of the population) were limited to no more than twice the habitual consumption; and (iv) other foods could be increased up to three times the habitual consumption.
Penalty score: any change in serving size as compared with the current diet contributes to an arbitrary penalty score with a penalty contribution that is food- and direction-dependent.
Diet was optimised in view of dietary recommendations only using quadratic programming; the environmental impact was not considered during the modelling, but estimated afterwards for the optimised diet model.
Diet was initially optimised in view of dietary recommendations only using smooth non-linear programming; thereafter additional diet models were optimised in view of environmental concerns, in particular a gradual reduction by 10 % of GHGE.